Keywords: Indoor localization, channel state information, entropy, array signal processing, kernel regression

bear in mind with enduring appreciations.

supports from lots of amazing people.

First and foremost, I would like to express my greatest gratitude to my thesis supervisors Prof. Didier Le Ruyet and Dr. Iness Ahriz. They have guided me throughout the research process, taught me how to frame problems and analyze them, inspired me to conquer all the tough challenges. Beyond this, Didier's unfailingly positive attitude and his excellent advice can always help me walk out of our meeting with a newfound vigor and enthusiasm for my coming works. In addition, Iness's ability to get to the heart of the issue incredibly facilitated my research and I really appreciate her thoughtful caring to my daily life in Paris. I have benefited tremendously from both relationships and fell extremely privileged to have worked with them in the past three years. I am immensely grateful to my former supervisor Prof. Hong Sun. Without her recommendation, I would not have this opportunity to study in CNAM and finally obtain the doctoral degree. I also greatly appreciate Dr. Haijian Zhang's research guidance before my Ph.D. study in Wuhan University. Besides, Mr. Christophe Alexandre had done a great contribution in the hardware part of my thesis and I will be always thankful for that. I thank my fellow lab mates Wafa Njima, Stanley Smith, Bastien Ligneul, Chaima Zammali, Xinying Cheng, Xiaotian Fu, Bruno Fontana da Silva, Yang Wu, Yi Yu, etc.. This wonderful experience we have shared in the lab will always be kept in my mind. I also cherish the enjoyable memories in Paris with my friends Gang Liu, Chenguang Liu i

Résumé

Le développement rapide des communications sans fil et le déploiement omniprésent des systèmes Wi-Fi ont nourri des services commerciaux et industriels de géolocalisation (LBS) dans le domaine de l'Internet des objets (IoT). La fonctionnalité la plus fondamentale consiste à localiser l'emplacement de la cible via des appareils sans fil. À cette fin, la localisation par empreinte radio (LF) basée sur la correspondance de motifs se distingue comme une technique prometteuse qui peut renvoyer l'estimation de l'emplacement la plus fine à partir d'un ensemble de points de référence (RP) géolocalisés, permettant une détermination précise de la position, même dans les environnement complexes riches en trajets multiples. Pour les solutions LF d'intérieur existantes, la plupart des travaux précédents font appel à l'empreinte RSS (Received Signal Strength) simple et facilement accessible comme indicateur de la qualité de liaison de la couche MAC (Medium Access Control). Cependant, RSS souffre d'une dégradation spectaculaire des performances due à une dynamique environnementale importante. L'information sur l'état du canal (CSI) de la couche physique indique la qualité du canal au niveau de plusieurs sous-porteuses orthogonales, donc capable d'apporter des informations spécifiques à l'emplacement plus riches pour les empreintes digitales en intérieur. Cette structure complexe de CSI conduit inévitablement à une complexité de calcul accrue pour la mise en oeuvre pratique de la localisation. En outre, l'environnement intérieur hostile peut également générer des signatures radio similaires parmi certains points de référence prédéfinis, qui peuvent être distribués de manière aléatoire dans la zone d'intérêt, altérant ainsi la précision de la cartographie de localisation.

Pour résoudre ces dilemmes, dans cette thèse, nous concevons et mettons en oeuvre v Résumé vi deux systèmes d'empreintes de localisation en intérieur basés sur CSI, à savoir EntLoc et AngLoc. Pour EntLoc, un schéma de filtrage des mesures basé sur la puissance est d'abord proposé pour supprimer la composante bruyante dans les mesures CSI brutes.

Pour capturer les informations de canal statistique les plus informatives tout en partageant la simplicité structurelle du RSS, nous adoptons l'entropie basée sur la modélisation autorégressive (AR) de l'amplitude CSI comme empreinte de l'emplacement pour construire une carte radio hors ligne robuste. Dans la phase en ligne, nous utilisons la distance de Manhattan comme métrique de similarité et avons recouru au schéma de régression par noyaux pour déterminer avec précision la position de la cible. En tant que version améliorée d'EntLoc, le système AngLoc exploite l'angle d'arrivée bien connu (AoA) comme empreinte supplémentaire, qui peut être récupérée avec précision à partir de la phase CSI grâce à un algorithme par sous-espace. Ce mécanisme dédié sert à éliminer davantage les candidats RP sujets aux erreurs, permettant ainsi d'atteindre la précision au niveau du décimètre. Plus précisément, en plus de la génération d'empreintes digitales basée sur l'entropie AR pour l'amplitude CSI dans la phase hors ligne, nous étudions également certaines erreurs de phase profondément enracinées dans les CSI bruts et utilisons plusieurs algorithmes d'étalonnage de phase pour les atténuer et garantir une estimation d'empreinte angulaire fiable. Dans la phase en ligne, en exploitant à la fois les informations d'amplitude et de phase CSI, un nouveau schéma de régression par noyaux bivarié est proposé pour déduire précisément l'emplacement de la cible. En outre, toutes les expériences en intérieur sont menées sur la plate-forme légère HummingBoard, ce qui facilite considérablement la mise en oeuvre des empreintes digitales chronophages et laborieuses.

En outre, les résultats d'expériences montrent les meilleures performances de localisation de nos systèmes proposés par rapport aux approches précédentes.

Mots clés:

Localisation indoor, informations des canaux, entropie, traitement du signal du réseau, régression par noyaux.

Résumé de la Thèse en Français Chapitre 1: Introduction

Avec la prolifération à grande échelle des communications sans fil et de l'informatique omniprésente, le service basé sur la localisation (LBS) est devenu un catalyseur clé pour une myriade d'applications de pointe dans le domaine de l'Internet des objets (IoT). Malgré cela, le système mondial de navigation par satellite (GNSS) peut déjà offrir une localisation extérieure réussie et précise. Cependant, il souffre d'une dégradation spectaculaire des performances dans l'environnement intérieur complexe en raison du blocage des signaux satellites. Grâce à la disponibilité omniprésente et au déploiement à faible coût, la connaissance de la localisation intérieure basée sur le Wi-Fi se distingue comme l'une des solutions les plus attrayantes vis à vis des autres techniques de communication sans fil. Parmi les solutions émergentes pour le positionnement intérieur basé sur le Wi-Fi, l'empreinte digitale de localisation (LF) bénéficie d'un mécanisme de correspondance de modèle, qui comprend une phase de formation hors ligne et une phase d'estimation de localisation en ligne. Plus précisément, dans la phase hors ligne, les signatures sans fil sont collectées sur un ensemble de points de référence (RP) géolocalisés dans la zone d'intérêt pour construire la base de données d'empreintes digitales (carte radio par exemple). Pendant la phase en ligne, la signature mesurée à une position inconnue est associée à la carte radio hors ligne pour renvoyer l'estimation de l'emplacement la mieux adaptée.

Comparé à la puissance du signal reçu (RSS) qui souffre d'une dégradation spectaculaire des performances due à la décoloration par trajets multiples à petite échelle et à la vii Résumé de la Thèse en Français viii dynamique temporelle à l'intérieur, les informations d'état de canal (CSI) de couche PHY sont capables de caractériser le canal pour chaque paire d'antennes d'émission-réception au niveau de plusieurs sous-porteuses orthogonales. Ainsi, il peut servir de géo-signature préférable pour apporter des informations spécifiques à l'emplacement plus riche.

Dans cette thèse, nous proposons d'abord EntLoc, un système d'empreinte digitale de localisation probabiliste basé sur le Wi-Fi utilisant des informations d'amplitude CSI.

Il recourt à la métrique entropique basée sur la modélisation autorégressive (AR), qui équivaut à une transformation directe à partir de la PDF d'origine des amplitudes CSI sous forme de densité spectrale de puissance (PSD). Grâce à des expériences approfondies menées dans des bancs d'essai réalistes, nous démontrons que notre métrique entropique AR proposée surpasse son empreinte digitale CSI ou RSS d'origine. Comment exploiter correctement les informations de phase CSI dans notre système d'empreintes digitales de localisation basé sur l'entropie reste ouvert.

Inspiré par les récents progrès du traitement du signal en réseau phasé, l'exploitation de l'AoA comme empreinte digitale supplémentaire nous permet de revisiter l'exploitation de la phase CSI avec un nouvel horizon. Étant donné qu'il peut exister des candidats RP distants dont les lectures AoA diffèrent beaucoup de celles de la cible en ligne, ces faux RP hors ligne peuvent être exclus pour affiner davantage la précision de la prise d'empreintes digitales de l'emplacement. Sur cette base, nous concevons plus avant AngLoc, un système de localisation intérieure probabiliste compatible AoA utilisant un appareil Wi-Fi standard. Toutes les expériences sont menées sur la plate-forme légère HummingBoard, ce qui facilite considérablement la mise en oeuvre des empreintes digitales chronophages et laborieuses. Les résultats expérimentaux valident les performances supérieures de notre système proposé par rapport aux approches d'empreintes digitales de localisation précédentes.

Chapitre 2: Préliminaires

Dans ce chapitre, nous examinerons l'empreinte digitale du signal sans fil de base de cette thèse, c'est-à-dire les informations sur l'état des canaux.

Dans les systèmes de communication sans fil, le récepteur de signaux opère une estimation de canal grâce au mécanisme de sondage de canal. Plus précisément, pour le système IEEE 802.11n basé sur les paquets, l'émetteur envoie des séquences d'information, y compris la trame à haut débit (HT-LTF) dans le préambule. Une fois que le récepteur détecte la position de départ du premier HT-LTF, il commence à dériver immédiatement les informations sur l'état du canal. Plus précisément, CSI décrit les propriétés des canaux de la couche PHY dans le domaine fréquentiel et révèle les effets combinés de la propagation par trajets multiples du signal qui inclut l'atténuation d'amplitude et le décalage de phase.

La réponse en fréquence du canal (CFR) est représentée par chaque entrée CSI. Il peut être exprimé par

H(f ) = |H(f )|e j∠H(f ) (1)
ici H(f ) est la valeur complexe de CFR à la sous-porteuse avec une fréquence centrale de f . Dans ce qui suit, nous décrirons les empreintes digitales plus basées sur l'entropie générées dans le système EntLoc.

Estimation des empreintes digitales d'entropie AR

Rappelons que la métrique d'entropie est considérée comme une empreinte digitale de localisation souhaitée en raison de sa simplicité structurelle ainsi que de son mode de réalisation statistique d'informations riches spécifiques à la localisation. En réalité, il est impossible de dériver directement l'entropie de Shannon à partir de données réelles.

La raison de ce dilemme est double: (i) Étant donné que le vrai PDF est normalement inconnu, l'approximation d'entropie n'est accessible qu'à partir des simples échantillons de données. (ii) Le calcul conventionnel de l'entropie de Shannon nécessite une intégration numérique lourde car il n'existe pas de substitut de forme fermée.

Pour relever les défis ci-dessus, dans cette thèse, nous proposons d'estimer avec précision l'entropie en s'appuyant sur l'approche de modélisation AR, dont le principe de base est d'estimer la PSD équivalente au PDF d'un processus AR de variance unitaire.

Cette contrainte de variance unitaire est importée pour répondre aux exigences de base du PDF (c'est-à-dire une fonction positive unitaire). Plus précisément, nous définissons En outre, en appliquant la formule de Plancherel-Parseval sur le côté droit de (3), une alternative de forme fermée réalisable sans aucune intégration numérique peut être obtenue

comme φβ = - ∞ ∑ i=-∞ R W (i)Z * W (i) (4)
ici (•) * est l'opérateur conjugué et Z W (i) désigne la composante i th du cepstrum du processus AR, qui peut être obtenue en appliquant l'IFFT à log ŜW (β). R W (i) représente la fonction d'autocorrélation des données d'amplitude.

Résultats Expérimentaux

La figure 2 (ii) Parmi ces emplacements candidats, un nouveau schéma de régression par noyau bivarié est proposé pour réduire davantage le nombre de RP sujets aux erreurs, abordant ainsi la détermination de l'emplacement de la cible avec une précision améliorée.

Résultats Expérimentaux

La Figure 6 affiche le plan détaillé de la salle de classe utilisée pour les tests. which enormously facilitates the operation efficiency. The consumers in the fancy commercial mall usually desire the dedicated product information through the proximity-based marketing advertisements. For some sensitive facilities like banking systems, the topic of intruder tracking is also of great significance in order to guarantee a round-the-clock security level and so forth. Accordingly, in order to meet the pressing need of human social activities, the most fundamental common ground for these LBS applications is to precisely and effectively pinpoint the location of the target in a wireless manner.

To this end, the well-known Global Navigation Satellite System (GNSS) such as Global

Positioning System (GPS) from the U.S. can already offer successful and accurate localization in the outdoor space. However, it suffers dramatic performance degradation in the complex indoor environment due to the blockage of satellite signals. Moreover, the location resolution demand for indoor positioning schemes is generally higher than that in the outdoor scenarios. Consequently, in addition to providing the seamless and ubiquitous location-aware services indoors, it brings us new challenges for designing indoor localization systems which are capable of covering the requirements of high accuracy, time-critical constraints and energy efficiency. As illustrated in Figure 1.1, we further present a wide variety of LBS applications from outdoor to indoor situations.

In light of the continuous mobile technique innovation and its hardware upgrading, accurate, reliable and ubiquitous indoor localization solutions have been extensively studied in recent years [4,5,[START_REF] Dardari | Indoor Tracking: Theory, Methods, and Technologies[END_REF]. Such examples comprise not only well-known Wireless Local Area Network (WLAN) based technologies like Wi-Fi [START_REF] Yang | WiFi-based Indoor Positioning[END_REF][START_REF] He | Wi-Fi Fingerprint-based Indoor Positioning: Recent Advances and Comparisons[END_REF][START_REF] Ma | WiFi Sensing with Channel State Information: A Survey[END_REF], Bluetooth [START_REF] Liu | Face-to-Face Proximity Estimation using Bluetooth on Smart Phones[END_REF], Radio Fre- quency Identification (RFID) [START_REF] Ni | LANDMARC: Indoor Location Sensing using Active RFID[END_REF], Ultra Wideband (UWB) [START_REF] Kempke | SurePoint: Exploiting Ultra Wideband Flooding and Diversity to Provide Robust, Scalable, High-fidelity Indoor Localization[END_REF], but also some emerging areas such as infrared [START_REF] Want | The Active Badge Location System[END_REF], visible light [START_REF] Pathak | Visible Light Communication, Networking and Sensing: A Survey, Potential and Challenges[END_REF][START_REF] Torkestani | Indoor Optical Wireless System Dedicated to Healthcare Application in A Hospital[END_REF], ultrasound [START_REF] Ward | A New Location Technique for the Active Office[END_REF], geomagnetic field [START_REF] Shu | Magicol: Indoor Localization using Pervasive Magnetic Field and Opportunistic WiFi Sensing[END_REF] and so forth. Among these techniques, the Wi-Fi based positioning is probably of the greatest popularity, mainly owing to the pervasive availability of the high-throughput and low-cost Wi-Fi technology. Thereupon, indoor position determination can be then operated in Wi-Fi based communication systems through firmware upgrades and software implementations.

In general, conventional Wi-Fi based Indoor Positioning Systems (IPSs) either adopt geometric mapping approach or resort to the Location Fingerprinting (LF) [START_REF] Yang | From RSSI to CSI: Indoor Localization via Channel Response[END_REF]. For geometric mapping, intermediate spatial parameters like distance or direction are first derived from certain physical measurements. Typical parameters include Time of Flight (ToF) [START_REF] Tadayon | Decimeter Ranging with Channel State Information[END_REF] and Angle of Arrival (AoA) [START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF]. Then, target's physical location can be further inferred by using geometric algorithms (e.g., trilateration or triangulation). Nevertheless, the performance of geometric mapping approach heavily relies on the Line-of-Sight (LoS) condition.

In wireless communications, when a signal emitted from a transmitter is reflected or scattered by a scatterer, an attenuated copy of the original signal is generated and reaches the receiver through a different path. The phenomenon that a signal is received by two or more paths is known as multipath propagation [START_REF] Wang | The Promise of Radio Analytics: A Future Paradigm of Wireless Positioning, Tracking, and Sensing[END_REF]. n/ac standard, Wi-Fi networks use Multiple-Input Mulitiple-Output (MIMO) [START_REF] Haimovich | MIMO Radar with Widely Separated Antennas[END_REF][START_REF] Boyer | Performance Bounds and Angular Resolution Limit for the Moving Colocated MIMO Radar[END_REF] and Orthogonal Frequency Division Multiplexing (OFDM) [START_REF] Weinstein | The History of Orthogonal Frequency Division Multiplexing [History of Communications[END_REF] techniques to modulate data on different orthogonal sub-channels and transmit them over multiple transmit-receive (TX-RX) antenna pairs simultaneously. Therefore, it can reflect the fine-grained channel feature known as channel response, which can be partially extracted from many commercial off-the-shelf Wi-Fi Network Interface Cards (NICs) [START_REF] Halperin | Tool Release: Gathering 802.11 n Traces with Channel State Information[END_REF][START_REF] Xie | Precise Power Delay Profiling with Commodity Wi-Fi[END_REF] in the format of Channel State Information (CSI). Specifically, CSI is aggregated by a set of channel estimations depicting the amplitude and phase information of each OFDM subcarrier. Different from coarse-grained RSS, the Physical (PHY) layer CSI measurement can serve as a preferable location signature characterized by the small-scale multipath fading, which significantly deteriorates the quality of its RSS counterpart. Furthermore, CSI indicates channel qualities in the level of multiple subcarriers and thus provides richer location-specific information than RSS-based localization schemes.

In principle, Wi-Fi fingerprinting algorithms can be categorized into deterministic and probabilistic ones [START_REF] He | Wi-Fi Fingerprint-based Indoor Positioning: Recent Advances and Comparisons[END_REF]. Deterministic approaches enjoy the easy implementation but fail to fully exploit environmental fluctuations, which consequently renders the location estimation error-prone. In contrast, probabilistic methods embrace the channel variation by inferring a signal distribution based statistical model, thus obtaining more robust and accurate positioning performance than its deterministic adversary. Nevertheless, there still exists three underlying challenges for probabilistic Wi-Fi fingerprinting systems:

(i) The accurate approximation of Probability Distribution Function (PDF) is largely driven by massive storage of signal measurements [START_REF] Alsindi | An Empirical Evaluation of A Probabilistic RF Signature for WLAN Location Fingerprinting[END_REF], which in turn brings huge system burden and computational requirement.

(ii) Most probabilistic location-aware solutions are well established on the assumption of Gaussian-distributed measurements [START_REF] Youssef | The Horus WLAN Location Determination System[END_REF][START_REF] Xiao | FIFS: Fine-grained Indoor Fingerprinting System[END_REF]. However, due to the complex nature of indoor environment and the imperfection of wireless devices, some practical measurements appear to be non-Gaussian distributed or even do not fit any known distribution [START_REF] Sen | You are Facing the Mona Lisa: Spot Localization using PHY Layer Information[END_REF][START_REF] Zhou | Omnidirectional Coverage for Device-free Passive Human Detection[END_REF][START_REF] Mirowski | KL-Divergence Kernel Regression for Non-Gaussian Fingerprint based Localization[END_REF]. This then complicates the fingerprinting process and incurs severe ambiguity for location estimation.

(iii) When it comes to multivariate fingerprint structure (e.g. multi-subcarrier CSI), traditional probabilistic methods turn powerless since existing statistical tools only work for measurements with identifiable distributions [START_REF] Chen | Probabilistic Indoor Position Determination via Channel Impulse Response[END_REF].

Therefore, it would be highly desirable for a fingerprint which shares the simplicity of RSS (scalar) and meanwhile conserves rich statistical location-specific information.

