Viet-Cuong Ta

Trung-Kien Dao
email: trung-kien.dao@mica.edu.vn

Dominique Vaufreydaz
email: dominique.vaufreydaz@inria.fr

Eric Castelli
email: eric.castelli@univ-grenoble-alpes.fr

Collaborative Smartphone-Based User Positioning in a Multiple-User Context Using Wireless Technologies †

Keywords: indoor localization, indoor navigation, multi-sensor fusion, multiple-user positioning

For the localization of multiple users, Bluetooth data from the smartphone is able to complement Wi-Fi-based methods with additional information, by providing an approximation of the relative distances between users. In practice, both positions provided by Wi-Fi data and relative distance provided by Bluetooth data are subject to a certain degree of noise due to the uncertainty of radio propagation in complex indoor environments. In this study, we propose and evaluate two approaches, namely Non-temporal and Temporal ones, of collaborative positioning to combine these two cohabiting technologies to improve the tracking performance. In the Non-temporal approach, our model establishes an error observation function in a specific interval of the Bluetooth and Wi-Fi output. It is then able to reduce the positioning error by looking for ways to minimize the error function. The Temporal approach employs an extended error model that takes into account the time component between users' movements. For performance evaluation, several multi-user scenarios in an indoor environment are set up. Results show that for certain scenarios, the proposed approaches attain over 40% of improvement in terms of average accuracy.

Introduction

Satellite navigation systems such as GPS rely heavily on the exact timing of signals. Therefore, in an indoor environment where radio signals usually suffer from hazardous propagation effects, including fading, multipath, reflection, etc., their applicability is generally ignored. Among others, Wi-Fi and Bluetooth widely available in nowadays smartphones could be considered as low-cost alternative wireless-based solutions for positioning purpose. These two technologies come with the Receive Signal Strength (RSS) or Receive Signal Strength Index (RSSI) as a source of information from the environment. The information can be used in different approaches to compute the device's position.

Novel Wi-Fi-based positioning methods on smartphones can find the position by scanning the available Wi-Fi access points in the surrounding environment. The mean distance error is around 5 m [START_REF] Torres-Sospedra | The Smartphone-Based Offline Indoor Location Competition at IPIN 2016: Analysis and Future Work[END_REF], due to the unreliable characteristics of the Wi-Fi signal propagation in an indoor environment. The Bluetooth characteristics are very similar to those of Wi-Fi in terms of the underlying physical radio characteristics and application aspect. Therefore, it is possible to develop a positioning system in an analogous manner to the Wi-Fi-based ones. However, the Bluetooth communication range is lower, which leads to a higher number of static beacons in deployment [START_REF] Faragher | An analysis of the accuracy of Bluetooth low energy for indoor positioning applications[END_REF].

Nevertheless, in a multiple-user positioning context, the Bluetooth data can complement the Wi-Fi data to base a collaborative positioning framework [START_REF] Jun | Social-Loc: Improving indoor localization with social sensing[END_REF]. When each user moves with a smartphone in a public area, it is possible to keep the smartphone's Bluetooth in visible mode. Then, if a device sees another one nearby, the RSS from Bluetooth data can give an approximation of the relative range between the two devices. Given the estimated pair-to-pair distance information, it is possible to refine the output positions from Wi-Fi data. This approach does not require installing additional infrastructures and is compatible with the standard Bluetooth protocol, which is generally supported by smartphones.

There are several key challenges of the proposed approach. The first difficulty is the nondeterministic propagation characteristics of radio signals in an indoor environment. The noise affects both Wi-Fi output positions and Bluetooth output distances, especially in the case of moving users. The second one is the asynchronous events between the Wi-Fi and Bluetooth scanning processes of the smartphones. In other words, the scanning cycles for each technology in the smartphones are not guaranteed to start and finish at the same time. The time difference adds a level of uncertainty between the output positions from Wi-Fi data and Bluetooth data.

In this work, we try to overcome these problems by considering the so-called Non-temporal and Temporal approaches. In the former one, the distance error of the Wi-Fi output position is modeled by a Gaussian distribution. Similarly, another Gaussian distribution is used to describe the distance error between two devices from the Bluetooth inquiry process. Wi-Fi and Bluetooth position outputs within a short time interval are treated as if they happened in the same time window. An error function is then defined to measure the mismatch between the two distributions. By neutralizing the mismatch, it is possible to improve the position results of the Wi-Fi output. In the latter approach, the time component of the users' movement is incorporated into the error function. The error function takes the positions of all the users as an input. We then make use of particle-filter-based tracking to minimize this error function. The observation model required by the particle filter is derived from a combination between Wi-Fi and Bluetooth scanning data.

This paper is an extension of a former conference article [START_REF] Ta | Smartphone-based user positioning in a multiple-user context with Wi-Fi and Bluetooth[END_REF] with more updated results, detailed explanation and discussion; in addition, it is part of a Ph.D. thesis [START_REF] Ta | Smartphone-Based Indoor Positioning Using Wi-Fi, Inertial Sensors and Bluetooth[END_REF] and is arranged as follows. In Section 2, related works on smartphone-based indoor positioning and collaborative positioning are discussed. Section 3 introduces different techniques available for Wi-Fi positioning, then our proposed approaches for combining Wi-Fi and Bluetooth data are described in Section 4. Experiments and results are represented and discussed in Section 5, and finally, Section 6 contains conclusionary remarks and future prospects.

Related Works

Works on smartphone-based positioning in an indoor environment involve various kinds of technologies such as GPS, camera, Personal Dead Reckoning, Bluetooth, Wi-Fi, etc. Among them, Wi-Fi has been drawing the most attention thanks to its ubiquity, low cost and privacy. Popular approaches include geometry-based and fingerprinting-based ones. The geometry-based approaches rely on the estimation of certain geometry properties, including distance and angle, to calculate the device's position. For calculating the distance, the well-known Log-Distance Path Loss (LDPL) model can be used [START_REF] Rappaport | Wireless Communications: Principles and Practice[END_REF]. More complex models are introduced in [START_REF] Bahl | RADAR: An in-building RF-based user location and tracking system[END_REF][START_REF] Bose | A practical path loss model for indoor WiFi positioning enhancement[END_REF][START_REF] Chintalapudi | Indoor localization without the pain[END_REF][START_REF] Huang | A Practical, Robust and Fast Method for Location Localization in Range-Based Systems[END_REF]. However, these models are defined with a set of parameters and usually require complex calibration processes.