To address the aforementioned substantial challenges, in this thesis, we first propose EntLoc [START_REF] Chen | CSI-based Probabilistic Indoor Position Determination: An Entropy Solution[END_REF], a Wi-Fi based probabilistic indoor location fingerprinting system using CSI amplitude information. It resorts to the Autoregressive (AR) modeling based Shannon entropy metric [START_REF] Shannon | A Mathematical Theory of Communication[END_REF][START_REF] Bercher | Estimating the Entropy of A Signal with Applications[END_REF], which equals a direct transformation from the original PDF of CSI amplitudes. Unlike traditional data-adaptive histogram estimator which entails a slow convergence rate, AR modeling approach provides a feasible parametric workaround to accurately infer the PDF in the form of Power Spectral Density (PSD) [START_REF] Stoica | Spectral Analysis of Signals[END_REF][START_REF] Kay | Model-based Probability Density Function Estimation[END_REF]. Despite its structural simplicity, this novel entropy fingerprint embodies the whole statistical information of CSI amplitudes. Through extensive experiments conducted in realistic testbeds, we demonstrate that our proposed AR entropy metric outperforms its original CSI or RSS fingerprint [START_REF] Chen | CSI-based Probabilistic Indoor Position Determination: An Entropy Solution[END_REF]. However, since CSI phases of one subcarrier are generally uniformly distributed [START_REF] Molisch | Wireless Communications[END_REF], this quantifies each RP location with an equally maximized entropy value (a.k.a. Gibbs' inequality [START_REF] Brémaud | An Introduction to Probabilistic Modeling[END_REF]), thereby hampering the location distinction to a great extend. How to properly exploit CSI phase information in our entropy-based location fingerprinting system still remains open.

Inspired by the recent advancement of phased array signal processing [START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF], leveraging AoA as supplementary fingerprint enables us to revisit CSI phase exploitation with a fresh horizon. Given the fact that there may exist some remote RP candidates whose AoA readings differ a lot with those around the online target, these false offline RPs can be ruled out to further refine the location fingerprinting accuracy. On this basis, we design AngLoc [START_REF] Chen | AoA-aware Probabilistic Indoor Location Fingerprinting using Channel State Information[END_REF], an AoA-aware probabilistic indoor localization system using commercial off-the-shelf Wi-Fi device. To remove the noisy component from the raw CSI measurements, we first introduce a power-based tap filtering scheme to preserve the most informative CSI signatures. For the purpose of precise AoA estimation, a set of phase calibration techniques are then employed to mitigate dramatic phase drifts. Subsequently, for the offline radio map construction, the pre-processed CSIs are simultaneously fed to two independent fingerprint generators, namely AR modeling based entropy estimator for CSI amplitude and the enhanced AoA-ToF estimator driven by Joint Angle and Delay Estimation (JADE) Multiple Signal Classification (MUSIC) algorithm [START_REF] Schmidt | Multiple Emitter Location and Signal Parameter Estimation[END_REF][START_REF] Vanderveen | Joint Angle and Delay Estimation (JADE) for Multipath Signals Arriving at An Antenna Array[END_REF][START_REF] Boyer | Oblique Projections for Direction-of-Arrival Estimation with Prior Knowledge[END_REF]. It is worth noting that ToF is utilized here to create measurable phase shift across subcarriers, by which realizes virtual antenna extension to overcome the antenna number restriction for classical MUSIC algorithm [START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF]. The other trick of ToF here is to identify the first incoming path (not necessarily the direct path) as the angular fingerprint benchmark, which serves to guarantee similar AoA recordings around closely-spaced RPs. Moreover, in the online phase, due to the simple structure of the radio map, the succinct Manhattan distance and Euclidean distance can be fully competent as the similarity metrics for AR entropy and AoA fingerprints, respectively. Afterwards, we propose an optimal bivariate kernel regression scheme to accurately infer the target's physical location. The entire experiments are conducted on the lightweight HummingBoard platform [45], which tremendously facilitates the time-consuming and labor-intensive fingerprinting implementation. Experimental results validate the superior performance of our proposed system over previous location fingerprinting approaches.

Contributions

In a nutshell, the major contributions of this thesis can be summarized and laid out below:

• The first contribution of this dissertation is that we design an AR entropy based indoor location fingerprinting system using fine-grained channel state information, namely EntLoc. As far as we are aware of, this is the first work to statistically study the AR modeling based entropy signature in CSI fingerprint localization system. This simple fingerprint structure helps decrease the pattern-matching complexity and its informative statistical embodiment also facilitates the location estimation accuracy.

• As an upgraded version of EntLoc, the pioneering AngLoc system is further proposed as the second main contribution of this thesis. Specifically, in AngLoc, we constructively incorporate the angular signature (AoA information) in CSI entropy based indoor location fingerprinting system, which manages to narrow down the error-prone RP candidates and further improves the positioning accuracy. It even fertilizes the opportunity to achieve a decimeter-level localization precision in our indoor experimental testbed.

• Since the raw CSI measurements retrieved from commercial Wi-Fi NICs contain various noises, which may severely jeopardize the localization performance, such noises have to be first removed before proceeding to conduct the location fingerprinting process. Accordingly, we propose a power-based tap-filtering program alongwith several CSI phase calibration pre-processing techniques to effectively mitigate CSI noisy component and sanitize CSI phase errors, respectively.

• Recall that for the part of the aforementioned AngLoc system, we fully exploit both CSI amplitude and phase information to pinpoint the online target's physical position. The respective AR entropy and AoA information are designated as dual location fingerprints in AngLoc. On this basis, we design a feasible bivariate kernel regression scheme for the online location estimation stage, which organically combines the weighting factors for both amplitude based entropy and phase-based AoA fingerprints.

• Last but not least, in view of the cumbersome laboring process for the traditional offline fingerprint database construction, based on the Linux CSI tool with a modified firmware, we build and implement extensive experiments on the lightweight HummingBoard Pro device for different indoor testbeds. In addition to the superior localization performance, our mobile CSI receiver prototype remarkably enhances the location fingerprinting efficiency.

Structure of the Thesis

This thesis focuses on the problem of Wi-Fi based indoor fingerprint localization using channel state information. We successfully and effectively design the whole framework of two location fingerprinting systems which leverage the AR entropy and enhanced AoA estimates as their location signatures, achieving a superior localization performance over the previous approaches. The remainder of this dissertation is organized as follows:

Chapter 2 reviews the overall technical background which is closely related to the domain of Wi-Fi based indoor localization. To be specific, we first introduce some Wi-Fi based physical measurements, which are extremely crucial to the localization performance, and discuss their respective strength and weakness in a comparative manner. Next, we dive into the two basic categories of the localization algorithms and present the relevant examples for both indoor location-aware techniques.

Chapter 3 lays out the in-depth structural presentation of our proposed EntLoc system.

First of all, we investigate several representative literature reviews to reach an overview understanding for the state-of-the-art. The overall EntLoc system architecture is then given in the sequel. In the offline phase, we introduce the tap filtering pre-processing scheme and the detailed fingerprint generation process of the CSI amplitude based AR entropy.

As for the online stage, the distance-based proximity comparison is carried out and then fed to the kernel regression algorithm to estimate the target's position. Subsequently, we evaluate the EntLoc's localization performance in comparison with the state-of-the-art.

In addition, the impacts of some defining experimental factors are also discussed in this chapter.

Chapter 4 further proceeds to illustrate the updated design of the AngLoc system. Specifically, compared with aforementioned EntLoc system, there are three significant upgrades in the AngLoc system. Firstly, since the raw CSI measurements are full of phase errors and ineligible for the accurate AoA estimation, we employ a set of phase calibration techniques for the CSI pre-processing to effectively mitigate these phase offsets. Secondly, after acquiring the AR entropy fingerprint, we leverage an enhanced subspace based algorithm to estimate the AoA information, which serves as an additional fingerprint to further improve the location fingerprinting accuracy. Thirdly, in view of the AngLoc's dual-fingerprint structure, we propose a novel bivariate kernel regression scheme to precisely infer the final location. In addition to providing the experimental evaluations for AngLoc, we also discuss some unsolved issues which may further increase the efficiency and accuracy of our AngLoc system.

Chapter 5 draws the conclusions of this thesis by briefly reviewing our main contributions. Moreover, we highlight some potential research directions that can be further explored in our future works.

Related Publications

The content of this dissertation is mainly based on the following publications:

•

Wi-Fi based

Introduction

In this chapter, we will review some technical backgrounds of Wi-Fi based indoor localization, whose methodological concepts are widely covered throughout this dissertation. Since the radio measurement lays the firm foundation for a decent wireless positioning system, we first study some typical WLAN measurements according to the wireless signal characteristics, such as signal transmission power decay, transmission time delay, transceiver spatial relations and the channel properties, etc.. Both the advantages and weaknesses for each signal measurement will be also discussed in particular.

In addition, by focusing on the Wi-Fi based indoor position determination, we will elucidate the principle of two conventional wireless localization algorithms, i.e., the geometric mapping approach and the location fingerprinting method. Some well-known localization methodologies for both algorithms will be also introduced, respectively.

Wi-Fi based Physical Measurements

For Wi-Fi based indoor location-aware solutions, acquiring an appropriate kind of physical measurement is of great importance for the accurate indoor position determination. There are many factors or properties which need to be considered when it comes to determine a good candidate. Such properties include the signal accessibility, the structure complexity, location dependency, power consumption and the robustness against environmental dynamics, etc.. In this section, we will present some popular physical measurements in the domain of indoor localization and compare them on the basis of these signal properties.

Power based Measurement

Signal power is widely used in both geometric mapping (especially in ranging) and location fingerprinting due to its handy accessibility from myriad commercial off-the-shelf wireless devices. Particularly, the MAC layer power signature, namely RSS, is one of the most prevalent power features, which attracts extensive popularities in the wireless techniques ranging from UWB, ZigBee [START_REF] Farahani | ZigBee Wireless Networks and Transceivers[END_REF], Wi-Fi to cellular networks [START_REF] Lee | Mobile Cellular Telecommunications: Analog and Digital Systems[END_REF].

In order to conduct indoor location determination, the intermediate power measurement is closely related to signal transmission distance due to the wireless signal's natural attenuation over physical distance. Therefore, a proper pass loss model should be first determined for the purpose of accurate indoor positioning. Consider a signal transmitted through free space to a receiver located at distance d from the transmitter. Assume there are no obstructions between the transmitter and receiver and the signal propagates along a straight line between the two. The simplest free-space power-distance relationship can be characterized as [START_REF] Tse | Fundamentals of Wireless Communication[END_REF]]

P r = P t G t G r λ 2 (4πd) n (2.1)
where P r and P t are the received and transmitted signal power, respectively. G r and G t denote the antenna gains at the receiver and transmitter, respectively. λ is the wavelength of the transmitted signal and n is the environmental attenuation factor.

Radio Wave Propagation

The initial understanding of radio wave propagation goes back to the pioneering work of James Clerk Maxwell, who in 1864 formulated the theory of electromagnetic propagation which predicted the existence of radio waves. In 1887, the physical existence of these waves was demonstrated by Heinrich Hertz. However, Hertz saw no practical use for radio waves, reasoning that since audio frequencies were low, where propagation was poor, radio waves could never carry voice. The work of Maxwell and Hertz initiated the field of radio communications: in 1894 Oliver Lodge used these principles to build the first wireless communication system, however its transmission distance was limited to 150 meters. By 1897 the entrepreneur Guglielmo Marconi had managed to send a radio signal from the Isle of Wight to a tugboat 18 miles away, and in 1901 Marconi's wireless system could traverse the Atlantic ocean. These early systems used telegraph signals for communicating information. The first transmission of voice and music was done by Reginald Fessenden in 1906 using a form of amplitude modulation, which got around the

P L(d)[dB] = P L (d 0 ) + 10n lg ( d d 0 ) + X σ (2.2)
where P L(d) denotes the measured path loss at distance d. P L(d 0 ) is the average path loss at reference point d 0 and n is the path loss exponent. X σ is a zero-mean normal random variable reflecting the attenuation in decibel caused by shadowing.

In conclusion, RSS benefits well from its easy accessibility and low-cost deployment.

However, the main drawback of RSS lies in its temporal fluctuations in complex indoor environments, making it a volatile and coarse-grained feature. The multipath-rich indoor environment complicates the wireless propagation and derails RSS-based ranging technique. Thus, more accurate power-based ranging then requires better characterizing and modeling of the small-scale multipath effects [START_REF] Wolf | Improved Multi-Channel Ranging Precision Bound for Narrowband LPWAN in Multipath Scenarios[END_REF].

Temporal Measurement

The For the TDOA based method, it is typically employed when some anchor nodes are synchronized among them to a common clock while the mobile node, whose position is unknown, is not synchronized with the anchors. In particular, this scheme consists of measuring the difference of ToF between the mobile node with respect to two anchors. node broadcasts a ranging message. Since the mobile node is not synchronized with the anchors' clock, the anchors do not know the exact sending time. However, the anchor nodes are able to use the corresponding arrival times (T 1 , T 2 and T 3 ) and calculate the TOA (t 1 , t 2 , t 3 ) with respect to an initial time that is different from T 0 . Next, the TDOA can be calculated as t 12 = t 1 -t 2 and t 23 = t 2 -t 3 . Finally, given the two independent TDOA estimations, the location of the mobile node is calculated as the intersection of two hyperbolas with foci at the three anchor nodes.

To summarize, a striking advantage of time based wireless technique lies in its superior ranging accuracy. But the greatest weakness of this method is that it requires an accurate time synchronization, either between the transmitter and receiver for TOA or among the anchor nodes for TDOA. For example, just a synchronization error of 10 ns will lead to a ranging error of around 3 meters.

Angular Measurement

Angular information provides an orthogonal dimension with regard to the distance for geometric mapping. Angle can be combined with distance estimates to enable single- To this end, directional antennas are often capable of obtaining both angle and distance estimates while avoiding interferences from other directions, yet at the cost of dedicated infrastructure. Recently, antenna arrays have also attracted increasing interests with the rapid development of MIMO technology [START_REF] Haimovich | MIMO Radar with Widely Separated Antennas[END_REF], which sets a handy path to achieve a desired AoA estimation performance. However, the environmental noise, the limited number of array antennas and the small-scale multipath propagation might drastically impact the accuracy of the final position estimation. In the later part of this thesis, we will explore the problem of accurate AoA estimation in Chapter 4 and provide some insightful discussions for our future work.

Channel Response based Measurement

Recall that RSS is merely an indicator of the MAC layer' link quality, it suffers from severe variation due to the constructive and destructive superposition of multipath signal components. On the contrary, the finer-grained PHY layer channel response based measurements characterize the channel properties and embrace the channel diversity, thus providing richer location-dependent information and achieving superior localization performance over its RSS counterpart. In this section, we begin with the introduction of MIMO-OFDM mechanism and then elaborate the technical background of the PHY layer channel state information.

MIMO-OFDM Mechanism

In general, without properly compensating for the wireless signal propagation and the asynchronization effects, the receiver has no way of detecting what has been transmitted [START_REF] Tadayon | Decimeter Ranging with Channel State Information[END_REF]. To this end, through a mechanism named channel sounding, the receiver obtains an estimate of wireless channel. This is accomplished by sending a training sequence which is known to both transmitter and receiver. For a wideband MIMO-OFDM system, the estimate of the channel is a collection of complex matrices for each OFDM subcarrier. In this part, we present the detailed mechanism of this MIMO-OFDM technology under the framework of IEEE 802.11 n/ac standard [START_REF]IEEE Standard for Information Technology -Local and Metropolitan Area Networks-Specific Requirements -Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications -Amendment 5: Enhancements for Higher Throughput[END_REF][START_REF]IEEE Standard for Information Technology -Telecommunications and Information Exchange Between Systems -Local and Metropolitan Area Networks -Specific Requirements -Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications -Amendment 4: Enhancements for Very High Throughput for Operation in Bands Below 6 GHz[END_REF]. In reverse, upon receiving the signals, the receiver block first samples them and digitizes them through analog-to-digital converters (ADCs). Subsequently, a forward FFT procedure is conducted to convert the data samples back to the frequency domain. The desired channel estimation then becomes achievable after the signal demodulation process.

Channel State Information

In

H(f ) = |H(f )|e j∠H(f ) (2.3)
where H(f ) is the complex value of CFR at the subcarrier with central frequency of f .

|H(f )| and ∠H(f ) denote its amplitude and phase, respectively. Moreover, the frequency domain CFR consists of amplitude-frequency response and phase-frequency response, characterizing the frequency-selective fading caused by the constructive and destructive phases in the multipath-rich environment [START_REF] Yang | From RSSI to CSI: Indoor Localization via Channel Response[END_REF]. It thus contains more channel information than the power based RSS measurement.

Additionally, in order to fully characterize the indoor multipaths, the time domain counterpart of CFR, also termed as Channel Impulse Response (CIR), is able to model the wireless propagation channel as a temporal linear filter. Mathematically, it can be denoted as

h(τ ) = L ∑ i=1 α i e -jφ i δ(τ -τ i ) (2.4)
where α i , φ i and τ i are the amplitude, phase and time delay spread of the i th path, respectively. L is the total number of multipaths and δ(•) is the Dirac delta function.

Each impulse represents a delayed multipath component, multiplied by the corresponding amplitude and phase. As depicted in Figure 2.5, by focusing on the amplitude response of CIR, the first appearing path normally represents the LoS direct path, which is followed by several resolvable time delayed NLoS paths.

Wi-Fi based Localization Algorithms

The previous section discussed some commonly adopted Wi-Fi signal patterns, which settle the precondition for accurate Wi-Fi based indoor position determination. In this section, we proceed to lay out the concepts of some popular Wi-Fi based localization algorithms. Since the traditional Wi-Fi based positioning approaches can be classified into two categories: geometric mapping and location fingerprinting. We then roll out this section by presenting these two parts respectively.

Geometric Mapping

In geometric mapping, intermediate geometric parameters such as distance or direction with regard to the reference points are first derived from certain physical measurements.

These relative parameters are then converted into locations by applying geometric algorithms. There are generally two sorts of geometric mapping methods, namely trilateration and triangulation. The former one corresponding to the distance-based mapping, in particular, is often termed as ranging, which involves power or time based physical measurements. The latter one is related to direction-based mapping, whose angular measurement is less popular than the ranging technique due to its cumbersome acquisition from pervasive devices. However, direction information is directly measurable at the receiver, while the derivation of distance involves the complex wireless propagation rules.

In this part, we will briefly introduce the typical trilateration and triangulation algorithms as follows.

Trilateration

Trilateration is the process of determining absolute or relative locations of points by measurement of distances, using the geometry of the environment. In addition to its interest as a geometric problem, trilateration has practical applications in surveying and navigation, including global positioning systems [START_REF] Fang | Trilateration and Extension to Global Positioning System Navigation[END_REF]. For the conciseness of presentation, we model the trilateration process as finding the position of an unknown node based on its distances to three anchors. As shown in Figure.

II. BACKGROUND KNOWLEDGE AND BASIC LOCALIZATION METHODS

A. Basic Terminologies

Anchor (Beacon) Node:

To localize a WSN in the global coordinate system, some special sensor nodes should be aware of their positions in advance either from GPS or by virtue of being manually placed, which are called anchor nodes or beacon These geometric constraints can be expressed by the following equations.

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ √ (x -x a ) 2 + (y -y a ) 2 = d a √ (x -x b ) 2 + (y -y b ) 2 = d b √ (x -x c ) 2 + (y -y c ) 2 = d c (2.5)
By solving Equation 2.5, we can get the matrix AX = B [START_REF] Li | Research of Localization and Tracking Algorithms based on Wireless Sensor Network[END_REF], where

X = [ x y ] T A = 2 [ (x a -x c ) (y a -y c ) (x b -x c ) (y b -y c ) ] B = [ x 2 a -x 2 c + y 2 a -y 2 c + d 2 c -d 2 a x 2 b -x 2 c + y 2 b -y 2 c + d 2 c -d 2 b ] (2.6)
Thus, the trilateration approach can be accomplished by solving the above liner equation to estimate the coordinate of the unknown node D.

Even though the basic trilateration can be easily implemented and is able to acquire accurate estimations under most conditions, in practice, due to the complex indoor environmental dynamics and the asynchrony of commercial wireless devices, it inevitably suffers a lot from aforementioned power and time based distance miscalculations.

Triangulation

Triangulation, unlike trilateration, computes the position of an unknown node based on the angular distance between three different pairs of anchor nodes. Consider the example depicted in Figure 2.8, suppose that the coordinate of an unknown node D is (x, y). The coordinates of three anchor nodes A, B, C are (x a , y a ), (x b , y b ) and (x c , y c ), respectively.

If we know the angles between the line segments connecting D and the anchors, then the unknown node's coordinates must be calculated using triangulation instead of trilateration.

Let ∠ADB, ∠ADC, ∠BDC denote the angles between the line segments connecting D to the anchors, respectively. D is the intersection point of the three circles. If the angular distance between the anchor nodes is known, the centers of the circles can be obtained. For anchor nodes A, C and the angle ∠ADC, if the arc AC is within the scope of the △ABC, the circle can be uniquely identified. Assume that the center of the circle is

O 1 (x O 1 , y O 1 )
, the radius is r 1 , thus, ∠AO 1 C = 2(π -∠ADC). O 1 and r 1 can be computed between D and A, B, C are d a , d b and d c , respectively. These geometric constraints can be expressed by the following system of equations [START_REF] Shu | Magicol: Indoor Localization using Pervasive Magnetic Field and Opportunistic WiFi Sensing[END_REF],

⎧ ⎪ ⎨ ⎪ ⎩ (x -x a ) 2 + (y -y a ) 2 = d a (x -x b ) 2 + (y -y b ) 2 = d b (x -x c ) 2 + (y -y c ) 2 = d c . ( 1
)
By solving Eq. ( 1), we can get the matrix AX = B, where

X = x y T , A = 2 (x a -x c ) (y a -y c ) (x b -x c ) (y b -y c ) , b = x 2 a -x 2 c + y 2 a -y 2 c + d 2 c -d 2 a x 2 b -x 2 c + y 2 b -y 2 c + d 2 c -d 2 b ,
2) Triangulation: Triangulation, unlike trilateration, computes the position of an unknown node based on the angular dis-

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ √ (x O 1 -x a ) 2 + (y O 1 -y a ) 2 = r 1 √ (x O 1 -x b ) 2 + (y O 1 -y b ) 2 = r 1 (x a -x c ) 2 + (y a -y c ) 2 = 2r 2 1 -2r 2 1 cos ∠AO 1 C (2.7)
Similarly, anchor nodes A, B, the angle ∠ADB and anchor nodes B, C, the angle

∠BDC can determine O 2 (x O 2 , y O 2 ), r 2 and O 3 (x O 3 , y O 3 ), r 3 , respectively. Thus, knowing the coordinates of O 1 (x O 1 , y O 1 ), O 2 (x O 2 , y O 2 ) and O 3 (x O 3 , y O 3 ), the coordinate of D(x, y)
can be calculated by applying Equation (2.5).

To conclude, in triangulation, distances are computed from angle observations. This inherently makes the triangulation scheme more expensive than trilateration in terms of deployment and computational cost. Especially for the indoor scenario implementation, the pressing demand of the accurate angular metric estimation renders the triangulation approach even more challenging.

Location Fingerprinting

In addition to geometric mapping, as a promising alternative to analyzing the sophisticated signal propagation, location fingerprinting technique adopts a pattern-matching approach. It roughly consists of two main phases: the offline fingerprint database generating (training) phase and the online location estimation (testing) phase. • Offline Training Phase: To be specific, in the offline phase, the area of interest is first divided into a reasonable number of spatial grids, where the reference points are situated at the vertexes and their coordinates are known a priori. Then, a mobile receiver moves around among these predefined reference points to conduct a comprehensive site survey, whose main idea is to collect wireless signal signatures at all reference points to finally construct a fingerprint database.

Particularly, Sometimes before the process of fingerprint generating, the recorded measurements should be pre-processed in order to refine the measurement quality for further improving the localization performance. Typical Wi-Fi based pre-processing techniques consist of measurement noise reduction, signal transformation and signal extraction [START_REF] Ma | WiFi Sensing with Channel State Information: A Survey[END_REF][START_REF] Qian | Enabling Contactless Detection of Moving Humans with Dynamic Speeds using CSI[END_REF]. For noise reduction, the phase offsets removal and outliers removal are the most appealing approaches. In Chapter 4, we will provide an in-depth overview on the CSI phase compensation issue. For signal transformation, techniques like FFT [START_REF] Abdelnasser | UbiBreathe: A Ubiquitous Noninvasive WiFi-based Breathing Estimator[END_REF], short time Fourier transform [START_REF] Chen | Rapid: A Multimodal and Devicefree Approach using Noise Estimation for Robust Person Identification[END_REF], discrete Hilbert transform [START_REF] Yu | QGesture: Quantifying Gesture Distance and Direction with WiFi Signals[END_REF] and discrete wavelet transform [START_REF] Fang | Channel State Reconstruction using Multilevel Discrete Wavelet Transform for Improved Fingerprintingbased Indoor Localization[END_REF] are widely employed in CSI pre-processing related works. As for the signal extraction, it is for extracting target signals from raw CSI measurements. Sometimes it needs thresholding [START_REF] Abdelnasser | WiGest: A Ubiquitous WiFi-based Gesture Recognition System[END_REF], filtering [START_REF] Arshad | Wi-Chase: A WiFi based Human Activity Recognition System for Sensorless Environments[END_REF] or signal compression [START_REF] Zhou | CSI Fingerprinting with SVM Regression to Achieve Device-Free Passive Localization[END_REF] (e.g. Principal Component Analysis (PCA)) to remove unrelated or redundant signals. In some cases, it requires the composition [START_REF] Huang | Feasibility and Limits of Wi-Fi Imaging[END_REF] of multiple signal sources and data interpolation to get more location-specific information.

• Online Testing Phase: Subsequently, in the online phase, localization is then simply the process of matching the measured fingerprints at an unknown location with those in the database by calculating the similarity and returning the location corresponding to the best-fitted fingerprint by the location estimation algorithms.

Based on the statistical property, conventional indoor localization algorithms comprise deterministic and probabilistic methods. Accordingly, we will present each kind of locationaware methods in the coming part.

Deterministic Methods

Deterministic algorithms use a similarity metric to differentiate online signal measurement and the offline fingerprint data. Target is then estimated at the closest fingerprint RP location in signal space [START_REF] Han | Building A Practical Wi-Fi-based Indoor Navigation System[END_REF]. Assume that there are M RPs in the area of interest, whose coordinates are denoted by {ℓ m } 1≤m≤M . The basic deterministic target position determination of lo can be expressed by the following equation.

lo = arg min ℓm D[H m , G o ], m = 1, • • • , M (2.8)
where H m represents the offline fingerprints at the m th RP location and G o denotes the online signal measurements. D[H m , G o ] is the specific similarity metric between H m and G o . For instance, the Euclidean distance [START_REF] Feng | Received Signal Strength based Indoor Positioning using Compressive Sensing[END_REF], cosine similarity [START_REF] He | SectJunction: Wi-Fi Indoor Localization based on Junction of Signal Sectors[END_REF], cross correlation [START_REF] Sen | You are Facing the Mona Lisa: Spot Localization using PHY Layer Information[END_REF],

Time Reversal Resonating Strength (TRRS) [START_REF] Chen | Indoor Global Positioning System with Centimeter Accuracy using Wi-Fi[END_REF] and fuzzy logic similarity [START_REF] Wang | A Privacy-Preserving Fuzzy Localization Scheme with CSI Fingerprint[END_REF] have been prevalently implemented for the signal comparison [START_REF] Honkavirta | A Comparative Survey of WLAN Location Fingerprinting Methods[END_REF].

The major advantage of the deterministic methods is their ease of implementation. Traditional deterministic methods can be easily implemented based on k-Nearest Neighbors (kNN) and the computational complexity is often low. Some other more advanced deterministic algorithms such as Support Vector Machine (SVM) [START_REF] Wu | WLAN Location Determination in E-Home via Support Vector Classification[END_REF][START_REF] Zhou | CSI Fingerprinting with SVM Regression to Achieve Device-Free Passive Localization[END_REF] and Linear Discriminant Analysis (LDA) [START_REF] Nuño-Barrau | A New Location Estimation System for Wireless Networks based on Linear Discriminant Functions and Hidden Markov Models[END_REF] show better localization accuracy with higher computational cost. Other probabilistic algorithms such as Bayesian network [START_REF] Madigan | Bayesian Indoor Positioning Systems[END_REF][START_REF] Nandakumar | Centaur: Locating Devices in An Office Environment[END_REF], expectation maximization [START_REF] Ouyang | Indoor Location Estimation with Reduced Calibration Exploiting Unlabeled Data via Hybrid Generative/Discriminative Learning[END_REF], Kullback-Leibler Divergence (KLD) [START_REF] Mirowski | Probability Kernel Regression for WiFi Localisation[END_REF][START_REF] Chen | Probabilistic Indoor Position Determination via Channel Impulse Response[END_REF], Gaussian process [START_REF] Ferris | WiFi-SLAM using Gaussian Process Latent Variable Models[END_REF] and conditional random field [START_REF] Xiao | Lightweight Map Matching for Indoor Localisation using Conditional Random Fields[END_REF] can also achieve high localization accuracy through probabilistic inference.

Probabilistic Methods

Unlike

Moreover, for probabilistic algorithms, since each location estimation can be indicated by a confidence interval [START_REF] Jun | Social-Loc: Improving Indoor Localization with Social Sensing[END_REF], it is also amendable to fuse different sensors such as motion [START_REF] Sun | MoLoc: On Distinguishing Fingerprint Twins[END_REF] and sound [START_REF] Nandakumar | Centaur: Locating Devices in An Office Environment[END_REF]. For example, the location can be estimated by maximizing the joint probability or likelihood with the sensor measurements. However, these algorithms usually require some probabilistic assumptions (such as Gaussian noise or probabilistic independence [START_REF] Chen | Probabilistic Indoor Position Determination via Channel Impulse Response[END_REF]). Furthermore, training probabilistic models may be complicated, and require more datasets than traditional deterministic algorithms.

For our Wi-Fi based indoor positioning problem, since probabilistic algorithm embraces the wireless channel variation by inferring a probabilistic model reflected by the signal distribution, it can fully depict the location-specific information, thus capable of achieving better localization performance than its deterministic counterpart. Therefore, we only consider probabilistic based location fingerprinting schemes in this thesis.

Introduction

Location fingerprinting technique has drawn tremendous attractions in recent years due to its huge potential values for industrial and commercial applications. The design of an effective and successful indoor location fingerprinting system, which properly addresses the balancing between positioning accuracy and complexity, still remains challenging.

In this chapter, we propose EntLoc, a CSI based indoor location fingerprinting system using the structurally simple and spatially informative AR entropy fingerprint. We first revisit some related works and form a set of comparative candidates. The detailed design for each part of EntLoc will be displayed in the sequel. Moreover, we implement extensive and dedicated indoor experiments to evaluate the performance of the proposed system. Throughout this chapter, some interesting experimental observations will also be identified and discussed.

Literature Review

Prevalent Wi-Fi fingerprint localization approaches mainly exploit two types of wireless signal properties: the received signal strength and the channel response. We present related works in accordance with these two categories.

Fingerprinting via RSS: Due to the easy acquisition of wireless signal power measurements, RSS-based fingerprinting plans have been widely adopted in various mainstream indoor positioning systems. Pioneering works such as RADAR [START_REF] Bahl | RADAR: An In-building RF-based User Location and Tracking System[END_REF] carried out comprehensive site surveys for the first time and generated the RSS based fingerprint radio map.

Subsequently, the deterministic kNN algorithm was utilized to determine the target's location with an average precision of 3 meters. Contrastively, in Horus system [START_REF] Youssef | The Horus WLAN Location Determination System[END_REF], Youssef et al. resorted to the Bayes based probabilistic method and a joint clustering algorithm to achieve an accuracy improvement of 2.1 m, which outperformed RADAR even with less computational complexity. However, the instability of RSS still remains challenging.

More recently, researchers of LiFS [START_REF] Yang | Locating in Fingerprint Space: Wireless Indoor Localization with Little Human Intervention[END_REF] brought up a novel fingerprint space by utilizing the spatial relations of RSS measurements, yielding low human cost for site survey and com-petitive accuracy over RADAR. Khatab et al. [START_REF] Khatab | A Fingerprint Method for Indoor Localization using Autoencoder based Deep Extreme Learning Machine[END_REF] Fingerprinting via Channel Response: In recent years, channel response based fingerprinting approaches have attracted massive attention due to their capability of harnessing the rich multipath information indoors. The authors of FIFS [START_REF] Xiao | FIFS: Fine-grained Indoor Fingerprinting System[END_REF] explored the spatial and frequency diversity of CSI for Wi-Fi fingerprinting localization. Additionally, FIFS took the power summation for all independent subcarriers as location fingerprint and adopted Maximum A Posteriori (MAP) approach to yield an improved performance compared with RSS based Horus system. Meanwhile, for PinLoc [START_REF] Sen | You are Facing the Mona Lisa: Spot Localization using PHY Layer Information[END_REF], the whole location-aware platform was established on a set of 1m × 1m spots. The underlying observation of PinLoc was that the CSIs on a single subcarrier were illustrated to be clustered distributed on the complex plane. The Gaussian mixture distribution was then introduced to properly model the channel measurements for the purpose of accurate localization. Experimental result validated PinLoc's impressive performance with an 89% mean accuracy for 100 spots. Furthermore, when it comes to the time domain CIR, authors in [START_REF] Jin | Indoor Localization with Channel Impulse Response based Fingerprint and Nonparametric Regression[END_REF] proposed to exploit the amplitude of CIR (ACIR) vector to accomplish location estimation through nonparametric kernel regression scheme. Simulation results showed a distinguished performance superiority over the traditional RSS based fingerprinting methods.

Contributions

In summary, our main contributions of this chapter are set out below:

• As far as we are aware of, this is the first work to statistically study AR modeling based entropy signature in CSI fingerprint localization system. This simple fingerprint structure helps decrease the pattern-matching complexity and its informative statistical embodiment also facilitates the location estimation accuracy.

• We propose a power based pre-processing filtering scheme to mitigate the irrelevant noisy component in CSI measurements, thus further improving the location fingerprinting performance.

• We implement extensive positioning experiments on the lightweight HummingBoard Pro device, which remarkably enhances the experimental efficiency.

Chapter Organization

The rest of this chapter is organized as follows. In Section 3.2, we elaborate the overall architecture design of our proposed EntLoc localization system along with detailed methodology. We present the realistic experimental setup and provide the experimental results in Section 3.3. Conclusions are drawn in Section 3.4.

Localization Methodology

In this section, we focus on the overall introduction of our proposed EntLoc positioning system, whose theoretical methodology will be revealed in a divide-and-conquer manner.

EntLoc System Architecture

The overall architecture of the proposed system is illustrated in Figure 3.1. In general, it consists of two major functionality components: the offline fingerprint radio map construction and the online target's position estimation. For CSI fingerprint database construction, once getting the received raw CFR packets through signal war-driving, we first employ a tap filtering based pre-processing scheme to extract the most informative and location-dependent components in the multipath-rich indoor scenario. Subsequently, we model the statistical features of filtered CFR amplitude by calculating an AR modeling based entropy metric and then build a representative fingerprint radio map after removing the ambiguous endpoint subcarriers. Afterwards, for online location estimation process, when a mobile target arrives into the area of interest, it executes the same procedures to acquire the entropy vector and matches against the learned offline attributes. Finally, the simple Manhattan distance based kernel regression approach can be fully leveraged to accomplish the physical position estimation of the mobile target. In what follows, we will dissect each component of the proposed system in a divideand-conquer manner.

Offline Radio Map Construction

First of all, we start to elaborate our location fingerprinting methodology with the presentation of the problem formulation. In the offline phase, M reference points are predefined and properly marked in the area of interest.

H s m = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ H s m (1, 1) • • • H s m (1, r) • • • H s m (1, R) . . . . . . . . . . . . . . . H s m (n, 1) • • • H s m (n, r) • • • H s m (n, R) . . . . . . . . . . . . . . . H s m (N , 1) • • • H s m (N , r) • • • H s m (N , R) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (3.1)
where

n ∈ [1, N ] and r ∈ [1, R].
During the online stage, the mobile user at an unknown position ℓ o = (x o , y o ) records the same structural CSI matrix from the s th AP. We denote this matrix as G s o , which also shares the same dimension with H s m . Likewise, the online measured CSI signature at the location ℓ o can be expressed by the set G o = {G 1 o , . . . , G s o , . . . , G S o }. Accordingly, the mobile user's location can be then estimated as lo = (x o , ŷo ) by exploiting these online CSIs and the stored offline database.

Tap Filtering Preprocessing Technique

Recall that channel state information completely characterizes the multipath channel and preserves the fine location dependency, which makes it a good choice for location fingerprint. However, it would be fair to state that for the existing Wi-Fi networks, bandwidth limitation introduces severe location ambiguity which leads to limited localization accuracy [START_REF] Chen | Achieving Centimeter-Accuracy Indoor Localization on WiFi Platforms: A Multi-antenna Approach[END_REF]. By using the commodity Wi-Fi with center frequency of 2.4 GHz, the bandwidth of the system is therefore 20 MHz in this case. Since CFR can be converted into CIR via inverse fast Fourier transform, an estimation of CIR with time resolution of 1/20MHz =50 ns is exposed. Since typical indoor maximum excess delay τ max is smaller than 500 ns [START_REF] Zhou | WiFi-based Indoor Line-of-Sight Identification[END_REF], given a time resolution of 50 ns, approximately only the first 10 out of Hence, based on the system bandwidth, a reasonable number of relevant time samples should be chosen for the sake of computation efficiency and accuracy. In this research, we design a power-based tap filtering method to preserve the most informative channel features for fingerprinting. Specifically, for the conciseness of expression, we define the individual raw CFR signature as H ∈ C 1×K . Through IFFT, we first convert H into the same dimensional CIR vector h. For each 1 × K CIR packet, we calculate the average channel power for each time tap, denoted by U = (u 1 , . . . , u k , . . . , u K ), k ∈ [1, K], where u k = |h k | 2 and h k denotes the k th complex tap value of one CIR packet. Then, we define a cumulative contribution rate of the first k taps as

C k = k ∑ i=1 u i / K ∑ i=1 u i . ( 3

AR Entropy Estimation

As aforementioned in Chapter 2, probabilistic positioning algorithms analytically outperform their deterministic counterparts. Additionally, numerous literature [START_REF] Youssef | The Horus WLAN Location Determination System[END_REF][START_REF] Xiao | FIFS: Fine-grained Indoor Fingerprinting System[END_REF][START_REF] Shi | Accurate Location Tracking from CSI-based Passive Device-free Probabilistic Fingerprinting[END_REF] further reveal such superior localization performance of the probabilistic algorithms over their deterministic rivals in the complex indoor environment. Generic probabilistic methods include the Bayesian network [START_REF] Nandakumar | Centaur: Locating Devices in An Office Environment[END_REF], KLD [START_REF] Mirowski | Probability Kernel Regression for WiFi Localisation[END_REF][START_REF] Chen | Probabilistic Indoor Position Determination via Channel Impulse Response[END_REF], Gaussian process [START_REF] Homayounvala | A Novel Smartphone Application for Indoor Positioning of Users based on Machine Learning[END_REF], etc.. The essential cause resides in the fact that PDF contains the complete statistical characterizations of the complex random variables, which are capable of providing better location-specific RF signatures.