Recently, the Wi-Fi fingerprinting-based methods have been preferred as they benefit from the ubiquity of the WLAN infrastructure. Recent works on smartphone-based Wi-Fi fingerprinting have reached a mean distance error of around 5 m [START_REF] Torres-Sospedra | The Smartphone-Based Offline Indoor Location Competition at IPIN 2016: Analysis and Future Work[END_REF][START_REF] Mathisen | A comparative analysis of Indoor WiFi Positioning at a large building complex[END_REF]. In general, fingerprinting approaches include two phases: site survey and model training. In the first phase, a mapping from location to RSS/RSSI values in buildings is collected. The mapping is then used to learn the reverse relationship, from the scanned RSS/RSSI values to the locations. For learning techniques, the well-known K-Nearest Neighbors (KNN) and its alternatives are among the most popular ones [START_REF] Ma | An improved WiFi indoor positioning algorithm by weighted fusion[END_REF][START_REF] Liu | Smallest enclosing circle-based fingerprint clustering and modified-WKNN matching algorithm for indoor positioning[END_REF][START_REF] Abed | An adaptive KNN based on multiple services set identifiers for indoor positioning system with an ensemble approach[END_REF]. In [START_REF] Torres-Sospedra | Ensembles of indoor positioning systems based on fingerprinting: Simplifying parameter selection and obtaining robust systems[END_REF], the authors experiment with a wide range of KNN parameters to get a set of models. An ensemble result of the generated KNN models has a mean distance error of around 6 m. Besides KNN-based learning methods, decision tree-based learning methods can be used for learning the Wi-Fi signal characteristics with prominent results [START_REF] Ta | Smartphone-based user positioning in a multiple-user context with Wi-Fi and Bluetooth[END_REF][START_REF] Ta | Smartphone-based user location tracking in indoor environment[END_REF]. In [START_REF] Redondi | Building up knowledge through passive WiFi probes[END_REF], a comparison between a LDPL-based approach and fingerprinting-based approaches is introduced, showing that fingerprinting-based approaches have better performance. The accuracy of the fingerprinting-based approaches is not only dependent on the learning model but also on the quality of the mapping in the first phase. For the practicality of the system, the time and cost of the site-survey phase are important factors [START_REF] He | Wi-Fi fingerprint-based indoor positioning: Recent advances and comparisons[END_REF]. There are various works that aim to reduce the complexity of the site-survey phase in many aspects. In [START_REF] Kim | Passive WiFi fingerprinting method[END_REF], the authors introduce a passive collection method that collects unlabeled fingerprints of the Wi-Fi signal. In the context of multiple users, Wi-Fi probes information can be used to build a survey-free fingerprinting database, as presented in [START_REF] Potortì | Localising crowds through Wi-Fi probes[END_REF]. As different devices often have different Wi-Fi signal characteristics, [START_REF] Davies | A Bayesian approach to dealing with device heterogeneity in an indoor positioning system[END_REF] proposes a Bayesian approach for dealing with device heterogeneity-related issues in indoor positioning.

Given the efficiency of the Wi-Fi-based positioning, the outputs from the system are often considered a data source for integrating with other positioning techniques. In [START_REF] Evennou | Advanced integration of WiFi and inertial navigation systems for indoor mobile positioning[END_REF], the authors build a distribution of possible points given a Wi-Fi measurement. The distribution is assumed to be Gaussian. The center is calculated from a fingerprinting approach. The distribution is then used to correct the output of an inertial-sensor-based system. A more complex fusion approach is introduced in [START_REF] Chen | Intelligent fusion of Wi-Fi and inertial sensor-based positioning systems for indoor pedestrian navigation[END_REF], where the positions from the Wi-Fi system are used to shift the entire trajectory of PDR tracking by a gradient-descent-based search. In [START_REF] Deng | Continuous indoor positioning fusing WiFi, smartphone sensors and landmarks[END_REF], a fusion model for Wi-Fi, PDR and Landmark is proposed in such a manner that the Wi-Fi RSS measurements are used to build a measurement model based on kernel density estimation.

For positioning, Bluetooth technology can be used in the same way as Wi-Fi. Bandara et al. [START_REF] Bandara | Design and implementation of a bluetooth signal strength-based location sensing system[END_REF] using up to four Bluetooth antennas as static stations to locate a Bluetooth tag within a room with an area of 4.5 m × 5.5 m. The RSSI value is used to classify the tag's position between different subareas of the room. Pei et al. [START_REF] Pei | Using inquiry-based Bluetooth RSSI probability distributions for indoor positioning[END_REF] employ a fingerprinting-based approach to track a moving phone. The setup includes only three Bluetooth beacons in a corridor-like space of 80 m long approximately. The horizontal error is reported as 5.1 m. More recent works employ the new Bluetooth Low Energy (BLE) technology [START_REF] Gomez | Overview and evaluation of Bluetooth low energy: An emerging lowpower wireless technology[END_REF]. BLE beacons are smaller, more energy efficient, and able to power up for a longer period, and hence are more convenient for positioning purposes. Faragher and Harle [START_REF] Faragher | An analysis of the accuracy of Bluetooth low energy for indoor positioning applications[END_REF] provide an in-depth study of using BLE for indoor positioning. The distance error of their Bluetooth-based approach could reach as low as 2.6 m for 95% of the time. However, a high number of beacons should be deployed to reach the above performance. The study also addresses some issues of the BLE signal such as the scanning cycle, fast fading effects and Wi-Fi scanning interference. A similar performance for BLE-based indoor positioning is reported in [START_REF] Zhuang | Smartphone-based indoor localization with Bluetooth low energy beacons[END_REF], where the authors employ a fingerprintingbased approach with the RSS value from the installed BLE beacons.