The simplest probabilistic model for CFR is based on the assumption that there are a large number of statistically independent reflected and scattered paths with random amplitudes corresponding to a single subcarrier. By the central limit theorem, it can be reasonably modeled as circularly-symmetric Gaussian (complex Gaussian) random variables [START_REF] Goldsmith | Wireless Communications[END_REF]. Thus, the amplitudes of the complex Gaussian process are essentially Rayleigh distributed. If the channel has a fixed LoS component, the received signal then equals the superposition of a complex Gaussian component and this LoS component. In this case, the CFR amplitude follows the Rician distribution. However, due to the sophisticated indoor environment and the imperfection of wireless devices, most measured CFR values are non-Gaussian distributed or even do not fit any known distribution [START_REF] Sen | You are Facing the Mona Lisa: Spot Localization using PHY Layer Information[END_REF][START_REF] Alsindi | An Empirical Evaluation of A Probabilistic RF Signature for WLAN Location Fingerprinting[END_REF][START_REF] Wang | BiLoc: Bi-modal Deep Learning for Indoor Localization with Commodity 5GHz WiFi[END_REF]. Meanwhile, for multivariate fingerprint structure (e.g., multi-subcarrier CFR in our case), existing statistical tools only work under the condition of identifiably distributed measurements [START_REF] Chen | Probabilistic Indoor Position Determination via Channel Impulse Response[END_REF].

Besides, most probabilistic approaches require sufficient number of measurements stored in the fingerprint database, which guarantees an accurate PDF estimation but suffers huge system burden.

Therefore, in this thesis, we resort to the well-known Shannon entropy [START_REF] Cover | Elements of Information Theory[END_REF] as the fingerprint alternative in our localization system. Given the offline and online CFR amplitude PDF estimates pH s m (β; r) and pG s o (β; r), both of which are from the r th subcarrier and the s th AP. For the simplicity of presentation, here we define β as a general expression of CFR amplitude from the same subcarrier. Thus, the offline entropy definition can be expressed by φr

H s m = - ∫ ∞ -∞ pH s m (β; r) log pH s m (β; r)dβ (3.3)
Similarly, the online CFR entropy φr G s o can also be calculated as the fingerprint for the subsequent stage of target's location determination.

In practice, it is a challenging task to implement direct evaluation of the Shannon entropy from real data [START_REF] Kay | Fundamentals of Statistical Signal Processing[END_REF][START_REF] Bercher | Estimating the Entropy of A Signal with Applications[END_REF]. The reason behind this dilemma is twofold:

(i) Entropy has to be approximated from the mere sample data due to the fact that probability density function is generally unknown.

(ii) Equation (3.3) requires numerical integration since a closed-form solution of the entropy does not exist.

Typical data-adaptive PDF estimation methods comprise histogram estimator [START_REF] Moddemeijer | On Estimation of Entropy and Mutual Information of Continuous Distributions[END_REF], order statistics [START_REF] Correa | A New Estimator of Entropy[END_REF] or kernel method (a.k.a. Parzen method) [START_REF] Parzen | On Estimation of A Probability Density Function and Mode[END_REF]. However, all of them share the major drawback of slow convergence rate.

In this thesis, we address the entropy estimation problem by leveraging the more accurate and consistent Autoregressive (AR) modeling approach [START_REF] Kay | Fundamentals of Statistical Signal Processing: Practical Algorithm Development[END_REF]. The basic principle of this approach is to estimate the unknown PDF in the form of Power Spectral Density (PSD) of an unit variance AR process. This unit variance condition ensures that PSD shares the basic requirements of PDF (i.e., positive function that integrates to one).

Given the general expression of amplitude β, we define the input CFR amplitudes from one certain subcarrier as

β I = [β(1), • • • , β(n), • • • , β(N )] ⊤ ,
where N is the number of CFR packets and (•) ⊤ is the transpose operator. Since the law is modeled as the spectrum restriction on the interval of [-0.5, +0.5], the amplitude data have to be first rescaled on this interval. Meanwhile, an order p AR process W (n) is defined as the output of an all-poles filter driven by a white noise ϵ(n) with variance δ 2 ϵ . It can be mathematically denoted as [START_REF] Kay | Fundamentals of Statistical Signal Processing: Practical Algorithm Development[END_REF]

W (n) = p ∑ i=1 a i W (n -i) + ϵ(n). (3.4)
where a = {a i } 1≤i≤p are the AR model parameters.

Since the CFR amplitude PDF p(β) can be equivalently depicted by the PSD S W (β) of this AR process which is parameterized by a set of AR parameters, the entire relations can be then presented as [START_REF] Kay | Model-based Probability Density Function Estimation[END_REF] p

(β) = S W (β) = σ 2 ϵ |1 + ∑ p i=1 a i e -j2πiβ | 2 , β ∈ [-0.5, 0.5] (3.5)
where σ 2 ϵ is the model prediction error which is chosen so that

∫ 0.5 -0.5 S W (β)dβ = 1.
It is notable that AR model order needs to be chosen appropriately at first since a low order leads to inadequate resolution (estimator bias) while a high order incurs spurious peaks (excessive variance). Through extensive experiments, a well-run model order selection technique known as the Exponentially Embedded Family (EEF) [START_REF] Kay | Exponentially Embedded Families-New Approaches to Model Order Estimation[END_REF] is adopted to select a proper p which maximizes the following criterion.

F(p) = { ξ p -p(log( ξp p ) + 1), if ξ p ≥ p 0, otherwise (3.6)
Here ξ p is the Generalized Likelihood Ratio Test (GLRT) statistic which can be asymptotically computed as

ξ p = (N -p) log ⎛ ⎜ ⎝ λ ⊤ p λ p λ ⊤ p (I -Λ p ( Λ ⊤ p Λ p ) -1 Λ ⊤ p )λ p ⎞ ⎟ ⎠ (3.7)
where

λ p = [β(p + 1), β(p + 2), • • • , β(N )] ⊤ and Λ p = [λ p-1 , λ p-2 , • • • , λ 0 ]
. The detailed procedures are explicitly described in Algorithm 1.

Thereby, the succeeding task of estimating the AR parameters consists of two major steps [START_REF] Kay | Model-based Probability Density Function Estimation[END_REF]:

(i) We first estimate the autocorrelation function of the CFR amplitude data sequence β I by applying the sample moment estimator, which is the statistical average correlation estimate:

R W (i) = 1 N N ∑ n=1 e j2πiβ(n) , i ∈ [0, p] ( 3
if ξ i ≥ i then 5:
Obtain Make F(i) be zero;

F(i) = ξ i -i(log( ξ i i ) + 1)
8:
end if 9: end for 10: Execute p = arg max i∈ [1,pmax] F(i); 11: Return p;

(ii) AR coefficient estimation is then achieved by solving the Yule-Walker equations using the Levinson-Durbin recursion [START_REF] Yule | On a Method of Investigating Periodicities Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers[END_REF][START_REF] Walker | On Periodicity in Series of Related Terms[END_REF]:

R W a = -r W (0) (3.9)
where

R W = [r W (1), r W (2), • • • , r W (p)] and r W (i) = [R W (1-i), R W (2-i), • • • , R W (p- i)] ⊤ . Once the AR parameters have been estimated, say â = [â 1 , â2 , • • • , âp ] ⊤ , the
AR model prediction error can be then computed by

σ2 ϵ = R W (0) + p ∑ i=1 âi R W (-i) (3.10)
When AR PSD is determined, according to (3.5), the entropy estimation can be then converted to the following form: Additionally, a more feasible closed-form expression without any numerical integration can be obtained by applying Plancherel-Parseval formula to the right hand side of Equation (3.11) [START_REF] Bercher | Estimating the Entropy of A Signal with Applications[END_REF] and yielding

φβ = - ∞ ∑ i=-∞ R W (i)Z * W (i) (3.12)
where (•) * is the conjugate operator and Z W (i) denotes the i th component of the AR process's cepstrum, which can be calculated by proceeding the inverse Fourier transform of log ŜW (β). The whole entropy estimation process can be presented in Algorithm 2.

Endpoint Subcarrier Removal

In this part, we continue to exploit the AR modeling based entropy and shed light on some interesting observations in the sequel.

For location fingerprinting, the spatial resolvability is a key performance indicator for the proposed location fingerprint. In order to validate such property of our AR entropybased fingerprint, a simple test was taken in our lab corridor. Concretely, we linearly selected 15 sample locations with 1m spacing. A RF transmitter was placed at one end of the corridor, sending wireless packets continuously. In the meantime, we moved a mobile receiver in sequence at these sample locations. Around 500 CFR measurements were collected at each location. After calculating the AR entropies of all subcarriers at each position, we applied confusion matrix to portray the entropy differences among these 15 locations for each CFR subcarrier. In Location Index Location Index Given that this is only a visual indication, we then utilize the statistical Cumulative Distribution Function (CDF) to carefully study the behavior of these entropy differences.

As depicted in Figure 3.9, most subcarriers display an obvious entropy differences for different locations while the endpoint subcarrier #1 and #30 still show the opposite, inducing potential location differentiation errors in the next online pattern-matching stage. Therefore, we propose in this work to remove the two null endpoint subcarriers from the estimated AR entropies, which also serves as a dimension reduction strategy to further improve the execution efficiency of our AR entropy approach. Recall that we combine the CFR measurements of the total R subcarriers from all N r receiving antennas, the estimated AR entropy fingerprint in the offline stage can be hereby represented as

ΦH s m = [ φ1 H s m , . . . , φr ′ H s m , . . . , φR ′ H s m ], r ′ ∈ [1, R ′ ] (3.13)
where R ′ = R -2 • N r is the reduced number of subcarriers in this case. Likewise, the online estimated AR entropy is denoted by

ΦG s o = [ φ1 G s o , . . . , φr ′ G s o , . . . , φR ′ G s o ], r ′ ∈ [1, R ′ ].

Online Location Estimation

As the final task of EntLoc, the online location estimation consists of two functional part: the distance based proximity comparison and the kernel regression based location inference. We lay out the details of both parts in the following.

Distance-based Proximity Comparison

For the online location determination, the mobile target is required to be accurately mapped to the pre-designed radio map. To quantitatively measure the similarity between the stored entropy fingerprints and the estimated online CFR entropies, we employ Manhattan distance [START_REF] Krause | Taxicab Geometry: An Adventure in Non-Euclidean Geometry[END_REF] which is also known as taxicab metric, capable of measuring the gap between two points through the summation of the absolute differences of their corresponding components.

Given the offline and online entropy fingerprints ΦH s m and ΦG s o , we define the Manhattan distance between them as

D s m = ∥ ΦH s m -ΦG s o ∥ 1 = R ′ ∑ i=1 ⏐ ⏐ ⏐ φi H s m -φi G s o ⏐ ⏐ ⏐ (3.14)
where ∥ • ∥ 1 denotes the ℓ 1 norm. It concisely reveals the physical similarity between the online fingerprints at an unknown position and the offline dataset at the m th RP location, both of which are measured from the s th AP. Moreover, by using the chain rule for Shannon entropy [START_REF] Cover | Elements of Information Theory[END_REF], it can be proved that the Manhattan distance of a joint entropy of independent variables is equal to the sum of the distance for each variable's entropy.

Under S independent AP assumption, we therefore have the Manhattan distance for all available APs as follows.

D m = S ∑ s=1 D s m (3.15)

Kernel Regression

In order to properly obtain the location estimation of the target, the weighted kernel regression is further adopted by employing the distance based kernel function K and the whole set of known reference points [START_REF] Chen | Probabilistic Indoor Position Determination via Channel Impulse Response[END_REF]. The estimated location can be derived from the following equation.

lo = ∑ M m=1 K m ℓ m ∑ M m=1 K m (3.16)
Here K m is defined as the probability kernel of the m th RP position by exponentiating its corresponding Manhattan distance, which is presented as follows:

K m = exp(-ρD m ) (3.17)
where ρ is the kernel coefficient which is determined to optimally minimize the fingerprinting error by leave-one-out cross-validation in the offline phase [START_REF] Mirowski | Probability Kernel Regression for WiFi Localisation[END_REF]. The performance of aforementioned fingerprinting approaches will be evaluated in the follow-up section.

Performance Evaluation

In this section, we present the experimental evaluation of our proposed localization system.

First of all, we start by introducing the experimental setup and the detailed implementation methodology. Then, the results of localization performance will be discussed in the sequel.

Experimental Setup

Benchmarks and Performance Metrics

In this part, we evaluate three existing probabilistic fingerprint positioning systems for the comparison purpose. As discussed in the literature review section, these include Horus [START_REF] Youssef | The Horus WLAN Location Determination System[END_REF], FIFS [START_REF] Xiao | FIFS: Fine-grained Indoor Fingerprinting System[END_REF] and PinLoc [START_REF] Sen | You are Facing the Mona Lisa: Spot Localization using PHY Layer Information[END_REF]. Considering that the original PinLoc system conducted war-driving procedure in a set of predefined 1m × 1m grids, known as spots, in order to provide a fair comparison, we modify PinLoc to use the same training set that we use in the proposed EntLoc system.

As for performance metrics, we define the localization error as Euclidean distance between the estimated location and the mobile user's actual position, which is presented

as ∥ lo -ℓ o ∥ = √ (x o -x o ) 2 + (ŷ o -y o ) 2 .
When there are N a testing locations, we evaluate the localization performance by using Mean Error (ME) metric which can be calculated as

M E = 1 N a Na ∑ i=1 √ (x i -x i ) 2 + (ŷ i -y i ) 2 (3.18)
where (x i , y i ) and (x i , ŷi ) are the actual and estimated coordinates at the i th testing location, respectively.

Numerical Results

In this section, we evaluate the experimental performance and provide numerical results with relevant discussions.

AR Entropy Property Study

Since AR modeling based CFR amplitude entropy is the cornerstone of our fingerprint localization system, prior to accuracy analysis, we first evaluate the following two key characteristics of our proposed AR entropy fingerprint in location fingerprinting.

Temporal Stability Practically, the channel response fluctuate frequently as the indoor environment varies over time. To investigate the robustness of our AR entropy based fingerprinting system, we design and implement a daytime measurement test in our lab.

Specifically, the HummingBoard Pro was configured to periodically record CFR measurements at a fixed position from a transmitter placed in the next-door room from 9 a.m. to 5 p.m. during a busy working day. About 500 CFR packets were collected every 10 minutes. Indoor furniture remained static with several personnel in the vicinity moving around. Next, we divide the whole measurements into 100 groups and compute the AR entropy, averaged CFR amplitude and the corresponding RSS mean value, respectively.

For the purpose of fair comparison, we normalize the three metrics in the same range. As shown in Figure 3.15, our AR entropy based fingerprint displays the lowest variance while the coarse-grained MAC layer RSS suffers the most severe fluctuations. It is reasonable that the environment changes do impact the time-varying channel response but cause less influence over its statistical entropy derivate. Spatial Proximity For indoor fingerprinting localization system, a good online signature is deemed to be qualified when it is capable of presenting similar trait with the offline signatures from the neighboring reference points. Based on the realistic testbed shown in the fingerprints in the vicinity. For most subcarrier indices, the entropy value fits well in the center of its four neighbors. Especially for NLoS test location #2 in Figure 3.17, even though the neighboring entropies are relatively inconsistent (differ from different RX antennas), the overall multi-dimensional entropies at the center location can still capture the local minimal differences (Manhattan distance in our case) from its neighbors. This robust spatial property enables our AR modeling based entropy to be a strong candidate as fingerprint for most existing indoor positioning systems.

Localization Accuracy

This section provides a variety of numerical results in respect of localization accuracy, which firmly validates the superiority of our proposed localization system over other indoor geolocation schemes. Comparison with CFR We begin the localization accuracy evaluation by comparing our proposed AR entropy fingerprint with its original CFR amplitude. It is worth mentioning that these two fingerprint schemes follow the same online protocol (i.e., using Manhattan distance as similarity metric and kernel regression to figure out user location).

Figure 3.18 shows the CDF of localization errors for AR based entropy fingerprint and its original CFR amplitude. Specifically, our AR entropy approach shows a better performance with 90% positioning errors less than 2.69m while CFR amplitude signature can only reach the level of 50th percentile. The 1.84m ME of our proposed entropy scheme also precedes CFR amplitude based method whose mean sum error rises to 2.92m. Since AR modeling based entropy accurately reflects the statistical distribution of the given CFR amplitudes, which unfortunately endure much more channel fluctuations, it can thus achieve better localization performance. Comparison with CIR Given that CIR is the inverse Fourier version of CFR, both of them should convey equivalent physical information. One may anticipate similar localization performance for these two channel response signatures. However, as shown in Figure 3.19, our AR entropy based scheme maintains less than 2.69 meters localization error with the probability of 0.9, which outperforms CIR amplitude based entropy with only 63% percentage of the same positioning error. Meanwhile, the mean error of the proposed CFR amplitude entropy scheme is 1.84m, which is also superior over CIR entropy approach with the mean error of 2.64m. A possible explanation would be that most variations of CIR distribute within only a few time indices (i.e., first 10 taps), while the frequency diversity spans the entire range of CFR subcarrier indices, making the structures of CFR more distinguishable with each other [START_REF] Yang | From RSSI to CSI: Indoor Localization via Channel Response[END_REF]. Moreover, as expected, CIR entropy based fingerprint has better location estimation precision than its original CIR amplitude signature. The former precedes around 1.2m localization error of the 90th percentile accuracy. Comparison with State-of-the-Art After comparing with the two most potential competitors, namely CFR and CIR amplitude schemes, our EntLoc system is then readily set to challenge other existing location fingerprinting systems. More specifically, as mentioned in previous section, we design a fair framework to compare our proposed AR entropy based localization approach with PinLoc-like, FIFS and Horus systems, respectively. As can be observed in Figure 3.20, our proposed system achieves the 90th percentile error of 2.69m, which outperforms PinLoc-like approach, FIFS and Horus with the same error level of 63%, 57% and 28%, respectively.

Additionally, in order to provide an in-depth and comprehensive comparison for these localization systems, we enumerate the respective maximum error (Max. err.), minimum error (Min. err.), mean error (Mean err.) and the 90th percentile accuracy (Acc. at 90%) in Table 3.1. Apart from the 90th percentile accuracy, our EntLoc system is able to achieve the lowest mean error of 1.84m compared with PinLoc-like, FIFS and Horus systems, improving the localization precision by 27.3%, 34.9% and 47.4%, respectively.

As for maximum and minimum errors, EntLoc can still dominate the general accuracy evaluation. It only falls behind FIFS with 0.08m in terms of minimum error, which can be neglected in realistic indoor environment.

Impact of Preprocessing Technique

Recall that we present a tap filtering based pre-processing technique before conducting Subcarrier Index for one RX Antenna Subcarrier Index for one RX Antenna To this end, we design a fingerprint robustness based evaluation scheme. In particular, we manually record 10000 raw CFR measurements at one predefined location. By taking into account three RX antennas, we divide these CFRs into 100 subgroups and calculate the AR entropy of their amplitudes for each subgroup. Afterwards, we conduct the same procedures on the filtered CFR measurements and lay out the differences. As displayed in Figure 3. Furthermore, we can also observe from Figure 3.23 that for considering all three RX antennas, the filtered CFR entropy has an overall lower variance than its original raw CFRs. The above observations reveal that our pre-processing technique makes AR entropy based fingerprint more robust and can thus guarantee a preferable localization performance in the online location estimation phase.