In a scenario involving multiple devices, there are several works on collaborative localization. Those works rely on some specific wireless technologies that support peer-to-peer communication, including Bluetooth and Wi-Fi Direct, which are capable of discovering the existence of nearby neighbors. In [START_REF] Liu | Face-to-face proximity estimation using Bluetooth on smartphones[END_REF], the task of detecting face-to-face proximity is studied. Smartphones are used to scan nearby visible Bluetooth devices in daily usage. From the received RSSI, the relative distance between two devices is calculated. The distance is then used to detect whether the two users are close to each other. To deal with noisy Bluetooth signals, additional techniques such as RSSI smoothing and light sensor data are introduced for calculating a more accurate distance. In [START_REF] Jun | Social-Loc: Improving indoor localization with social sensing[END_REF], the Social-Loc system is proposed and uses Wi-Fi Direct technology for detecting two events, namely Encounter and Non-encounter, between each pair of users. In that work, the authors found the RSSI peak for separating Encounter and Non-Encounter events. These detected events are then used to improve the Wi-Fi fingerprinting and Dead Reckoning tracking. The drawback of Wi-Fi Direct technology is that it does not allow regular Wi-Fi scanning. Therefore, the proposed Social-Loc is more suitable for improving the Dead Reckoning tracking than the Wi-Fi fingerprinting tracking. In [START_REF] Nowicki | A multi-user personal indoor localization system employing graph-based optimization[END_REF], a graph-based optimization process is used to combine different trajectories from multiple users. The graph is built by using the Personal Dead Reckoning data from the phone as moving constraints. It is then used to correct and extend the existing fingerprinting database.

Wi-Fi Fingerprinting for Indoor Positioning

In a large public area, fingerprinting-based approaches are often more preferable thanks to their lower labor cost in deployment.

In this section, different approaches of Wi-Fi fingerprinting methods for dealing with such types of training data are summarized. Based on the performance of these approaches, several ensemble strategies are proposed to improve the overall positioning performance. By combining uncorrelated models, it is expected to reduce the errors in cases of lacking training data. Alternative fingerprinting approaches rely on statistical models without directly dealing with the signal propagation complexity. The feature space is the RSS feature vector, and the target is the device's position. Signal filtering can be added to boost the position accuracy.

Ensemble methods for improving learning models are a well-known approach in machine learning. For Wi-Fi fingerprinting-based positioning, Torres-Sospedra et al. in [START_REF] Torres-Sospedra | Ensembles of indoor positioning systems based on fingerprinting: Simplifying parameter selection and obtaining robust systems[END_REF] propose an ensemble framework based on KNN models. The authors vary a set of parameters and then combine all the generated models to have a more stable performance. These parameters include the number 𝐾 of considered neighbors, the distance/similarity measure of signal feature vector, the data representation, and the method of filtering out weak signals. However, because all the models are derived from the KNN model, their learning capability can be highly correlated. Thus, it may lead to an overfitting model when the ensemble step is carried out, especially in the context of limited training data. This study shares the similar idea of ensemble models but in a different way. Mostly, we aim to reduce the dependence on the KNN model by varying the Wi-Fi-signal-based features and the learning models.

In our approach, the Wi-Fi fingerprinting problem is first transformed into a standard learning problem. The learning problem includes a set of feature vectors and its desired labels. The label in this case is the coordinates of each sample. Two other feature sets, filter-based and hyperbolic-based features, are derived directly from the default raw signal features. The two additional features are reported with good performance for building Wi-Fi fingerprinting models. Three different learning models, which are KNN, Random Forest and Extreme Gradient Boost, can be used in the learning phase. The KNN model is well-known for working with Wi-Fi fingerprinting data. Both Random Forest and Extreme Gradient Boost models are tree-based methods that have good performance against various types of data. The two additional learning models are added to make the following ensemble step rely less on the KNN method. The learning targets are also selected between the regression and the classification objective functions.

Wi-Fi Fingerprinting Features

For building fingerprinting models, it is necessary to collect the training Wi-Fi signal data. Based on these data, signal characteristics are determined for each point. We can start with the raw features that only include the RSS value of nearby access points. The raw RSS value is expected to have a stable feature space for learning the target positions. Besides that, as our target is to vary learning spaces, two feature sets, the Filtering-based features [START_REF] Marques | Combining similarity functions and majority rules for multibuilding, multi-floor, WiFi positioning[END_REF] and the Hyperbolic Location Fingerprinting features [START_REF] Kjaergaard | Hyperbolic location fingerprinting: A calibration-free solution for handling differences in signal strength (concise contribution)[END_REF], are added. Generally, the two latter feature sets could be considered as an improvement from the standard raw features. We add some minor modifications to make the added features applicable with the lack of training Wi-Fi RSS data.

Raw Features

From the scanning process, the Wi-Fi access points in the surrounding environment are usually presented as pairs of MAC addresses and RSS values. The MAC address is used as the access point's identifier, and the RSS value is the access point's signal quality at the position of the mobile device. Each Wi-Fi data package within a short time window is grouped in the same scanning cycle. The raw features are built from a list of these two values of a scanning cycle. The length of a specific scanning cycle depends on the smartphone's operating system. Practically, one could use a fixed time interval for defining a complete Wi-Fi scanning process of smartphones.

To create a matrix representation of the raw features, it is necessary to collect all the appeared access points within the collected data. With 𝐷 access points, namely 𝐴𝑃 , 𝐴𝑃 ,..., 𝐴𝑃 , the feature vector has exactly 𝐷 dimensions. Assume at time 𝑡, there is a complete scan cycle at point 𝑃. Each scan cycle is then used to create a fixed-length feature vector 𝑟 where each value 𝑟 is the RSS value of the access point 𝐴𝑃 if it appears in the scan. In the other case, the 𝑟 takes the minimum value 𝑀𝐼𝑁 , which is selected to be lower than any other scanned RSS values that appear in the data. The selection of 𝑀𝐼𝑁 could affect several types of learning models, such as KNN-based ones. More specifically, the KNN models use the distance metrics for comparing the similarity between two feature vectors. Therefore, the value of 𝑀𝐼𝑁 can be selected to put more emphasis on the differences between the list of unseen access points from each feature vector.

Filtering-Based Features

The filtering-based approach could be considered a direct improvement from the standard raw features. In the original version [START_REF] Marques | Combining similarity functions and majority rules for multibuilding, multi-floor, WiFi positioning[END_REF], Marques et al. split the whole feature space into sub-regions. The split criterion is the indices of the two strongest access points of the raw signal vector 𝑟. In a later study [START_REF] Moreira | Wi-Fi fingerprinting in the real world-RTLS@UM at the EvAAL competition[END_REF], the number of considered strongest access points was extended to three. Both works have good results when combined with KNN-based learning models. However, the results are tested in a large training data set (nearly 10,000 samples). The large training samples allow the filtering step to be able to split the feature space into sufficiently smaller subspaces. With smaller training data, its performance is moderate, as stated in [START_REF] Torres-Sospedra | The Smartphone-Based Offline Indoor Location Competition at IPIN 2016: Analysis and Future Work[END_REF].

In our context, to promote simplicity in deployment, suppose that only a small amount of data are available, then it is not a good option to adopt the original approach. Instead, the feature space could be split indirectly by adding features to the standard RSS feature vector. From the starting 𝐷 dimensions, each corresponding to an appeared access point, an additional 𝐷 features 𝑠 𝑠 , 𝑠 , . . . , 𝑠 is added to the standard 𝑟 𝑟 , 𝑟 , . . . , 𝑟 . The value of 𝑠 is defined as:

𝑠 𝐼𝑁𝐹 if 𝑟 is one of two highest values of r, 0 otherwise. (1)
Then, the new feature vector 𝑞 is a combination of 𝑟 and 𝑠: 𝑞 𝑟 , 𝑟 , . . . , 𝑟 , 𝑠 , 𝑠 , . . . , 𝑠 .

The purpose of using 𝐼𝑁𝐹 instead of a simple value constant 1 is to allow the combined vector 𝑞 to work with several types of distance metrics. By selecting an appropriate value of 𝐼𝑁𝐹 , it is possible to put more weight into the difference in 𝑠 rather than the difference in 𝑟.

The resulting vector length is double the standard one's. The number of strongest access points can be selected as an adjustable parameter. Normally, a value of 2 or 3 is chosen for effective splitting of the standard RSS feature spaces. In comparison to the original filter version, there is a minor modification in our implementation version.

Hyperbolic Location Fingerprinting Features

As the RSS value is highly dependent on the device, several methods have been proposed to overcome the hardware-dependent issue, including mean normalization, application of linear transformations, and usage of signal-calibration free approaches. Roughly speaking, most methods rely on a linear correlation of RSS values for different devices. The calibration-free approaches can be considered more general as they do not need to additionally calibrate data to find the linear transform. The methods encode the transforms' parameters directly into the feature vector. Popular methods include the RSS difference [START_REF] Dong | A calibration-free localization solution for handling signal strength variance[END_REF] and hyperbolic location fingerprinting (HLF) features [START_REF] Kjaergaard | Hyperbolic location fingerprinting: A calibration-free solution for handling differences in signal strength (concise contribution)[END_REF].

For reducing the effect of noisy RSS value between different devices, the HLF takes the relative difference for every pair of access points. Other than that, the RSS values is transformed into logarithm space. More specifically, from the standard raw features 𝑟 with 𝐷 dimensions, the HLF is a vector ℎ which has a size of 𝐷 𝐷 1 /2. The explicit values of ℎ are given as:

ℎ diff 𝑟 , 𝑟 , … , diff 𝑟 , 𝑟 , diff 𝑟 , 𝑟 , … , diff 𝑟 , 𝑟 , … , diff 𝑟 , 𝑟 , (3)
where the different operations between two RSS values 𝑟 and 𝑟 is given by:

diff 𝑟 , 𝑟 log 𝑟 𝑟 log 1 𝑟 , (4)
with 𝑟 being the maximum RSS value. When there are hundreds of access points available in the environment, the transformation in Equation ( 3) results in thousands of dimensions in the feature spaces. Thus, collecting enough data for training the HLF features could be problematic. Therefore, applying a further dimension reduction operator to get a suitable feature representation from the generated HLF features could be suitable to reduce the dimensions from 𝐷 𝐷 1 /2 to 𝐷′. Several possible approaches are Random Tree Embedding [START_REF] Geurts | Extremely randomized trees[END_REF], Principle Component Analysis, and Truncated-Single Value Decomposition [START_REF] Halko | Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions[END_REF]. The value of 𝐷′ should be chosen as small to make the learning process in later training phases feasible.

After the feature selection step, the collected data can be represented as the lists of pairs:

𝑆 𝑋 , 𝑃 , 𝑋 , 𝑃 , . . . , 𝑋 , 𝑃 , (5)
with 𝑋 being the correspondent 𝑁-dimensional vector and 𝑃 the position of the 𝑖 sample for 𝑖 ∈ 1, 𝑀 . For simplicity, the notation 𝑋 could be in one of three types of features, the raw features 𝑟, the filters-based features 𝑠, or the HLF-based features ℎ.

Learning Models

For learning the mapping from RSS-based vector to position, a number of model families are available for usage, which include Nearest Neighbors, Random Forest [START_REF] Breiman | Random forests[END_REF] and Extreme Gradient Boost [START_REF] Chen | Xgboost: A scalable tree boosting system[END_REF]. While the KNN model is a popular choice to work with the Wi-Fi fingerprinting data, the others are tree based. They are capable of learning on a small amount of training data. Each type of model can also be applied with either options, i.e., classifier or regressor.