Impact of Packet Number for Entropy Estimation

Since AR entropy estimation process requires sufficient CFR samples, larger number of samples can provide more accurate entropy estimation while increasing computational complexity. How to determinate the CFR packet number for entropy calculation becomes a trade-off problem which needs to be balanced in our localization system. Here we devise an AR entropy variance based scheme to select the optimal number of CFR packets. The motive lies in the fact that if the entropy variance is small enough, which can already guarantee a good accuracy, there is no need to import more CFR samples to increase computational burden. To be more specific, by testing the packet number ranging from 10 to 5000, we observe in Figure 3.24 that 50 CFR packets can provide stable enough AR entropy estimates, which can further promote robust fingerprinting performance. So we choose and fix this packet number for all entropy estimation processes in our indoor positioning implementations.

Impact of RX Antenna Numbers

In this part, we study the impact of RX antenna number on the localization performance. Intuitively, using more antennas at receiver end brings about more diverse channel response measurements, thus containing more location-specific information. We then study the localization accuracy differences for three RX antennas to deepen the understanding of our proposed localization system. As exhibited in Figure 3.25, our AR entropy based localization system with three RX antennas is able to obtain superior estimation error precision over the same platforms with less antennas. Numerically, the three-antenna configuration can achieve less than 2.69m localization error within the probability of 0.9, while the two and single antenna structures can only reach the same percentage level with the larger error of 4.1m and 5.2m, respectively. It validates the aforementioned assumption and encourages us to make full use of all three RX antennas in our indoor location fingerprinting system.

Introduction

As an updated version of the previous EntLoc system, in this chapter, we bring out AngLoc, an enhanced AR entropy based indoor location fingerprinting system involving an additional AoA fingerprint. The resulting localization accuracy has been elevated in comparison with EntLoc.

Likewise, after reviewing the state-of-the-art, we put forward the in-depth localization methodology of proposed AngLoc. We also add more experimental testbeds for the performance evaluation and provide some visionary perspectives in order to further improve AngLoc's localization performance in the future works.

State-of-the-Art

Since the biggest design highlight of the AngLoc localization system is that the geometric concept of AoA-aware directional RP refining further enhances the positioning accuracy. We ought to involve some geometric mapping based techniques in the state-ofthe-art presentation. Additionally, given that we have conducted comprehensive literature review of the current location fingerprinting schemes in Chapter 3, in this chapter, we will further supplement some recent advancements to the current literature framework.

Geometric Mapping based

Contributions

Prior to listing the relevant contributions of this chapter, in comparison with the aforementioned EntLoc system, we first elaborate the core concept and the major upgrade of our proposed AngLoc positioning system. (i) For some offline surveying receivers at the corresponding RP positions, whether they are in the vicinity (blue ones) of the online receiver (red one) or in the distance (green one), their CSI measurements may share the similar entropy values.

(ii) These neighboring receivers also record the similar AoAs from parallel incident paths with this online receiver, whether it is for direct paths in LoS scenario or reflected paths in NLoS condition. Hence, the remote receiver can be selectively ruled out in accordance with the distinct AoA difference, which further improves the location estimation accuracy.

Accordingly, by adopting the above AoA aided RP refining approach, our inherited AngLoc positioning system is capable of achieving superior localization performance over its predecessor EntLoc system.

In a nutshell, the main contributions of this chapter can be laid out as follows:

• To the best of our knowledge, this is the first work to constructively incorporate angular signature in CSI entropy based indoor location fingerprinting system, fertilizing the opportunity to achieve a decimeter-level accuracy.

• We propose a power-based tap-filtering program alongside several phase calibration pre-processing techniques to effectively mitigate CSI noisy component and sanitize CSI phase errors, respectively.

• We design a feasible bivariate kernel regression scheme for the online location estimation stage, which organically combines the weighting factors for both amplitude based entropy and phase-based AoA fingerprints.

• Compared with EntLoc's performance evaluation, we further build and implement extensive experiments on the lightweight Hummingboard device for different testbeds.

In addition to the superior performance, our mobile prototype remarkably enhances the fingerprinting efficiency.

Chapter Organization

The remainder of this chapter is organized as follows. The overall architecture design of our proposed system is elaborated in Section 4.2. We provide experimental results and the corresponding analyses in Section 4.3 and dive into some insightful perspectives in Section 4.4. Conclusions are drawn in Section 4.5.

Localization Methodology

In this section, we proceed to lay out the detailed design of our proposed AngLoc fingerprint localization system.

AngLoc System Architecture

As illustrated in Figure 4.2, the overall architecture of our proposed AngLoc system has a block-wise design. To be specific, in the offline radio map construction block, once recording the raw CSI measurements through war-driving, we first introduce a tap filtering scheme to extract the most informative location-specific component from noisy CSIs.

For the purpose of accurate AoA estimation, several phase calibration techniques are then leveraged to compensate the corresponding phase offsets, which exist in prevalent commodity WiFi devices. Subsequently, for CSI amplitudes, we statistically model them as the simply structural AR entropy metric. The JADE-MUSIC algorithm is then adopted for CSI phases to infer the angular estimates. Hence, the entire offline database can be fully embodied by the integration of entropy and AoA fingerprints, making full use of both CSI amplitude and phase information. For the online location estimation block, when a mobile target enters the area of interest, it executes the same pre-processing protocols to obtain the entropy and AoA estimates. The following location estimation task then consists of two major steps: (i) The online entropy vector is first matched with offline database to find the most likely candidates from nearest RP positions.

(ii) Among these candidate locations, a novel bivariate kernel regression scheme is proposed to further narrow down the number of error-prone RPs, thus tackling the target's location determination with an improved accuracy.

In the sequel, we will take an in-depth structural dissection for each block of our proposed AngLoc system.

Offline Fingerprint Database Generation

For the offline training phase, we adopt the same problem formulation as presented in Chapter 3. Specifically, after acquiring the respective offline and online fingerprint data sets {H m } 1≤m≤M and G o , the mobile target's position can be then determined as lo by exploiting these online CSIs and the stored offline database.

CSI Phase Calibration

In this part, we focus on some technical details of CSI pre-processing techniques which serve as the precondition to attain superior localization performance.

Due to the inherent OFDM baseband operations and the hardware's imperfect signal processing, the CSI obtained from the commodity Wi-Fi devices is distorted with various errors [START_REF] Tadayon | Decimeter Ranging with Channel State Information[END_REF][START_REF] Ma | WiFi Sensing with Channel State Information: A Survey[END_REF][START_REF] Zhuo | Perceiving Accurate CSI Phases with Commodity WiFi Devices[END_REF], rendering the accurate AoA and ToF estimation much more challenging. For a transmission chain, the phase measurement ∠ Ĥf k for subcarrier k with carrier frequency f k can be presented as

∠ Ĥf k = ∠H f k + 2πf δ k(ζ csd + ξ sfo ) + φ sto + φ cfo + φ cpo + Z (4.1)
where ∠H f k denotes the true phase from wireless propagation. f δ is the OFDM subcarrier spacing. ζ csd , ξ sfo , φ sto , φ cfo and φ cpo are the phase errors caused by Cyclic Shift Diversity (CSD), Sampling Frequency Offset (SFO), Symbol Timing Offset (STO), Carrier

Frequency Offset (CFO) and Carrier Phase Offset (CPO), respectively. Z signifies the additive measurement noise. In the following, we will address these deep-rooted CSI phase issues in a divide-and-conquer manner.

• CSD: As described in Chapter 2, CSD is operated by sending cyclically shifted OFDM symbols over different TX antennas so that unintended beamforming is avoided.

But this incurs an additive phase shift for each TX antenna in CSI matrix which potentially degrades the localization performance. SignFi [START_REF] Ma | SignFi: Sign Language Recognition using WiFi[END_REF] compensated the CSD errors by applying a multiple linear regression scheme. However, as a easier alternative suggested in [START_REF] Tadayon | Decimeter Ranging with Channel State Information[END_REF], CSD can always be removed by the receiver when direct mapping takes place, under which the SMM equals an unitary matrix. Hence, in our data acquisition process, we can configure the Intel 5300 shipset to make N ss = N t , thus yielding the CSD-free CSIs.

• SFO: In OFDM transceiver system, SFO occurs when the receiver's ADC sampling rate differs from the transmitter's synthesization rate. Consequently, SFO manifests itself as an additive phase shift proportional to the subcarrier index, which gives rise to the first-order channel linearity (e.g. Figure 4.3). We then resort to a simple linear regression method to remove the residual SFO. It can be mathematically expressed as follows. of the shifted PDP peak due to STO can be identified as

N sto (n) = arg max k |h k (n)| 2 , 1 < k ≤ K (4.3)
After applying (4.3) for multiple packets, the most frequent value of N sto is then determined to finally shape the estimated STO as φsto = -2πkN sto /K.

• CFO/CPO: Due to the residual errors in receiver's Phase Locked Loop (PLL), CFO emerges when the receiver's carrier frequency for down-conversion mismatches with the transmitted carrier frequency. Meanwhile, since each time when the synthesizer restarts, a random initial phase will be generated by the receiver's voltage controlled oscillator and PLL cannot fully compensate for this phase difference, CPO is then experienced. According to [START_REF] Tadayon | Decimeter Ranging with Channel State Information[END_REF], after the PDP-based STO removal, the ToF estimation becomes naturally immune to CPO. Additionally, during our site survey, we only initiate the transceiver devices for once, which makes CPO negligible in our fingerprinting system. As CFO is also an accumulative error that has to be compensated by the receiver, we then employ a non-overlapping moving window with length N p for geometric averaging to further smooth out CFO. Specifically, we first obtain K-dimensional H by conducting element-wise multiplication for N p packets.

H = H(1) • • • • H(n p ) • • • H(N p ), n p ∈ [1, N p ] ( 4

Enhanced AoA Fingerprint Estimation

After the noise removal and phase sanitization, the pre-processed CSIs then proceed readily to establish a self-contained fingerprint database which involves both amplitude and phase information.

For considerable wireless location-aware applications, accurate AoA measurement is non-trivial on commodity devices. In view of the super-resolution advantage, the classical subspace-based MUSIC algorithm is of the greatest appeal. The basic idea of standard MUSIC algorithm is that incident signals from different bearings give rise to different phase changes on each antenna at the receiver [START_REF] Schmidt | Multiple Emitter Location and Signal Parameter Estimation[END_REF].

Assume that there are L incoming signals γ 1 , . . . , γ L arriving from directions θ 1 , . . . , θ L at N r RX antennas of a linear array. The RX antennas are evenly-spaced with a distance d, which is about half of the signal's wavelength. As shown in Figure 4.5, for the l th signal (l ∈ [1, L]), a phase difference of -2πf dsin(θ l )/c is introduced at two adjacent antennas, where f is the signal frequency and c denotes the speed of light. For the whole antenna array, we can thereby define these phase shifts relative to the first antenna as the following where W is the noise vector.

Note that there is an inherent constraint when applying the conventional MUSIC algorithm to Equation (4.6), which requires array antennas should outnumber the resolvable incident multipaths (i.e. N r > L). However, in typical indoor environments, there are about 5-10 dominant multipath clusters [START_REF] Czink | Number of Multipath Clusters in Indoor MIMO Propagation Environments[END_REF] while our commodity Intel 5300 NIC only supports up to N r = 3 antennas. This means it can merely capture 2 incident paths through MUSIC, thus largely limiting the AoA resolution and severely deteriorating the fidelity of the MUSIC outcome. To overcome this bottleneck, we leverage the fact that alongside AoA-related phase shifts across physical antennas, the incoming signals also invite phase differences across equispaced OFDM subcarriers due to ToF [START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF][START_REF] Vanderveen | Joint Angle and Delay Estimation (JADE) for Multipath Signals Arriving at An Antenna Array[END_REF]. Therefore, we further extend the N r -antenna physical array to a virtual sensor array with the size of K • N r , by which JADE-MUSIC algorithm can be readily employed to exploit CSI phase information in two dimensions. Specifically, the second steering vector which contains phase shifts relative to the first subcarrier can be defined as follows.

Ω(τ l ) = [1, e -j2πf δ τ l , . . . , e -j2π(K-1)

f δ τ l ] ⊤ (4.7)
where τ l is the time delay of the l th path and f δ is the two adjacent subcarrier spacing.

Accordingly, the combined AoA-ToF steering vector can be updated by

a(θ l , τ l ) = Ψ(θ l ) ⊗ Ω(τ l ) (4.8)
where ⊗ denotes the Kronecker product. After aggregating all L signal multipaths, the corresponding KN r × L steering matrix is thereby presented as

A = [a(θ 1 , τ 1 ), . . . , a(θ l , τ l ), . . . , a(θ L , τ L )] (4.9)
Hence, the received signals at RX antennas in Equation (4.6) can be rewritten by X = AΓ + W (4.10)

Next, we then move to apply JADE-MUSIC by first deriving the covariance matrix R X of the received signal, which is calculated as

R X = E{ X XH } = AR S A H + σ 2 W I (4.11)
where (•) H and E{•} demotes the Hermitian transpose and expectation operator, respectively. R S is the noise-free covariance matrix of the complex signal vector and σ 2 W indicates the noise variance. Among K • N r eigenvalues of R X , the smallest (KN r -L) eigenvalues represent the noise and the remaining L eigenvalues correspond to L incident signals. The eigenvectors corresponding to these smallest eigenvalues then form the noise subspace E N .

Since the signal subspace and noise subspace are orthogonal, the spatial pseudo-spectrum function can be expressed as follows.

P (θ, τ ) = a H (θ, τ )a(θ, τ ) a H (θ, τ )E N E H N a(θ, τ ) (4.12)
By searching on the 2-D angle and delay continua, the sharp peaks in P (θ, τ ) will occur at the bearings of incident signals with their corresponding time delays.

Forward-Backward Spatial Smoothing

In practice, subspace techniques like MUSIC also require the signal covariance matrix R S has full rank. However, our stacked CSI measurements X from all the subcarriers at all RX antennas is just a single column unit rank matrix. Due to the coherence of multiple signals, all subspace based methods suffer complete failure from the rank deficiency of R S . To address this issue, we propose to apply forward-backward spatial smoothing to mitigate the random noise and further improve the joint AoA-ToF estimation performance [START_REF] Pillai | Forward/Backward Spatial Smoothing Techniques for Coherent Signal Identification[END_REF]. As shown in Figure 4.6, after reshaping the single measurement vector to the N r × K CSI matrix, we first partition the CSI matrix into uniformly overlapping subarrays with the size of K ′ N ′ r , where K ′ and N ′ r are the number of subcarriers and antennas in the subarray, respectively. To ensure measurable phase shifts across RX antennas, here N ′ r is fixed as 2 in our case. The total number of overlapping subarrays is then T K T N , where

CFR(
T K = K -K ′ + 1 and T N = N r -N ′ r + 1.
In the sequel, a hardened spatially smoothed covariance matrix can be derived by averaging across those subarrays' covariance matrices with a forward direction (blue arrow). It is defined as follows.

R f = 1 T K T N T K T N ∑ i=1 R i s (4.13)
where R i s is the covariance matrix of the i th subarray. This covariance hardening processing achieves an improved rank, thus closer to the true source covariance matrix. Moreover, the invariant structure of CSI also enables a backward directional smoothing (red arrow) to further enhance the accuracy of MUSIC estimator. This averaged forward-backward covariance matrix can be expressed as

R f b = 1 2 (R f + JR * f J) = 1 2 (R f + R b ) (4.14)
where J is the K ′ ×K ′ exchange matrix with only ones on its anti-diagonal and R b denotes the backward covariance matrix.

Optimal Smoothing Length Selection Note that SpotFi only treats smoothed CSI matrix with a fixed smoothing length of K ′ N ′ r = 30, which fails to dive deeper into the optimal selection of the smoothing length. As the smoothing length decreases, the noise level in estimated AoA spectrum gets lower, which helps to narrow the peak and improve the accuracy. But in the meantime, this also reduces the effective antenna sensors, which increases the risk of eliminating the peak from the direct path. To carefully cope with this trade-off problem, we perform a micro-benchmark which computes AoA spectra in a near LoS scenario (so the direct path bearing dominates) with different smoothing lengths. As observed in Figure 4.7, the smoothing length of 16 (K ′ = 8) shows a good compromise during our experiments and thus is chosen for the performance evaluation section. It is also worth noting that since subcarrier index k = 0 is null due to the large direct current (DC), in addition to making smoothing length larger than the number of multipaths indoors (say 10 [START_REF] Czink | Number of Multipath Clusters in Indoor MIMO Propagation Environments[END_REF]), we also need to ensure that no partitioned subarray contains k = 0 subcarrier, which avoids 2f δ error for AoA estimation.

Augmented Multi-Packet Smoothing Considering that we only perform the forwardbackward smoothing in the frequency domain, to fully acquire the empirical covariance matrix, different packet snapshots are also needed to implement the time-domain averaging, which can be denoted by

R mp = 1 N mp Nmp ∑ i=1 R i f b (4.15)
where N mp is the number of multiple CSI packets for sample smoothing. We can observe in Figure 4.8 that the joint AoA and ToF estimation is further refined (the red dots are more centralized than the blue stars) after the process of multi-packet sample smoothing, which is conductive to provide better performance for location fingerprinting. As a result, along with AR entropy fingerprints which are introduced in Section 3.2, the final estimated AoA with the smallest ToF at the m th RP location from the s th AP can be also determined and stored as ( θs m , τ s m ) for the following online position estimation. Likewise, the online acquired AoA-ToF fingerprint can be expressed by ( θs o , τ s o ).

Online Position Determination

Unlike the previous EntLoc positioning system, the online location determination phase for AngLoc involves additional AoA element. The corresponding similarity metric calculation and final location estimation have been enriched and enhanced, which will be systematically discussed in the sequel.

Similarity Metric Calculation

In the online location estimation phase, the mobile target is required to be accurately mapped with the pre-defined fingerprint database. In order to quantify the similarity between the offline stored fingerprints and the online measured CSIs, we manage to independently adopt two simple distance metrics for the respective AR entropy and AoA fingerprints. For amplitude based AR entropy, the Manhattan distance is employed to measure the gap between two vectors through the summation of the absolute differences of their corresponding components. Given the offline and online entropy fingerprints ΦH s m and ΦG s o , the Manhattan distance between them is represented as

D s m = ∥ ΦH s m -ΦG s o ∥ 1 = R ′ ∑ i=1 ⏐ ⏐ ⏐ φi H s m -φi G s o ⏐ ⏐ ⏐ (4.16)
where ∥•∥ 1 denotes the ℓ 1 norm. Moreover, by following the chain rule for Shannon entropy [START_REF] Cover | Elements of Information Theory[END_REF], it can be proved that a joint entropy difference for multiple independent variables is equal to the sum of all these variable's entropy differences. Under the S independent AP assumption, we therefore have the Manhattan distance for all available APs as follows.

D m = S ∑ s=1 D s m (4.17)
For the estimated 2-D AoA and ToF fingerprints, we naturally resort to the simple Euclidean distance to capture the discrepancy between the offline ( θs m , τ s m ) and online ( θs o , τ s o ) from all S APs. It can be then defined as

D m = √ ∑ S s=1 (( θs m -θs o ) 2 + (τ s m -τ s o ) 2 ) (4.18)
Thus, the dissimilarities of both AR entropy fingerprint D m and AoA fingerprint D m for the m th RP location are further obtained for the following target's position determination.

Bivariate Kernel Regression

In general, both of the two metrics are fully capable of concisely reflecting the spatial proximity between the offline learned traits at the m th RP and the online measurements The overall performance of our AngLoc fingerprinting system will be evaluated in the following section.

Performance Evaluation

In this section, we carry out the experimental evaluation of our proposed localization system. We will begin with the experimental setup introduction and the detailed results of localization performance will be discussed in the sequel.

Experimental Setup

1) Additional Test Environment:

To evaluate the performance of our AngLoc system, the entire experiments are implemented at two different indoor testbeds in CNAM.