K-Nearest-Neighbor Model

The K-Nearest Neighbors (KNN) model requires a distance function between two vectors in the feature space. Similar distance errors could be achieved with a group of distance functions including cosine, Euclidean, Hellinger, and Chi-square. We choose the Euclidean function for measuring the distance between two feature vectors. For an input 𝑋 , the standard KNN algorithm finds 𝐾 samples in 𝑆, which have the smallest distances to 𝑋 . Assume the list of 𝐾 samples is:

nearest 𝑋 , 𝑑 𝑋 , 𝑌 , 𝑋 , 𝑌 , . . . , 𝑋 , 𝑌 , (6)
then the corresponding 𝑃 is computed as the centroid of all 𝑃 in the above list. Parameter 𝐾 defines how many nearest samples in the feature space are taken for computing 𝑃 . A small value of 𝐾 tends to make to model overfitting. For example, with 𝐾 1, 𝑃 is the position with the nearest sample in the training set 𝑆. When 𝐾 increases, more nearest samples are taken into the computation, thus making the output more robust. However, if there are only a few samples, 𝑃 may fluctuate between them. In the specific task of Wi-Fi fingerprinting, 𝐾 is usually chosen from in the range of 1, 10 .

There are some variants of the KNN model. The most popular one is the weighted-KNN approach, in which 𝑃 is calculated by a weighted sum of average of 𝑃 . The specific weight is a function, which is computed from the similarity between 𝑋 and 𝑋 .

Random Forest Model

Random Forest (RF) model is based on building a list of decision trees. Each tree would split the feature space into random subspaces. Each subspace is expected to contain the samples that have identical or similar target positions. The work in [START_REF] Lin | Random forests and adaptive nearest neighbors[END_REF] shows that the RF model can be justified as an adaptive weighted-KNN model.

For training a standard decision tree, the training data 𝑆 is split from top down by a pair of feature and values until a certain criterion is met. The criterion is based on the depth of the tree or errors within for defining a leaf node. Table 1 shows a set of three training samples on the raw RSS data. A decision tree could be built as shown in Figure 1. In this example, the building process stops when every leaf contains only one sample. There are also other decision trees with different node splitting criteria that can split the tree samples 𝑋 , 𝑋 and 𝑋 . A decision tree with two internal and three leaf nodes for splitting 𝑋 , 𝑋 , 𝑋 in Table 1.

Given a training data set, there are several well-known methods for building a decision tree such as ID3 [START_REF] Quinlan | Induction of decision trees[END_REF] or CART [START_REF] Breiman | Classification and Regression Trees[END_REF]. Because the building decision tree process always seeks for an optimal way to split the feature space, the resultant tree is likely overfitting. The RF model is introduced for overcoming the overfitting issue by building a set of decision trees. In general, none of the trees are optimal, but all have a predictive capability. Bagging methods and a random subset of features are employed for lowering the correlation between each tree in the forest. The output of the RF model is the mean of all the predictions of each decision tree in the forest.

Extreme Gradient Boost Model

Extreme Gradient Boost (XGB) model is also a tree-based learning method. The training process includes several rounds. Starting from a simple prediction, trees are added to the model based on a boosting approach, which tries to reduce the error of the objective function of the previous step. Popular objective functions for the XGB model include the mean square error for regression or logistic function for classification. Apart from the objective function, additional components that measure the model complexity are also added. The objective function is chosen in a way that it can compute the gradient based on features values. Therefore, at each splitting step, the built tree can choose the right ways to split the feature space. The model is also included with other techniques for preventing overfitting such as a random subset of features or early stopping criteria.

Using Bluetooth Data to Improve Wi-Fi Positioning

Wi-Fi and Bluetooth are two data streams which provide different information that can contribute to the derivation of the users' position. In the case of multiple users, the distance from one user to others can be calculated from the Bluetooth scanning process. A way to combine the two different data streams is to use a central server that keeps all the available positioning information from each participating device. More precisely, the information includes the estimated positions from Wi-Fi data and the estimated distances between pairs of devices from Bluetooth data.

Fusion Framework for Wi-Fi and Bluetooth

For the fusion, Wi-Fi and Bluetooth data are sent to the server. For each completed Wi-Fi scan cycle, the device sends its identifiers (MAC addresses) of the found access points and the corresponding RSS values. Each Wi-Fi scan cycle takes a few seconds and is dependent on the device itself as well as the number of access points. The second type is the Bluetooth scanned information, which also includes the Bluetooth MAC addresses of visible devices and the corresponding RSS values. On the server, the data from Wi-Fi and Bluetooth scans give different ways to calculate the users' positions.

Figure 2 illustrates the principle of our approach with an example context that involves two users, namely 𝑖 and 𝑗. The two users' devices keep gathering information on Wi-Fi access points and Bluetooth devices in the environment and sending them to the server. Once the server receives the data, it will store it as events associated with either Wi-Fi or Bluetooth typed labels. The figure illustrates three events: two Wi-Fi scans and a Bluetooth scan. Assume that the real positions of users 𝑖 and 𝑗 at time 𝑡 are denoted as 𝑥 , , 𝑦 , and 𝑥 , , 𝑦 , , respectively, the real distance between the two users is denoted as 𝑑 , . At time 𝑡 , the position of user 𝑖 can be estimated from the Wi-Fi scan information device 𝑖, and is denoted as 𝑥 , 𝑦 . Similarly, at time 𝑡 , when the Wi-Fi information from device 𝑗 is available when it completes a scan, we can estimate the position of user 𝑗, which results in 𝑥 , 𝑦 . Besides that, the Bluetooth scan information when available can lead to an estimated relative distance between these two users. At time 𝑡 , if device 𝑖 is found by device 𝑗 with its Bluetooth scan process, we can also make an estimation 𝑙 of the relative distance real distance 𝑑 , , based on the corresponding RSS value.

Alternatively, we can estimate 𝑑 , differently by using the output position from the Wi-Fi information for the two users. As the true value 𝑑 , is unknown, our task is looking for ways to minimize the difference between the values estimated independently from the two sources. However, this Wi-Fi information is generally not available in a synchronous manner with the Bluetooth information. In the current example, it is available at times 𝑡 and 𝑡 , but not 𝑡 . To address the asynchronous fusion of the relationship between Wi-Fi and Bluetooth for improving positioning results, we propose two approaches that utilize the timestamp differently:



The first approach is called Non-temporal, where the temporal relationship between events which are within a time interval window is ignored. They are treated as if they happened at the same time. An error estimation function is established by using the users' position as the function's parameters. By minimizing the error function, it can be used to smooth the mismatch between Wi-Fi data and Bluetooth data, thus reducing the positioning error from Wi-Fi.