As exhibited in Figure 3.11, the first testbed is a 15m × 15m laboratory office in a multistorey building, which is comprised of a main corridor alongside several office and meeting rooms. Many desks, chairs, computers and shelves are furnished inside to form a complex indoor radio propagation environment. The second testbed in NIC and run 64-bit Ubuntu 14.04 OS and Debian 8.0 OS, respectively. In addition, as for the antenna settings, each wireless NIC-compatible device is also capable of installing up to three omni-directional antennas so that the 3×3 MIMO configuration can be supported.

3) Data Acquisition: As aforementioned in the beginning, we implement the CSI data collections in both laboratory and classroom environments. Figure 3.14 and Fig. 4.10 display the detailed floor plans and experimental layouts for our laboratory and classroom testbeds, respectively. First of all, for both testbeds, the laptop serves as signal transmitter whose placement is fixed on the table and known a priori.

Under packet injection mode, it is designated to intermittently send at the rate of 100 packets per second using only one transmitting antenna. It is notable that such 12.6m Moreover, every receiver end is operated at the same height, constructing a simple 2-D platform for the precise indoor position estimation.

7.8m

4) Benchmarks and Performance Metrics:

In this section, we establish the whole benchmark program for the performance evaluation of our AngLoc system, which is com-pared with aforementioned systems like Horus [START_REF] Youssef | The Horus WLAN Location Determination System[END_REF], FIFS [START_REF] Xiao | FIFS: Fine-grained Indoor Fingerprinting System[END_REF] and PinLoc [START_REF] Sen | You are Facing the Mona Lisa: Spot Localization using PHY Layer Information[END_REF]. We also compare it with our previously proposed EntLoc system [START_REF] Chen | CSI-based Probabilistic Indoor Position Determination: An Entropy Solution[END_REF], which only exploits the CSI amplitude based entropy metric for indoor fingerprint localization. Besides, considering that the original PinLoc system conduct the war-driving procedure in a set of predefined 1m × 1m grids, known as spots, in order to provide a fair comparison, we modify PinLoc to use the same training set that we use in the proposed AngLoc system. Particularly, for AoA accuracy evaluation, we take SpotFi [START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF] as the comparative rival due to its representativeness among recent AoA based indoor positioning systems.

As for the performance metrics, we define the localization error as Euclidean distance between the estimated location and the mobile user's actual position, which is presented as

∥ lo -ℓ o ∥ = √ (x o -x o ) 2 + (ŷ o -y o ) 2 .
When there are N a testing locations, we evaluate the localization performance by using the Mean Error (ME) metric which can be calculated as

M E = 1 N a Na ∑ i=1 √ (x i -x i ) 2 + (ŷ i -y i ) 2 (4.21)
where (x i , y i ) and (x i , ŷi ) are the actual and estimated coordinates at the i th testing location, respectively.

Numerical Results

Prior to exhibiting the localization results of our proposed system, we first reveal the effects of different system parameters which play a defining role for our AngLoc's performance. In addition, some other experimental factors will also be evaluated at the end of this section.

Impact of Packet Number Selection for Entropy Estimate

For the sake of efficiently implementing our AngLoc positioning system in the practical testbeds, a reasonable number of CSI packets should be first determined to ensure a desired localization performance while maintaining a low computational cost. Since AngLoc inherits the AR entropy fingerprint from the previous EntLoc system, we then adopt the same scheme of the packet number selection for AR entropy estimation, which is also chosen in the EntLoc system. As shown in Figure 3.24, we hereby choose 50 and fix this packet number for all entropy estimation processes in our AngLoc positioning implementations. To address this issue, we devise an accuracy based packet number selection scheme to efficiently conduct AoA calculation. Considering that the multi-packet smoothing is required in our AngLoc system, we begin the testing packet number from 5 packets and extend it to 10, 15 and 40 packets, respectively. In addition, since the LoS-friendly class-room is more convenient and can provide a clear ground truth (direct path) to compare the AoA estimation errors. It is thus chosen as the experimental environment in this part.

As shown in Figure 4.11, we can observe that even with 15 packets, our AngLoc system works well and accurately identifies the true AoA with a mean error of 5 degrees, which shares the similar performance with 40 packets. The underlying explanation lies in the fact that once we determine the first arrival path through the smallest ToF, more CSI packets will not bring further improvement with regard to the AoA estimation accuracy.

Impact of Kernel Regression Parameters

Recall that in the online location estimation phase, we first find M c closest RP locations in accordance with the amplitude's AR entropy. Then, a weighted bivariate kernel regression scheme is proposed to accurately calculate the target's location by exploiting both entropy and AoA informations. As a result, a proper selection of the relevant kernel regression parameters in the offline phase is of great importance in the final localization outcome. As listed in Table 4.1, by leveraging leave-one-out cross-validation, we optimally choose the M c , weighting factors w e , w a and kernel coefficients ρ e , ρ a for both testbeds.

It is interesting to observe that in the larger and more NLoS laboratory scenario, the AoA-driven RP refining scheme outweighs the AR entropy factor (i.e. w a > w e ), which indicates the fact that the entropy metric tends to bring more ambiguities in more complex environment. On the contrary, the more LoS classroom testbed renders the AR entropy competent enough to differentiate locations since the channel property in such case appears to be more stable. range of [START_REF] Küpper | Location-Based Services: Fundamentals and Operation[END_REF][START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF] and [START_REF] Küpper | Location-Based Services: Fundamentals and Operation[END_REF][START_REF] Liu | Face-to-Face Proximity Estimation using Bluetooth on Smart Phones[END_REF], we can identify the optimal selection of M c for both testbeds as 12 and 8, under which the localization mean errors reach minimum. It is fair to state that for the larger and multipath-richer room, a greater number of RP candidates should be required in order to well perform the position determination.

Localization Accuracy

In this part, by using the same parameters for all competing IPSs, we then move forward to evaluate the localization performance and present numerical results with relevant discussions. our proposed AngLoc system shows a mean error of 1.18m in the lab and 0.95m in the classroom, which even achieves the decimeter-level localization accuracy, outperforming other counterparts in both testbeds. Meanwhile, for all the competing IPSs, we can also observe that the mean error performance in the classroom is generally better than that in the laboratory scenario, which further validates our previous assumption. In order to provide an in-depth and comprehensive comparison for these localization systems, we also enumerate the respective maximum error (Max. err.), minimum error (Min. err.), mean error (Mean err.) and the 90th percentile accuracy (Acc. at 90%) in Table 4.2 and Table 4.3 for the laboratory and classroom, respectively. As can be observed, apart from the minimum error, our AngLoc system broadly dominates the general accuracy evaluation for the maximum error, mean error and 90th percentile accuracy. When it comes to the particular minimum error, AngLoc only falls behind FIFS and EntLoc with 0.01m and 0.03m in the respective testbed #1 and #2, which can be reasonably neglected in both realistic indoor environments.

AoA Estimation Accuracy in LoS Condition

In comparison with our previous EntLoc system, the most productive advancement for AngLoc is that CSI phase based AoA information is organically combined to facilitate the improvement of localization performance. Since one of SpotFi's key insights is to identify the direct path AoA for geometric mapping, even in strong NLoS case, it still needs multiple APs to achieve this through a likelihood scheme. In contrast, the inherent difference of our AngLoc is that the physical direct path AoA is not necessary for fingerprinting as long as the test target's AoA reading (i.e. the first arrival path) is similar with those of its neighboring RP locations. In order to create a fair competition, we only compare the AoA estimation errors with SpotFi under the LoS condition. For the NLoS scenario, we design a different evaluation mechanism for the comparison purpose, which will be discussed in the next part. In practice, for the LoS classroom illustrated in Figure 4.10, by applying our AngLoc's enhanced AoA estimation approach as well as the SpotFi's method, we record the AoA readings at all 40 RP locations and compare them with their corresponding ground truth.

Here it is worth mentioning that after obtaining several AoA-ToF estimates (clusters) from multiple CSI packets, SpotFi declares the direct path AoA from the cluster with the highest likelihood value. For a fair comparison, we modify the last part of SpotFi to determine the AoA from the first arrival path, which is exactly what we adopt in the AngLoc system. As shown in Figure 4.17, our AngLoc's AoA estimation method can yield the 90th percentile error of 17 degrees, outperforming SpotFi's 26 degrees error in the LoS condition. The total gain of nearly 10 degrees validates the superior performance of our super-resolution JADE-MUSIC algorithm.

Impact of AoA Proximity in NLoS Condition

For NLoS environment such as the laboratory shown in Figure 3.14, we design and implement a dedicated experiment to manifest the AoA based fingerprinting feasibility of our AngLoc system. Specifically, we first choose 20 test locations which are in the obvious NLoS conditions from the transmitter. Each of them is surrounded by four predefined RPs.

After acquiring the AoA estimates from all these test positions and their neighboring RP locations, we then calculate the AoA differences between each test location and its corresponding four RPs in the vicinity. As displayed in Figure 4.18, compared with SpotFi's method, the box plot shows that our AngLoc's AoA estimation method is capable of deriving the overall lower level of AoA differences with the four RP neighbors, which nicely indicates the similar AoA estimations around the neighboring locations. This advantage further promotes our AngLoc-derived AoA to be a well-qualified position fingerprint for the accurate indoor location determination.

Discussions

In this section, we discuss several unsolved issues in this chapter and propose some possible solutions, which could further enhance the performance of our proposed AngLoc localization system.

Device Orientation Calibration

During the fingerprint site survey, we frequently move the HummingBoard embedded antenna stand among all the RP locations to collect CSI data. In principle, to achieve preferable AoA estimations, one should always maintain the same device orientation when moving the antenna stand from place to place. Otherwise, it may incur additional manual operational error for AoA estimates. To address this potential problem, the commodity smart robot can be leveraged in our future work, by which we can plan the moving path in down the candidate RP locations by finding RPs with the smallest AR entropy differences.

A novel bivariate kernel regression method was then adopted to precisely infer the target's location. In comparison with our previous EntLoc system, experimental results from the lightweight HummingBoard device showed a superior localization performance of our proposed AngLoc system with an average accuracy improvement of 35.9% and 28.6% in both laboratory and classroom testbeds. Additionally, we also examined the impacts of several parameters on AngLoc's performance in different indoor scenarios, which empowers us with deepening insights to efficiently and productively conduct our indoor location fingerprinting.

Chapter 5

Conclusions and Future Works Last but not least, the pursuit towards the easy fingerprinting implementation never gets tired. Throughout the entire practical study of the CSI based indoor positioning, we gradually manage to develop the more lightweight and feasible CSI data acquisition platform based on the HummingBoard Pro embedded system. It tremendously facilitates our location site survey process and enables us with insightful and bold visions to shed light on some more complex indoor wireless sensing applications in the future research.

Perspectives for Future Works

Despite the increasing research interest in recent years, wireless indoor location fingerprinting is still in its infancy. This thesis mainly focuses on leveraging channels state information on the commodity Wi-Fi infrastructure to improve the accuracy of the probabilistic localization systems. Herein we also point out some possible future research directions.

• Machine Learning based Feature Extraction: Depending on the indoor area of interest, the amount and size of measurements recorded at all the reference points could be incredibly huge. Traditional signal processing approaches turn to be highly ineligible. Under such circumstance, we may resort to the prevalent data-driven machine learning techniques such as Convolutional Neural Network (CNN) [START_REF] Murphy | Machine Learning: A Probabilistic Perspective[END_REF][START_REF] Wang | CSI-based Fingerprinting for Indoor Localization: A Deep Learning Approach[END_REF]. Some representative features hidden in the acquired CSI measurements can be extracted and exploited to match against the stored fingerprint database and finally infer the target's physical position.

• Crowdsourcing based Radio Map Updating: In fingerprint based localization systems, the offline database is often obtained through site survey, where a professional surveyor walks around the site to measure signal signatures at all RP positions. Since signals may evolve over time, this survey has to be conducted frequently to maintain a desired performance. This is laborious, time-consuming and costly [START_REF] Wang | Indoor Smartphone Localization via Fingerprint Crowdsourcing: Challenges and Approaches[END_REF]. Therefore, we can also consider CSI based fingerprinting crowdsourcing scheme by using Bayesian Compressive Sensing (BCS) [START_REF] Yang | Updating Wireless Signal Map with Bayesian Compressive Sensing[END_REF] or sparse Bayesian learning [START_REF] Zhang | Extension of SBL Algorithms for the Recovery of Block Sparse Signals with Intra-block Correlation[END_REF][START_REF] Chen | Source Position Estimation via Subspace based Joint Sparse Recovery[END_REF] to efficiently update the database and further reduce the labor work for the process of the fingerprint database construction.

• CSI Temporal Variation Exploitation: Different from the last perspective which addresses the signal temporal dynamics by crowdsourcing based updating, a promising alternative for the location fingerprinting can treat this issue from two aspects. For small-scale time variations (normally in one day), a threshold based decision-making scheme [START_REF] Patwari | Temporal Link Signature Measurements for Location Distinction[END_REF] can be leveraged to decide whether the dissimilarity of two signatures are due to the location difference or just the normal temporal dynamics at the same site. For the large-scale temporal dynamics (e.g. days or weeks), channel responsebased signatures tend to be in distinct states. Therefore, these large-scale temporal dynamics can be modeled as a Markov chain in practice [START_REF] Zhang | Advancing Wireless Link Signatures for Location Distinction[END_REF], which can be properly exploited to pinpoint the target's location.

• Multi-target Simultaneous Localization: One major limitation of fingerprint-based techniques is that the training phase consumes a significant amount of time and effort. This situation is particularly true when we scale our system to simultaneously identifying multiple targets, since the training overhead increases exponentially with the combination of all subjects. In the context of device-based localization system, RF propagation tool [START_REF] Scholz | Devicefree Radio-based Low Overhead Identification of Subject Classes[END_REF] and the approach in [START_REF] Lim | Zero-Configuration, Robust Indoor Localization: Theory and Experimentation[END_REF] can be applied to ease the effort of radio map construction, thus promoting the commercial practicability of the promising indoor location-aware industry.

  |H(f )| et ∠H(f ) désignent respectivement son amplitude et sa phase. De plus, le domaine fréquentiel CFR se compose d'une réponse amplitude-fréquence et d'une réponse phasefréquence, caractérisant l'évanouissement sélectif en fréquence provoqué par les phases constructives et destructrices dans l'environnement riche en trajets multiples. Il contient ainsi plus d'informations sur les canaux que la mesure RSS basée sur la puissance.

Figure 1 :

 1 Figure 1: L'architecture du système EntLoc.

. 5 - 0 . 5 S

 505 une notation générale de l'amplitude CSI β d'une sous-porteuse et l'ensemble des relations PDF-PSD est présenté par p(β) = S W (βp(β) et S W (β) sont respectivement le PDF et le PSD d'amplitude β. L'ensemble de {a i } 1≤i≤p sont les coefficients AR d'un processus AR d'ordre p et σ 2 ϵ est l'erreur de Résumé de la Thèse en Français xii prédiction du modèle qui est choisi de telle sorte que ∫ 0W (β)dβ = 1. Il est à noter que puisque la loi est modélisée comme la restriction du spectre sur l'intervalle de [-0.5, +0.5], les données d'amplitude doivent d'abord être redimensionnées sur cet intervalle. Pour résoudre l'équation (2), un ordre de modèle approprié p doit d'abord être choisi car un ordre faible conduit à une résolution inadéquate et un ordre élevé entraîne des pics parasites (variance excessive). Nous adoptons ainsi la technique de la famille exponentiellement intégrée (EEF) pour déterminer l'ordre du modèle AR en raison de ses performances supérieures grâce à nos expériences approfondies. Par la suite, les coefficients AR et son erreur de prédiction de modèle correspondante peuvent être estimés en résolvant les équations de Yule-Walker bien connues en utilisant la récursion de Levinson-Durbin. Une fois que l'AR PDF est déterminé à partir de (2), le calcul d'entropie peut alors être exprimé par la forme suivante:

Figure 2 :Figure 3 ,Figure 3 :Chapitre 4 :

 2334 Figure 2: Le plan d'étage de notre laboratoire.

Figure 4 :Figure 4 ,Figure 5 :

 445 Figure 4: Un exemple illustratif du mécanisme du système AngLoc.

Figure 7 :Figure 8 :

 78 Figure 7: Précision de localisation pour le laboratoire.

Figure 1 . 1 :

 11 Figure 1.1: Different applications of location based services.

Figure 1 .Figure 1 . 2 :

 112 Figure 1.2: Diagram for typical indoor multipath propagation.

  Luan Chen, Iness Ahriz and Didier Le Ruyet. "AoA-aware Probabilistic Indoor Location Fingerprinting using Channel State Information", IEEE Internet of Things Journal, 2020. (IF: 9.515) • Luan Chen, Iness Ahriz and Didier Le Ruyet. "CSI-based Probabilistic Indoor Position Determination: An Entropy Solution", IEEE Access, 2019. (IF: 4.098) • Luan Chen, Iness Ahriz, Didier Le Ruyet and Hong Sun. "Probabilistic Indoor Position Determination via Channel Impulse Response", in Proceedings of the 29th Annual IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), 2018. • Luan Chen, Iness Ahriz, Hong Sun and Didier Le Ruyet. "Source Position Estimation via Subspace based Joint Sparse Recovery", in Proceedings of the 13th IEEE International Conference on Signal Processing (ICSP), 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2 . 1 :

 21 Figure 2.1: Path Loss, Shadowing and Multipath versus Distance.

Figure 2 . 1 :

 21 Figure 2.1: Path loss, shadowing and multipath versus distance [49].

Figure 2 . 2 :

 22 Figure 2.2: The diagram of the TOA technique.

Figure 2 .IsochronousFigure 2 . 3 :

 223 Figure 2.3 shows the procedure related to the TDOA method. At time T 0 , the mobile

  anchored localization. In comparison with distance based estimation, the cost of angle measurements is generally higher. Technically, angle-based techniques estimate the position of a mobile node by measuring the Angle of Arrival (AoA) of signals arriving at the measuring node. With perfect physical measurements, the positioning problem can be geometrically solved by finding the intersection of a number of straight lines representing the signal AoAs (e.g. triangulation). In 2-D scenarios, two AoA recordings are just sufficient.

Figure 2 .Figure 2 . 4 :

 224 Figure 2.4 depicts the holistic structure of the end-to-end MIMO-OFDM wireless transceiver. It consists of two major functionality blocks: signal transmitter block and RF receiver block. In the transmitter block, the scrambler and Forward Error Correction (FEC) encoder first convert the input data into high-rate bit stream(s). The stream parser is then applied on bit stream(s) to generate N ss spatial streams, whose number is determined by the parameter of Modulation and Coding Scheme (MCS). After interleaving and constellation mapping (e.g. Quadrature Amplitude Modulation (QAM)), N ss spatial

Figure 2 . 5 :

 25 Figure 2.5: A simple diagram of the channel impulse response.

Figure 2 . 6 :

 26 Figure 2.6: An example of CIR time samples with 20 MHz bandwidth

2 . 7 ,Fig. 2 .

 272 Fig. 2. An example of trilateration.

Figure 2 . 7 :

 27 Figure 2.7: An example of the trilateration algorithm [56].

Fig. 3 .

 3 Fig. 3. An example of triangulation.

Fig. 4

 4 Fig. 4. An

Figure 2 . 8 :

 28 Figure 2.8: An example of the triangulation algorithm [56].

Figure 2 . 9 Figure 2 . 9 :

 2929 Figure 2.9: The basic system flow diagram for Wi-Fi fingerprint localization.

  deterministic approaches, probabilistic algorithms are based on statistical inference between the target signal measurement and stored fingerprint database. Using a training set, these algorithms can be applied to find the target's location with the maximum likelihood, which is inferred by a probabilistic model reflecting the signal distributions. It can represented by lo = arg max ℓm P (ℓ m |G o ), m = 1, • • • , M (2.9) where P (ℓ m |G o ) indicates the probability of the target at location ℓ m given the online measurements G o .