The second approach is called a Temporal one, in which we introduce the time component into the basic error function of the first approach. More precisely, the new error function includes the devices' position at each timestamp. For minimizing the new error function, a particle-based approximation is carried out.

For both approaches, in principle, any Wi-Fi and Bluetooth models that are able to deduce the relative user distance can be used. In this study, a fingerprinting model is used for Wi-Fi, and the LDPL model for Bluetooth.

Non-Temporal Approach

In the Non-temporal approach, a sliding window of size Δ𝑡 seconds is used. All the events from 𝑡 to 𝑡 Δ𝑡 are considered as if they happened at the same time. Given a pair of users 𝑖 and 𝑗, one can assume that there exists both Wi-Fi data and Bluetooth data within the time frame from 𝑡 to 𝑡 Δ𝑡. Let 𝑤 and 𝑤 be the Wi-Fi scan information from the two users, and 𝑟𝑠𝑠 be the RSS value of the Bluetooth scan. In this Non-temporal approach, we remove the time variable 𝑡 from the parameters. The likelihood function with the two users' positions 𝑥 , 𝑦 and 𝑥 , 𝑦 , and the parameters 𝑃 𝑥 , 𝑦 , 𝑥 , 𝑦 |𝑤 , 𝑤 , 𝑟𝑠𝑠 are created by decomposing the function into three separate components:

𝑃 𝑥 , 𝑦 , 𝑥 , 𝑦 |𝑤 , 𝑤 , 𝑟𝑠𝑠 𝑃 𝑥 , 𝑦 |𝑤 𝑃 𝑥 , 𝑦 |𝑤 𝑃 𝑥 , 𝑦 , 𝑥 , 𝑦 |𝑟𝑠𝑠 , (7)
where 𝑃 𝑥 , 𝑦 |𝑤 and 𝑃 𝑥 , 𝑦 |𝑤 are the error estimations from Wi-Fi data of users 𝑖 and 𝑗, respectively, and 𝑃 𝑥 , 𝑦 , 𝑥 , 𝑦 |𝑟𝑠𝑠 is the error from the Bluetooth data. Let 𝑥 , 𝑦 be the computed position from the scan 𝑤 . By assuming that the distribution of the real position 𝑥 , 𝑦 is a 2D Gaussian around the estimated position 𝑥 , 𝑦 , then 𝑃 𝑥 , 𝑦 |𝑤 is determined by:

𝑃 𝑥 , 𝑦 |𝑤 √ 𝑒 . (8)
Similarly, 𝑃 𝑥 , 𝑦 |𝑤 can also be determined given the estimated position 𝑥 , 𝑦 from the Wi-Fi positioning model:

𝑃 𝑥 , 𝑦 |𝑤 √ 𝑒 . (9)
To estimate the Bluetooth part of the estimated likelihood, we first calculate 𝑙 from 𝑟𝑠𝑠 by using the LDPL model:

𝑙 𝑙 10 . ( 10
)
where 𝑟𝑠𝑠 is the RSS value at distance 𝑙 , and 𝑛 is the path-loss exponent. The three values 𝑟𝑠𝑠 , 𝑛, and 𝑙 are known constant parameters. The value of 𝑙 is the estimation of the real distance 𝑑 , which comes directly from the real positions of users 𝑖 and 𝑗, that are 𝑥 , 𝑦 and 𝑥 , 𝑦 :

𝑑 𝑥 𝑥 𝑦 𝑦 . (11)
One can assume that 𝑙 has a Gaussian distribution around 𝑑 , then the Bluetooth likelihood can be estimated by another Gaussian kernel:

𝑃 𝑥 , 𝑦 , 𝑥 , 𝑦 |𝑟𝑠𝑠 1 √2𝜋𝛿 𝑒 , ( 12
)
where 𝛿 is a constant characterizing the reliability of the LDPL on the RSS Bluetooth signal.

From Equations ( 8)-( 10), the likelihood function in Equation ( 7) can be rewritten as:

𝑃 𝑥 , 𝑦 , 𝑥 , 𝑦 |𝑤 , 𝑤 , 𝑟𝑠𝑠 𝐶 𝑒 , (13)
where 𝐶 is a constant, and 𝑔 is a function of 𝑥 , 𝑦 , 𝑥 , 𝑦 , that is: For a fast computation of the minimum value of 𝑔 , two constraints can be used based on its symmetric property. The first constraint is that the four points 𝑥 , 𝑦 , 𝑥 , 𝑦 , 𝑥 , 𝑦 , and 𝑥 , 𝑦 are aligned. The second constraint is that the distance between 𝑥 , 𝑦 and 𝑥 , 𝑦 and the distance between 𝑥 , 𝑦 and 𝑥 , 𝑦 are equal. The function is then rewritten as a function of the distance 𝑟 between 𝑥 , 𝑦 and 𝑥 , 𝑦 , whose minimum value can be easily computed. The updated positions of users 𝑖 and 𝑗 are then calculated from 𝑟 by using the two mentioned constraints:

𝑔 𝑥 𝑥 𝑦 𝑦 𝑥 𝑥 𝑦 𝑦 2𝛿 𝑥 𝑥 𝑦 𝑦 𝑙 2𝛿 . (14)
𝑔 𝑟 𝑟 𝛿 𝑑 2𝑟 𝑙 2𝛿 . (15)
The time interval of validity for the incoming Wi-Fi and Bluetooth data makes the error probability able to be approximated by function 𝑔. However, it introduces several drawbacks. The first one is due to the users' movement, i.e., the distances estimated using Wi-Fi and Bluetooth data may vary in different time windows. The second drawback is the difficulty to determine the time interval length Δ𝑡 for grouping consecutive Wi-Fi and Bluetooth data. The later Temporal approach is designed to address these problems of the Non-temporal approach.