29

 29

  used auto-encoder based deep extreme learning machine to extract high level data features from RSS fingerprint, which further improved the localization performance. Moreover, Wu et al. designed DorFin [87], a RSSbased location fingerprinting system which successfully tackled error mitigation problem by quantifying APs' distinction, alleviating RSS outliers and amending transitional RSS recordings. It reduced the mean and 95th percentile errors to respective 2.5m and 6.2m, outperforming both RADAR and Horus by nearly 50% accuracy improvement.

Figure 3 . 1 :

 31 Figure 3.1: The EntLoc system architecture.

Figure 3 . 2 :

 32 Figure 3.2: Channel impulse response.

  u l a t i v e C o n t r i b u t i o n R a t e T i m e T a p s C = 9 9 %

Figure 3 . 3 :

 33 Figure 3.3: Power threshold.

. 2 )Figure 3 . 4 :

 234 Figure 3.4: The raw CFR.

Figure 3 . 5 :

 35 Figure 3.5: CFR after tap filtering.

Algorithm 2 AR 1 : 2 : 3 : 6 :Figure 3 . 6 :Figure 3 . 7 :

 212363637 Figure 3.6: AR modeling based PDF estimation at location #1.

Figure 3 . 8 ,

 38 for the visual clarity, we only exhibit subcarrier index 1, 10, 20, 30 and experimentally observe that the endpoint subcarriers #1 and #30 show a clear ambiguity in terms of location differentiation.

Figure 3 . 8 :

 38 Figure 3.8: Ambiguity test for 4 subcarriers, namely #1, #10, #20 and #30.

29 Figure 3 . 9 :

 2939 Figure 3.9: Ambiguity test for all 30 available subcarriers.

Figure 3 . 10 :

 310 Figure 3.10: A simple example of the kernel function with ρ = 2.

Figure 3 .

 3 Figure 3.10 displays a simple kernel function which changes with distance. It is notable that the kernel K m is equal to one if the distributions of the given two fingerprints are identical (i.e., D m = 0) and decays to zero as the dissimilarity of the two fingerprints increases. In other words, this probability kernel provides a flexible way to naturally

3. 3 . 1 . 1

 311 Experimental Presentation (a) Environment: The entire experiments are conducted in the CEDRIC laboratory of CNAM (a typical office environment in a multistorey building as shown in Figure 3.11). This lab office is a large room with an area of over 200m 2 . The indoor space is partitioned into several office and meeting rooms with many desks, chairs, computers, shelves furnished inside, which forms a complex radio propagation environment. The whole CSI database was collected during the working time in February, 2019. (b) Configuration: We conduct our real experiments on commodity-ready off-the-shelf Wi-Fi devices [25]. Specifically, by working in the 5GHz band of IEEE 802.11n monitor mode, we use an HP Elitebook 8530w laptop as the signal transmitter (TX) and an HummingBoard Pro (HMB) as the mobile receiver (RX), which are exhibited in Figure 3.12 and Figure 3.13. Both devices are equipped with Intel Wi-Fi Link (IWL) 5300 NIC and run 64-bit Ubuntu 14.04 OS and Debian 8.0 OS, respectively.Additionally, for our antenna settings, each Wi-Fi device is equipped with three omni-directional antennas to support 3 × 3 MIMO configuration.

Figure 3 . 11 :Figure 3 . 12 :Figure 3 . 13 :Figure 3 . 14 :

 311312313314 Figure 3.11: CNAM laboratory scenario.

Figure 3 . 15 :

 315 Figure 3.15: Temporal stability for three fingerprint signatures during the entire working times of one day (8 hours).

Figure 3 .

 3 Figure 3.14, we experimentally chose two testing locations which are under LoS and NLoS condition, respectively. At each location, the multi-dimensional estimated AR entropy from all three RX antennas is compared with the entropy vectors of the corresponding four neighboring RP positions. Results illustrated in Figure 3.16 demonstrate that for LoS test location #1, our AR modeling based entropy shows good spatial proximity with

8 Figure 3 . 16 : 8 Figure 3 . 17 :

 83168317 Figure 3.16: Proximity test under LoS condition. 0 10 20 30 40 50 60 80 90Subcarrier Index for three RX Antennas

Figure 3 . 18 :

 318 Figure 3.18: Localization accuracy of AR entropy against its original CFR amplitude.

Figure 3 . 19 :

 319 Figure 3.19: Localization accuracy of AR entropy against its time domain CIR.

Figure 3 . 20 :

 320 Figure 3.20: Localization accuracy of proposed EntLoc against state-of-the-art.

  location fingerprinting. Firstly the raw CFR measurements are converted into its time domain CIR by IFFT. Once removing irrelevant noise component in CIR, we can subsequently obtain a smoothed and finer version of CFR by applying FFT. It is interesting to study the impact of this approach to see how it can improve our localization performance.

Figure 3 . 21 :

 321 Figure 3.21: AR entropy box plot for raw CFR.

Figure 3 . 22 :

 322 Figure 3.22: AR entropy box plot for filtered CFR.

Figure 3 . 23 :

 323 Figure 3.23: AR entropy variances for raw CFR and filtered CFR.

Figure 3 . 24 :

 324 Figure 3.24: AR entropy variance changes with different CFR packet number selections.

Figure 3 . 25 :

 325 Figure 3.25: Localization accuracy under three different RX antenna configurations.

  Techniques: The geometric modeling of the RF propagation is fundamental to the ranging or direction based positioning systems.Wu et al. explored the frequency diversity of PHY layer CSI information to refine distance estimation and pinpoint the target's location through trilateration in FILA system[START_REF] Wu | FILA: Fine-Grained Indoor Localization[END_REF], which achieved median accuracy of 1.2 m in the multi-room environment. Alternatively, ArrayTrack[START_REF] Xiong | ArrayTrack: A Fine-Grained Indoor Location System[END_REF] embraced the trend of MIMO technology and exploited increased number of antennas at commodity access points (APs) to obtain high-resolution AoAs, which were further aggregated to infer the client location within 23 centimeters median accuracy. Unlike Ar-rayTrack which requires dedicated hardware modifications, Kotaru et al. designed SpotFi[START_REF] Kotaru | Spotfi: Decimeter Level Localization using WiFi[END_REF], an accurate indoor localization system capable of identifying direct path AoAs with only three physical RX antennas. Moreover, after incorporating the observed RSS infor-mation for an optimization processing, SpotFi was able to achieve the median accuracy of 40 cm. More recently, the researchers of Chronos[START_REF] Vasisht | Decimeter-Level Localization with a Single WiFi Access Point[END_REF] leveraged a novel Chinese remainder theorem based algorithm to compute sub-nanosecond ToF with a single Wi-Fi access point. This distance-related metric was then formulated into a quadratic optimization problem for accurately locating clients within tens of centimeters. Recent Fingerprinting based Techniques: Regardless of measurements' geometric relation, the pattern-matching based fingerprinting techniques have attracted a large body of research interests for the last decades. Wang et al. designed DeepFi [107], a deep learning based indoor location fingerprinting system using CSI amplitude information. In the offline phase, DeepFi enabled a deep network to train all the weights as location fingerprints, and harnessed the Radial Basis Function (RBF) based probabilistic scheme to accomplish the position estimation in the online phase. It outperformed FIFS system with 20% accuracy improvement.

Figure 4 . 1 :

 41 Figure 4.1: An illustrative example of the AngLoc system mechanism.

Figure 4 . 2 :

 42 Figure 4.2: The overall AngLoc system architecture.

Figure 4 . 4 :

 44 Figure 4.4: CIR amplitude changes after SFO, STO and CFO removal.

. 4 )

 4 where • denotes the Hadamard product operator and H(n p ) is the n th p CFR packet. The sanitized CFR can be then acquired by Ĥ = {( Hk )1 Np } 1≤k≤K .As illustrated in Figure4.3 and Figure4.4, the above adopted phase calibration techniques have effectively compensated CSI phase errors after the respective SFO, STO and CFO removal.

Figure 4 . 5 :

 45 Figure 4.5: An incident signal arrives at an antenna array with an angle θ.

Figure 4 . 6 :

 46 Figure 4.6: The mechanism of forward-backward spatial smoothing.

Figure 4 . 7 :

 47 Figure 4.7: Optimal smoothing length selection through AoA spectrum.

Figure 4 . 8 :

 48 Figure 4.8: The comparison of AoA estimation with and without multi-packet smoothing.

  from an uncharted position. For the design of AngLoc, the remaining location estimation process consists of two main steps. First, by adopting the classical kNN theory, we can claim M c out of M RP locations which signify M c smallest AR entropy differences among {D m } 1≤m≤M . Then, a novel bivariate kernel regression scheme is further proposed to infer the final target's location by exploiting the distance based kernel function and the selected set of M c reference points. The estimated location lo is expressed bylo = ∑ Mc mc=1 K mc ℓ mc ∑ Mc mc=1 K mc (4.19)where m c ∈ [1, M c ] and K mc denotes the probability kernel of the m th c RP location which is obtained by exponentiating and weighting its corresponding entropy and AoA based distances. It can be mathematically presented as follows:K mc = w e exp(-ρ e D mc ) + w a exp(-ρ a D mc ) (4.20)Here w e and w a are the weighting factors for the respective AR entropy and AoA based kernel function and w e + w a = 1. ρ e and ρ a are their corresponding kernel coefficients which are chosen to optimally minimize the fingerprinting error by leave-one-out crossvalidation in the offline phase. It is noteworthy that this bivariate kernel K mc equals to one if the given two fingerprints are identical and decays to zero as the dissimilarity of two fingerprints increases. Simply put, this bivariate kernel provides a flexible way to naturally harness the CSI data and therefore makes full use of our probabilistic AR entropy and AoA information, thus leading to an improved localization performance.

Figure 4 . 2 )

 42 Figure 4.9 is an ample classroom scenario with an area of around 100 m 2 . It lays out less obstacles within the fingerprinting area which presents a relative LoS scenario.It can then serve as a supplementary contrast with testbed #1. As for the implementation time, the CSI databases for these two testbeds were collected and stored in February and July of 2019, respectively.

Figure 4 . 9 :

 49 Figure 4.9: CNAM classroom scenario.

Figure 4 . 10 :

 410 Figure 4.10: The floor plan of our classroom.

Figure 4 . 11 :

 411 Figure 4.11: AoA estimation errors by using different number of CSI packets.

Furthermore, we also

  lay out the training results for choosing parameter M c in Figure 4.12 and Figure 4.13 from both laboratory and classroom environments. Given a respective

Figure 4 . 12 :

 412 Figure 4.12: Optimal neighbor number selection for laboratory testbed.

Figure 4 . 13 :

 413 Figure 4.13: Optimal neighbor number selection for classroom testbeds.

Figure 4 . 14 :

 414 Figure 4.14: Localization accuracy for the laboratory.

Figure 4 . 15 :

 415 Figure 4.15: Localization accuracy for the classroom.

Figure 4 . 16 :

 416 Figure 4.16: Bar plot of localization mean error comparison for both testbeds.

Figure 4 . 17 :

 417 Figure 4.17: AoA estimation errors in LoS condition.

Figure 4 . 18 :

 418 Figure 4.18: The box plot for AoA differences between 20 test locations and their corresponding 4 neighboring RP locations.

Contents 5 . 1 96 5. 2 97 95 5 . 1

 519629751 Dissertation Conclusions . . . . . . . . . . . . . . . . . . . . . . . Perspectives for Future Works . . . . . . . . . . . . . . . . . . . Dissertation Conclusions Due to the economical deployment beyond existing networks and superior adaptivity to the sophisticated indoor environment, fingerprint based localization, represented by Wi-Fi fingerprinting, has attracted much attention in recent academic and industrial trials.In this dissertation, we demonstrate the feasibility of exploiting the PHY layer channel state information available on commodity Wi-Fi infrastructure to boost the capabilities of accurate indoor position determination. On the ground of designing effective location fingerprinting systems, we summarize this thesis in the following.First, due to the presence of channel bandwidth limitation and unintentional device noise, we design a power based tap filtering scheme to largely mitigate the CSI measurement noise. Specifically, we seek the solution in the more intuitive time domain channel impulse response by converting CFR via IFFT and analyze the resolvable time taps. Through a power based thresholding scheme, we experimentally unveil the most multipath-informative, or location-dependent CIR taps. By removing the irrelevant noisy components, we are able to achieve a more robust probabilistic fingerprint performance while retaining the desired accuracy. Additionally, we also dive into some deep-rooted CSI phase error issues. As the sanitized or compensated CSI phase information is of critical importance for the accurate ranging and direction estimation, we manage to leverage several phase calibration techniques to acquire adequate and reliable CSI measurements, which lays a solid foundation for the upcoming location fingerprinting implementation.Second, in order to exploit the probabilistic inference of the complex indoor wireless channel properties, we experimentally validate the infeasibility of traditional channel statistic based on the Gaussian assumption and resort to the AR modeling based entropy metric, which shares the structural simplicity with RSS while embodying the rich statistical channel information. On this basis, we proposed EntLoc, an AR entropy of CSI amplitude based fingerprint localization system using commercial off-the-shelf Wi-Fi device. Through extensive experiments conducted in a typical laboratory office scenario, EntLoc demonstrated a superior localization performance with an average accuracy improvement of 27.3%, 34.9% and 47.4%, when compared with the state-of-the-art PinLoc, FIFS and Horus system, respectively. We envision this work as an early step towards a generic, pervasive and finer-grained CSI location fingerprinting framework in the complex indoor environments.Third, on top of the amenable EntLoc positioning system, which only harnesses the CSI amplitude information, we further prototype AngLoc, an upgraded location fingerprinting system involving CSI phase information. It is capable of unleashing the complete locationaware potentials by employing additional AoA based fingerprint. To be specific, since the intricate indoor environments can breed similar AR entropy based signatures among certain predefined reference points, which may be randomly distributed in the area of interest. It may mightily tamper the location estimation accuracy when some of the remote RP candidates are falsely involved. The geometric nature of AoA based fingerprint, from another perspective, complementarily helps to rule out these error-prone RPs and further improve the location fingerprinting accuracy. In comparison with EntLoc, the experimental results of our proposed AngLoc from both laboratory and classroom testbeds validate its improved positioning performance with the mean error reduction of 35.9% and 28.6%, respectively.

Table RX

 RX bien exécuté dans ce scénario de laboratoire. Si nécessaire, nous pouvons recourir à plusieurs émetteurs pour le futur banc d'essai plus grand. Les points bleus représentés sur la Figure 2 désignent les 70 points de référence d'entraînement avec un espacement d'un mètre et les 30 emplacements de test sont marqués comme des étoiles rouges. Dans la phase de formation hors ligne, les mesures CSI sont collectées par le HMB léger à ces points de référence pour construire la carte radio brute. À chaque point, environ 5000 paquets CSI sont stockés sous forme de signatures RF dans le micrologiciel. Dans la phase en ligne, nous déplaçons ensuite le récepteur HMB parmi 30 emplacements de test

	7m	TX
	15m 3m
	5m
	3m	15m

montre le plan d'étage du laboratoire de 15m × 15m avec un couloir principal le long de plusieurs bureaux et salles de réunion. L'ordinateur portable HP servant d'émetteur de signal est fixé sur la table du bureau central. En mode injection, il est conçu pour transmettre par intermittence à raison de 100 paquets par seconde en utilisant une seule antenne d'émission. Il convient de mentionner qu'un réglage de l'émetteur est Résumé de la Thèse en Français xiii hautement suffisant et pour obtenir la même taille de paquets CSI. De plus, toutes les extrémités du récepteur sont placées à la même hauteur, construisant une plate-forme 2-D simple pour l'estimation précise de la position intérieure.

6m 7.8m PC Table TX RX Figure

		1
		0.8
	CDF	0.6 0.4					AngLoc EntLoc
							PinLoc-like
		0.2					FIFS Horus
		0	0	2	4	6	8	1 0
					Localization Error (m)

Tout d'abord, l'ordinateur portable sert d'émetteur de signal dont le placement est fixé sur la table et connu a priori. En mode d'injection de paquets, il est conçu pour envoyer par intermittence à raison de 100 paquets par seconde en utilisant une seule antenne d'émission. Il est à noter qu'un tel réglage d'antenne répond à l'exigence d'une cartographie spatiale directe, qui peut produire des données CSI sans CSD. Pendant ce temps, la précision de localisation peut également être garantie avec le coût de calcul le plus bas. Pour la disposition expérimentale, les points bleus montrés sur la figure 6 indiquent les 40 emplacements RP d'entraînement avec un espacement d'un mètre et les 28 positions de test sont marquées comme des étoiles rouges. Pendant la phase de formation hors ligne, environ 5000 paquets CSI sont collectés et stockés par le HMB léger à chaque point de référence pour créer la carte radio CSI brute. Dans la phase en ligne, nous déplaçons ce récepteur HMB parmi tous les emplacements de test pour acquérir la même taille de paquets CSI à des fins de localisation. De plus, chaque extrémité du récepteur fonctionne à la même hauteur, construisant une plate-forme 2-D simple pour l'estimation précise de la position intérieure. En vertu de la fonction de distribution cumulative (CDF), nous évaluons d'abord la précision de localisation de notre système AngLoc proposé par rapport à l'état de l'art. Comme on peut l'observer dans la Figure 7, pour l'environnement de laboratoire, notre Résumé de la Thèse en Français xviii 12.6: Le plan d'étage de notre salle de classe. système proposé est capable d'atteindre l'erreur du 90e centile de 2.27 m, ce qui surpasse les systèmes EntLoc, PinLoc-like, FIFS et Horus avec la même erreur niveau de 2.69 m, 4.15 m, 5.56 m et 5.64 m, respectivement. De même, dans le scénario de la salle de classe, nous pouvons remarquer dans la Figure 8 que AngLoc précède toujours les autres rivaux en termes d'erreur du 90e centile. Concrètement, il peut garantir que 90% des emplacements de test ont une erreur de positionnement inférieure à 1.99 m, dépassant les systèmes EntLoc, PinLoc-like, FIFS et Horus avec le même pourcentage d'erreur de 82.1%, 64.3%, 57.1% et 28.6%, respectivement.

Table of Contents 1 Introduction 1

 of .3.1.2 Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Location Fingerprinting . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.1 Deterministic Methods . . . . . . . . . . . . . . . . . . . .

	List of Figures List of Figures List of Figures Abbreviations Symbols	xxv xxvi xxvii xxx xxxii
	2.9 The basic system flow diagram for Wi-Fi fingerprint localization. . . . . . . 3.21 AR entropy box plot for raw CFR. . . . . . . . . . . . . . . . . . . . . . . . 58 4.18 The box plot for AoA differences between 20 test locations and their corre-PSD Power Spectral Density H s m The N × R dimensional CSI matrix which are acquired at the m th RP
	3.1 The EntLoc system architecture. . . . . . . . . . . . . . . . . . . . . . . . . sponding 4 neighboring RP locations. . . . . . . . . . . . . . . . . . . . . . 92 JADE from the s th AP Joint Angle and Delay Estimation 3.22 AR entropy box plot for filtered CFR. . . . . . . . . . . . . . . . . . . . . . 58 MUSIC Hm The N × SR dimensional CSI signature set which are acquired at the Multiple Signal Classification m th RP
	3.23 AR entropy variances for raw CFR and filtered CFR. . . . . . . . . . . . . . 59 FEC Forward Error Correction G s o The N × R dimensional CSI matrix which are acquired at the target's 3.2 Channel impulse response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Power threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.24 AR entropy variance changes with different CFR packet number selections. 60 List of Tables Abbreviations MCS unknown location from the s th AP Modulation and Coding Scheme QAM Symbols G o The N × SR dimensional CSI signature set which are acquired at the Quadrature Amplitude Modulation target's unknown location
	3.25 Localization accuracy under three different RX antenna configurations. . . . 61 STBC Space-Time Block Coding ΦH s m The AR entropy vector of CSI amplitudes at the m th RP from the s th 3.4 The raw CFR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CSD Cyclic Shift Diversity AP
	3.5 CFR after tap filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 An illustrative example of the AngLoc system mechanism. . . . . . . . . . . 65 SMM Spatial Mapping Matrix ΦG s The AR entropy vector of CSI amplitudes at the target's unknown lo-o cation from the s th AP
	IFFT	Inverse Fast Fourier Transform
	3.6 AR modeling based PDF estimation at location #1. . . . . . . . . . . . . . 3.7 AR modeling based PDF estimation at location #2. . . . . . . . . . . . . . 3.8 Ambiguity test for 4 subcarriers, namely #1, #10, #20 and #30. . . . . . . 4.2 The overall AngLoc system architecture. . . . . . . . . . . . . . . . . . . . . 68 4.3 CFR phase changes after SFO, STO and CFO removal. . . . . . . . . . . . 70 4.4 CIR amplitude changes after SFO, STO and CFO removal. . . . . . . . . . 71 3.1 Detailed localization accuracy of all different methods . . . . . . . . . . . . 4.1 Summary of parameters for both testbeds . . . . . . . . . . . . . . . . . . . 4.2 Localization accuracy for the laboratory scenario . . . . . . . . . . . . . . . LBS Location-Based Service IoT Internet of Things GNSS Global Navigation Satellite System GPS Global Positioning System DAC Digital-to-Analog Converting HT-LTF High Throughput-Long Training Fields CFR Channel Frequency Response CIR Channel Impulse Response θs The AoA estimate at the m th RP location from the s th AP m (•) ⊤ The transpose operator (•) * m The ToF estimate at the m th RP location from the s th AP τ s The conjugate operator θs The AoA estimate at the target's unknown location from the s th AP o (•) H The Hermitian transpose operator o The ToF estimate at the target's unknown location from the s th AP τ s The expectation operator E{•} K The probability kernel function
	3.9 Ambiguity test for all 30 available subcarriers. . . . . . . . . . . . . . . . . . WLAN Wireless Local Area Network kNN k-Nearest Neighbors δ(•) The Dirac delta function 4.5 An incident signal arrives at an antenna array with an angle θ. . . . . . . . 73 Dm The Manhattan distance of AR entropy between the online fingerprints 4.3 Localization accuracy for the classroom scenario . . . . . . . . . . . . . . . RFID Radio Frequency Identification KLD Kullback-Leibler Divergence ∥ • ∥ 1 The ℓ1 norm operator at target's unknown location and the offline fingerprints at the m th RP
	3.10 A simple example of the kernel function with ρ = 2. . . . . . . . . . . . . . 4.6 The mechanism of forward-backward spatial smoothing. . . . . . . . . . . . 75 UWB Ultra Wideband MAP Maximum A Posteriori • The Hadamard product operator Dm The Edclidean distance of AoA-ToF between the online fingerprints at
	4.7 Optimal smoothing length selection through AoA spectrum. . . . . . . . . . 76 IPS Indoor Positioning System AP Access Point ⊗ target's unknown location and the offline fingerprints at the m th RP The Kronecker product operator 3.11 CNAM laboratory scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . LF Location Fingerprinting SNR Signal-to-Noise Ratio ℓm The coordinates of the m th RP we The weighting factor for AR entropy based kernel function
	3.12 The laptop with Intel 5300 NIC as signal transmitter. . . . . . . . . . . . . 4.8 The comparison of AoA estimation with and without multi-packet smoothing. 77 ToF Time of Flight AWGN Additive White Gaussian Noise ℓo The coordinates of the online unknown target wa The weighting factor for AoA based kernel function
	4.9 CNAM classroom scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 AoA Angle of Arrival EEF Exponentially Embedded Family lo ρe The AR entropy based kernel coefficient The estimated coordinates of the online unknown target 3.13 The HummingBoard Pro as mobile receiver. . . . . . . . . . . . . . . . . . . LoS Line-of-Sight GLRT Generalized Likelihood Ratio Test Nss The number of spatial streams ρa The AoA based
	3.14 The floor plan of our laboratory. . . . . . . . . . . . . . . . . . . . . . . . . 4.10 The floor plan of our classroom. . . . . . . . . . . . . . . . . . . . . . . . . . 82 RP Reference Point RBF Radial Basis Function Nsts The number of space-time streams
	RSS SFO Nt 4.11 AoA estimation errors by using different number of CSI packets. . . . . . . 84 Received Signal Strength Sampling Frequency Offset The number of transmit antennas 3.15 Temporal stability for three fingerprint signatures during the entire working MAC Medium Access Control STO Symbol Timing Offset Nr The number of receive antennas
	times of one day (8 hours). . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Optimal neighbor number selection for laboratory testbed. . . . . . . . . . . 86 IEEE Institute of Electrical and Electronics Engineers CFO Carrier Frequency Offset M The number of reference points
	3.16 Proximity test under LoS condition. . . . . . . . . . . . . . . . . . . . . . . 4.13 Optimal neighbor number selection for classroom testbeds. . . . . . . . . . 86 MIMO Multiple-Input Mulitiple-Output CPO Carrier Phase Offset S The number of access points
	OFDM Orthogonal Frequency Division Multiplexing PDP Power Delay Profile K The number of OFDM subcarriers of one CSI packet
	3.17 Proximity test under NLoS condition. . . . . . . . . . . . . . . . . . . . . . 4.14 Localization accuracy for the laboratory. . . . . . . . . . . . . . . . . . . . . 87 NIC Network Interface Card PLL Phase Locked Loop R The dimensionality of one CSI packet measured at one RP location from
	3.18 Localization accuracy of AR entropy against its original CFR amplitude. . . CSI a single AP Channel State Information 4.15 Localization accuracy for the classroom. . . . . . . . . . . . . . . . . . . . . 87 PDF Probability Distribution Function N The number of CSI packets
	L	3.19 Localization accuracy of AR entropy against its time domain CIR. . . . . . 4.16 Bar plot of localization mean error comparison for both testbeds. . . . . . . 88 The number of multipaths
		. . 20 3.20 Localization accuracy of proposed EntLoc against state-of-the-art. . . . . . 4.17 AoA estimation errors in LoS condition. . . . . . . . . . . . . . . . . . . . . 90
			xxiv xxviii xxix xxxi

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Related Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Technical Background 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Wi-Fi based Physical Measurements . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Power based Measurement . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Temporal Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.3 Angular Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.4 Channel Response based Measurement . . . . . . . . . . . . . . . . . 17 xxi Table of Contents xxii 2.2.4.1 MIMO-OFDM Mechanism . . . . . . . . . . . . . . . . . . 2.2.4.2 Channel State Information . . . . . . . . . . . . . . . . . . 2.3 Wi-Fi based Localization Algorithms . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Geometric Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.1 Trilateration . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3.2.2 Probabilistic Methods . . . . . . . . . . . . . . . . . . . . . 3 AR Entropy based Location Fingerprinting using CSI Amplitude 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Chapter Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Localization Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 EntLoc System Architecture . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Offline Radio Map Construction . . . . . . . . . . . . . . . . . . . . 3.2.2.1 Tap Filtering Preprocessing Technique . . . . . . . . . . . . 3.2.2.2 AR Entropy Estimation . . . . . . . . . . . . . . . . . . . . 3.2.3 Online Location Estimation . . . . . . . . . . . . . . . . . . . . . . . 3.2.3.1 Distance-based Proximity Comparison . . . . . . . . . . . . 3.2.3.2 Kernel Regression . . . . . . . . . . . . . . . . . . . . . . . 3.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1 Experimental Presentation . . . . . . . . . . . . . . . . . . 3.3.1.2 Benchmarks and Performance Metrics . . . . . . . . . . . . 3.3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2.1 AR Entropy Property Study . . . . . . . . . . . . . . . . . 3.3.2.2 Localization Accuracy . . . . . . . . . . . . . . . . . . . . . 3.3.2.3 Impact of Preprocessing Technique . . . . . . . . . . . . . . 3.3.2.4 Impact of Packet Number for Entropy Estimation . . . . . 3.3.2.5 Impact of RX Antenna Numbers . . . . . . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 L'architecture du système EntLoc. . . . . . . . . . . . . . . . . . . . . . . . x 2 Le plan d'étage de notre laboratoire. . . . . . . . . . . . . . . . . . . . . . . xiii 3 Précision de la localisation de l'EntLoc proposé par rapport à l'état de l'art. xiv 4 Un exemple illustratif du mécanisme du système AngLoc. . . . . . . . . . . xv 5 L'architecture globale du système AngLoc. . . . . . . . . . . . . . . . . . . . xvi 6 Le plan d'étage de notre salle de classe. . . . . . . . . . . . . . . . . . . . . xviii 7 Précision de localisation pour le laboratoire. . . . . . . . . . . . . . . . . . . xix 8 Précision de localisation pour la salle de classe. . . . . . . . . . . . . . . . . xix 1.1 Different applications of location based services. . . . . . . . . . . . . . . . . 3 1.2 Diagram for typical indoor multipath propagation. . . . . . . . . . . . . . . 4 2.2 The diagram of the TOA technique. . . . . . . . . . . . . . . . . . . . . . . 15 2.3 The diagram of the TDOA technique. . . . . . . . . . . . . . . . . . . . . . 15 2.4 MIMO-OFDM transceiver architecture. . . . . . . . . . . . . . . . . . . . . 18 2.5 A simple diagram of the channel impulse response. . . . . . . . . . . . . . . 20 2.6 An example of CIR time samples with 20 MHz bandwidth . . . . . . . .

kernel coefficient Introduction Contents 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Related Publications . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation

	With the wide-scale proliferation of wireless communication and ubiquitous computing,
	Location-Based Service (LBS) has emerged as a key enabler for myriad cutting-edge ap-
	plications in the domain of Internet of Things (IoT) [1, 2, 3]. Examples of such widespread
	LBSs can be categorized into a number of groups. To name a few, for visually-impaired
	individuals, it is imperative for them to receive autonomous and accurate navigation ser-
	vices in the complicated surroundings. In the modern mega warehouse, by leveraging
	the logistic tracing and monitoring, staff can detect the goods and inventory in real time,

  wireless communication systems, the signal receiver operates channel estimation by virtue of channel sounding mechanism. Specifically, for the packet-based IEEE 802.11n system, the transmitter sends training sequences, including High Throughput-Long Training Fields (HT-LTF) in the preamble. Once receiver detects the starting position of the first HT-LTF, it commences to derive channel state information immediately. As aforementioned in Chapter 1, CSI portrays the PHY layer channel properties in the frequency

domain and reveals the combined effects of signal multipath propagation which includes the amplitude attenuation and phase shift. The Channel Frequency Response (CFR) is represented by each CSI entry. It can be expressed by

Chapter 3 AR Entropy based Location Fingerprinting using CSI Amplitude Contents 3

  .2.3 Online Location Estimation . . . . . . . . . . . . . . . . . . . . . 3.2.3.1 Distance-based Proximity Comparison . . . . . . . . . . 3.2.3.2 Kernel Regression . . . . . . . . . . . . . . . . . . . . . 3.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1 Experimental Presentation . . . . . . . . . . . . . . . . 3.3.1.2 Benchmarks and Performance Metrics . . . . . . . . . . 3.3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2.1 AR Entropy Property Study . . . . . . . . . . . . . . . 3.3.2.2 Localization Accuracy . . . . . . . . . . . . . . . . . . . 3.3.2.3 Impact of Preprocessing Technique . . . . . . . . . . . . 3.3.2.4 Impact of Packet Number for Entropy Estimation . . .

.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Chapter Organization . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Localization Methodology . . . . . . . . . . . . . . . . . . . . . . 3.2.1 EntLoc System Architecture . . . . . . . . . . . . . . . . . . . . 3.2.2 Offline Radio Map Construction . . . . . . . . . . . . . . . . . . 3.2.2.1 Tap Filtering Preprocessing Technique . . . . . . . . . . 3.2.2.2 AR Entropy Estimation . . . . . . . . . . . . . . . . . . 33.3.2.5 Impact of RX Antenna Numbers . . . . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Moreover, at each RP position, we propose to concatenate CSI packets from S available APs to form the raw CSI signature, whose total dimensionality then extends to be S • R.Mathematically, this offline radio signature measured at the m th RP location from all S APs is given by the setH m = {H 1 m , . . . , H s m , . . . , H S m }, s ∈ [1, S]. Specifically, H s m ∈ C N ×R contains N consecutive 1 × R dimensional CSIsamples which are adequately acquired at the RP location ℓ m from the s th AP. This CSI matrix can be presented by the following equation.

The coordinate of each RP location can be denoted as ℓ m = (x m , y m ), where x m and y m are the respective X-and Y-coordinate of the m th RP, m ∈ [1, M ]. Considering that we have S Access Points (APs) as signal transmitters, each of which has N t TX antennas. One mobile user equipped with N r RX antennas is regarded as the RF receiver. Thus each TX-RX antenna pair is capable of generating up to N t • N r radio links. As for the channel state information, each CSI packet shares the same number of K OFDM subcarriers. So the dimensionality of one CSI packet measured at one RP location from a single AP can be expressed by R = N t • N r • K.

  by using EEF criterion in (3.6);

	6:	else
	7:

Table 3 .

 3

	1: Detailed localization accuracy of all different methods
	Methods	Max. err. Min. err. Mean err. Acc. at 90%
	EntLoc	3.20m	0.23m	1.84m	2.69m
	PinLoc-like	5.85m	0.46m	2.53m	4.15m
	FIFS	7.70m	0.15m	2.83m	5.56m
	Horus	9.77m	0.55m	3.50m	5.64m

4.3.2.2 Impact of Packet Number Selection for AoA Estimate

  Due to the spatial-temporal diversity of CSI measurements, one CSI packet is able to derive the AoA estimate at one time. Likewise, the excess usage of CSI packets increases the unnecessary computational complexity while fewer number of CSIs risks generating more error-prone AoA estimations.

		1
		0.8
		0.6
	CDF	0.4					40 packets
							15 packets
		0.2					10 packets 5 packets
		0	0	10	20	30	40	50
					AoA Errors (degree)

Table 4 .

 4

	1: Summary of parameters for both testbeds
	Parameters M c	w a	w e	ρ a	ρ e
	Testbed #1 12 0.57 0.43 0.14 0.23
	Testbed #2	8	0.38 0.62 0.33 0.17

Table 4 .

 4 2: Localization accuracy for the laboratory scenario Methods Max. err. Min. err. Mean err. Acc. at 90%

	AngLoc	2.67m	0.16m	1.18m	2.27m
	EntLoc	3.20m	0.23m	1.84m	2.69m
	PinLoc-like	5.85m	0.46m	2.53m	4.15m
	FIFS	7.70m	0.15m	2.83m	5.56m
	Horus	9.77m	0.55m	3.50m	5.64m
	Table 4.3: Localization accuracy for the classroom scenario
	Methods	Max. err. Min. err. Mean err. Acc. at 90%
	AngLoc	2.14m	0.07m	0.95m	1.99m
	EntLoc	2.62m	0.04m	1.33m	2.20m
	PinLoc-like	2.99m	0.27m	1.72m	2.56m
	FIFS	3.38m	0.51m	1.98m	2.94m
	Horus	4.67m	0.24m	2.44m	3.54m

Acknowledgements

The whole journey of my Ph.D. study would not have been accomplished without the Acknowledgements ii and Xiangli Yang.

Meanwhile, I would also like to send heartfelt thanks to my thesis jury members for their valuable and constructive suggestions, which further help to improve my research work towards perfection.

My graduate work was fully supported by the China Scholarship Council (CSC). I will

Acknowledgements i

Summary

In this chapter, we presented EntLoc, an AR entropy based indoor location fingerprinting system using CSI amplitude information. In EntLoc, a tap filtering scheme was first utilized to remove the noisy component in raw CFR measurements. To capture the most informative statistical information of CFR while maintaining a simple structure, we adopted AR modeling based entropy as the fingerprint to construct a robust offline radio map. In the online phase, we proposed to use Manhattan distance as similarity metric and resorted to kernel regression scheme to infer the target's location. Experimental results from the lightweight HummingBoard device showed a superior localization performance of our proposed EntLoc system with an average accuracy improvement of 27.3%, 34.9% and 47.4%, in comparison with prominent PinLoc, FIFS and Horus system, respectively. In addition, we also examined the impacts of several different parameters on EntLoc's performance, which enables us with deepening insights to efficiently and productively implement our proposed localization system.

Unwrapped Phase where ρ and ω are curve fitting variables and φ k nt,nr denotes the unwrapped CSI phase for one packet at the k th subcarrier from n th t TX antenna to n th r RX antenna,

SFO+STO Removal

• STO: In general, the receiver utilizes the auto/cross-correlator to capture and detect the presence of the OFDM symbol header, which starts with short training fields.

However, the length limitation of these STFs brings great uncertainty to determine the symbol boundary. This results in the irreversible STO. Fortunately, given that any frequency domain phase shift due to STO leads to the same amount of circular rotation in time domain, STO can be embodied as peaks at the far end of Power Delay Profile (PDP) owing to the CIR's cyclic-shifting property (e.g. Figure 4.4).

On this basis, in order to estimate STO, we first derive the PDP from the CIR vector, i.e. {h k (n)} 1≤k≤K of the n th packet. The corresponding tap index N sto (n) advance and fix the device orientation automatically, thus further improving AoA based location fingerprinting accuracy.

Alternative Hardware Implementation

As aforementioned in last Section, our entire experimental framework is established on the basis of commodity wireless IWL 5300 NIC chipset, which provides IEEE 802.11n CSI in a format of 30 subcarrier groups for both 20 MHz and 40 MHz bandwidth. In practice, this sets the limitation for some CSI based applications which demand higher resolution of CSI subcarriers. Such examples include human activity recognition [START_REF] Yang | Device-free Occupant Activity Sensing using WiFi-enabled IoT Devices for Smart Homes[END_REF], indoor distance ranging [START_REF] Zhu | π-Splicer: Perceiving Accurate CSI Phases with Commodity WiFi Devices[END_REF] and so forth. Recently, some other CSI tools like Atheros CSI tool [START_REF] Xie | Precise Power Delay Profiling with Commodity Wi-Fi[END_REF] is getting prevalent in the academic domain due to its non-grouping and noncompressed CSI reporting. Unlike Intel's 5300 NIC, the Qualcomm Atheros NIC chipset is able to report CSI value for each subcarrier, i.e., 56 subcarriers for 20MHz channel and 114 subcarriers for a 40MHz channel. Furthermore, it can also display detailed payload records and retrieve rich status information about the received packet. These additional CSI information can be of great value to help further enhance the localization performance of our AngLoc fingerprinting system.

Summary

In this chapter, we presented AngLoc, an AoA-aware probabilistic indoor location fingerprinting system using CSI information. In AngLoc, a tap filtering scheme was first proposed to remove the noisy component in raw CSI measurements. Meanwhile, for achieving accurate AoA estimation, we employed several phase calibration techniques to further compensate CSI phase errors. In the offline phase, we adopted AR modeling entropy as the amplitude based fingerprint since it captures the most informative statistical information of CSI amplitude while maintaining a simple structure. In addition, an enhanced JADE-MUSIC algorithm was leveraged to derive AoA estimates as the CSI phase based fingerprint. A robust radio map containing both CSI amplitude and phase information is then readily constructed. In the online phase, for a mobile target, we first narrowed