Temporal Approach

In the Temporal approach, we attempt to use the temporal relationship in the likelihood function 𝑃. Instead of relying only on the position of two users at specific timestamps to measure the errors; the likelihood function is extended to include the moving path of all the users. Each moving path is considered as a sequence of points. The new likelihood function would take all the points as parameters.

We first construct the likelihood function 𝐹, which is a more complete form of 𝑃 that is based on three probability functions. A motion model 𝑀 is used to establish the relationship between the positions at time indices 𝜏 and 𝜏 1 when a user moves. Two functions 𝑊 and 𝐵 are defined as the probability distributions of the Wi-Fi scan results and the distance based on Bluetooth RSS values from each pair of devices, respectively.

Assume that there are 𝑁 users to track in 𝑇 time indices. The time component is added to the position of user 𝑖 at time index 𝜏 as 𝑥 , 𝑦 . Normally, we can select the time difference value based on the specific purpose of the positioning system. For modeling purposes, it is required that the time index 𝜏 contains all the event timestamps from Wi-Fi and Bluetooth of all the participant devices. Approximately, all the float-typed timestamps could be rounded to the nearest integer values. The motion model for each user 𝑖 is defined as a probability function characterizing the dependency of the current position to the previous one, or 𝑀 𝑥 , 𝑦 |𝑥 , 𝑦 . The moving component for 𝑇 time indices for each user 𝑖 is then calculated by:

𝐹 𝑀 𝑥 , 𝑦 𝑥 , 𝑦 . (16)
For each user 𝑖, assume that 𝐾 within 𝑇 time indices corresponds to the Wi-Fi scan records. Denote the timestamps for Wi-Fi events as 𝑢 , 𝑢 ,..., 𝑢 , then for each 𝑢 , the corresponding Wi-Fi scan information is denoted as 𝑤 . The function 𝑊 is used to estimate the likelihood probability 𝑊 𝑥 , 𝑦 𝑤 . Then, the Wi-Fi component 𝐹 of user 𝑖 is established from all the 𝐾 available Wi-Fi scans:

𝐹 𝑊 𝑥 , 𝑦 𝑤 . ( 17
)
The Bluetooth evolves for a pair of users 𝑖 and 𝑗. Suppose that there are 𝐿 Bluetooth data that arrive at timestamps 𝑣 , 𝑣 ,..., 𝑣 , it is possible to chain the error function over the 𝐿 timestamps as follows:

𝐹 𝐵 𝑥 , 𝑦 , 𝑥 , 𝑦 𝑟𝑠𝑠 . ( 18
)
By joining the three functions, the total likelihood function 𝐹 could be rewritten as:

𝐹 𝐹 𝐹 𝐹 . (19)
At this step, one could select the explicit form of 𝑀, 𝑊 and 𝐵 and process them to find the maximum value of 𝐹. The number of parameters in 𝐹 needing to be determined totally depends on the number of users and the tracking time. As 𝐹 includes a motion model 𝑀, particle-filter-based approximation is a natural way to find the maximum value of 𝐹. In addition, the particle filter process would be more flexible than writing down 𝑊 and 𝐵 in explicit forms.

Motion Model

For user 𝑖 at time 𝑡, there is a set 𝑆 of particles, which represents the position probability distribution. For motion model 𝑀 , without additional information from inertial sensors, the movement of the user could take random values as moving speed 𝑣 and heading direction ℎ. While there is no constraint on the value of ℎ, the moving speed 𝑣 should be suitable with a typical indoor movement. In our specific implementation, we generate the moving speed based on a normal distribution around a mean speed value. This mean value is determined statistically according to the walking action in an indoor environment. The heading is generated with a uniform distribution in the range 0, 2𝜋 . An additional wall-cross checking step is added for removing bad particles. Figure 4 depicts an example of the motion model 𝑀 for generating new particles. The black center dot is the initial particle. The wall boundaries are represented with black lines. New particles are then generated with a normally distributed moving speed around the mean value and a uniformly distributed heading direction. The green particles are valid and kept. The red ones, in contrast, which lie within the walls, are bad and removed.

Observation Model

With the particle-filter-based approximation, the likelihoods 𝐹 and 𝐹 given by Wi-Fi and Bluetooth components can be transformed into an observation model. The score for a specific particle 𝑝 ∈ 𝑆 is calculated by:

𝑠𝑐𝑜𝑟𝑒 𝑝 𝑠𝑐𝑜𝑟𝑒 𝑝 𝑠𝑐𝑜𝑟𝑒 𝑝 , (20)
where 𝑠𝑐𝑜𝑟𝑒 𝑝 and 𝑠𝑐𝑜𝑟𝑒 𝑝 are the Wi-Fi and Bluetooth components, respectively.

Wi-Fi Scoring Component Based on Classification

If there exists a Wi-Fi scan 𝑤 at time 𝑡 , then 𝑠𝑐𝑜𝑟𝑒 𝑝 is computed by using a local estimation of the probability output of the Wi-Fi fingerprinting model. Normally, 𝑠𝑐𝑜𝑟𝑒 𝑝 can be simply computed by assuming that the error distribution is 2D Gaussian with pre-defined standard deviation like in Equation ( 8). However, the estimation is heavily dependent on the accuracy of the Wi-Fi fingerprinting model. In addition, when the particles are close to each other, the score is nearly identical, which makes the selection step become difficult.

To remove the strong effect of a single output position and make the score more conservative, a local-based scoring system is used in our approach. The area is first divided into 𝐷 separated smaller ones whose centers are 𝐶 , 𝐶 ,..., 𝐶 . To compute the coordinates of the centers, a K-means clustering approach is used on all the appeared positions using the available fingerprinting data. Nearby positions are grouped into separated clusters. The center position of each cluster is the average of all the points that belong to each group. Figure 5 illustrates three centers with their boundaries. The boundaries are then used to transform the positions into appropriate indices. A 2D point 𝑥, 𝑦 can be assigned to label 𝑑 if the center 𝐶 is the nearest center to 𝑥, 𝑦 . With this mapping, it is possible to transform the Wi-Fi fingerprinting model from a standard regression problem into a classification problem [START_REF] Ta | Smartphone-based user location tracking in indoor environment[END_REF]. Assume the training samples in the fingerprinting database have the form 〈𝑟𝑠𝑠, 𝑃〉 where 𝑟𝑠𝑠 is the RSS vector and 𝑃 is the coordinates where the RSS is collected. The target value 𝑃 can be mapped to one of the labels from 1 to 𝐷, by assigning 𝑃 to the nearest center among 𝐶 , 𝐶 ,..., 𝐶 , as shown in Figure 5.

In the prediction step, let 𝑝𝑟𝑜𝑏 𝑎 , 𝑎 , … , 𝑎 be the probability of the predicted output of 𝑤 belonging to the clusters, then 𝑠𝑐𝑜𝑟𝑒 𝑝 can be computed as:

𝑠𝑐𝑜𝑟𝑒 𝑝 𝑠𝑐𝑜𝑟𝑒 𝑝 , (21)
where 𝑠𝑐𝑜𝑟𝑒 𝑝 is a scaled-value from 𝑝𝑟𝑜𝑏 , with respect to the maximum distance 𝑑 and minimum distance 𝑑 , corresponding to all the available particles:

𝑠𝑐𝑜𝑟𝑒 𝑝 𝑎 1 𝑑 𝑝, 𝐶 𝑑 𝑑 𝑑 . ( 22
)
A constant parameter Δ 𝑡 defines the effective window length for a Wi-Fi scan. This mechanism is illustrated in Figure 6.

Observation Model from Bluetooth

Similarly, 𝑠𝑐𝑜𝑟𝑒 𝑝 can be calculated if there is a Bluetooth scan involving user 𝑖 around time 𝑡. Without a loss of generality, we assume that the available Bluetooth scan is 𝑟𝑠𝑠 , which specifies the RSS value of device 𝑖 measured by device 𝑗. The update rule for 𝑠𝑐𝑜𝑟𝑒 𝑝 is defined as:

𝑠𝑐𝑜𝑟𝑒 𝑝 𝑠𝑐𝑜𝑟𝑒 𝑝 , 𝐵 𝑝 , 𝑝 , 𝑟𝑠𝑠 , ∈ , (23)
where the subscript 𝑘 indicates the need to calculate repeatedly for each 𝑝 , ∈ 𝑆 . The likelihood 𝐵 𝑝 , 𝑝 , 𝑟𝑠𝑠 is computed by using a similar process as the computation of the likelihood 𝑃 in the Non-temporal approach. Using Equation ( 12), the likelihood 𝐵 can be rewritten as a function of distance 𝑑 between two particles 𝑝 and 𝑝 , and distance 𝑙 derived from 𝑟𝑠𝑠 using the LDPL model. A constant parameter Δ 𝑡 is also added to define the effective interval length for a Bluetooth scan.

Experiment and Results

Data Collection

To evaluate the performance of the two proposed approaches, an experiment in an office environment that includes two floors is set up. All recordings follow one common trajectory, which is composed of the corridors, office rooms and stairs located in two consecutive floors. This trajectory is defined by several checkpoints. The path is illustrated in Figure 7. The length of the path is approximately 200 m, which usually takes about 300 s of walking at an average speed.

Different scenarios are designed in such a way that the additional Bluetooth scanning data can provide useful information for smoothing the Wi-Fi positioning output. Each of them involves groups of two to four users. The users were instructed to carry the devices and move along the designed path. While all the users walk along the same path, their relative distances are variable. In the recordings, we use a time interval of 0.5 s for tracking the users. Each time a checkpoint is reached, the time is recorded. As the checkpoint coordinates and their reaching timestamps are known, they can later be used to interpolate the ground truth for training and evaluation.

We selected four devices including two smartphones and two tablets for the positioning scenario (see Table 2). Each device is programmed to scan Wi-Fi access points and available Bluetooth devices in the environment. All of them run Android and use the same application for collecting Wi-Fi and Bluetooth data. Samsung Galaxy Tab Tablet

Bluetooth Model for Distance Deduction

In the first part, the model parameters for estimating the distance from RSS value need to be determined. From Equation [START_REF] Huang | A Practical, Robust and Fast Method for Location Localization in Range-Based Systems[END_REF], it is mandatory to find the appropriate 𝑙 and corresponding RSS value at 𝑙 , namely 𝑟𝑠𝑠 . In this experiment, we take the path loss exponent 𝑛 1.8 as the default parameter for the indoor office, as suggested by [START_REF] Rappaport | Wireless Communications: Principles and Practice[END_REF].

A test device is set to scan the other visible Bluetooth devices that are set up so that there is no obstacle between the two ends, thus, the effect of non-line-of-sight propagation is ignored. For each distance, the collection period is set to 300 s. With the devices in use, the Bluetooth inquiry cycle takes around 12 s on average. This results in around 25 to 30 samples per distance. However, when the distance is too large, the number of collected samples reduces. At the distance of 20 m, there are only 10 inquiry samples. Figure 8 illustrates the experiment results.

The distance 𝑙 of 0 m has the highest RSS value and the lowest standard deviation. The decrement pattern becomes more stable for the distance from 2 m to 10 m. Beyond the range of 10 m, the RSS value starts to be less predictable and packages are dropped. This explains why the mean distances at 15 m and 20 m are higher than at the 10 m. With this consideration, we selected 𝑙 2 m

and 𝑟𝑠𝑠 58 dBm.

To estimate the distance error, the two selected parameters 𝑙 and 𝑟𝑠𝑠 are substituted into the model in Equation [START_REF] Huang | A Practical, Robust and Fast Method for Location Localization in Range-Based Systems[END_REF] to compute the distance from the RSS value. The cumulative distance error distribution is illustrated in Figure 9. From the plot, we set the value of 𝛿 in Equation ( 12) to 4.2 m, which corresponds to the 90 th percentile of the distance error distribution.

Baseline Wi-Fi Fingerprinting Model

A Wi-Fi fingerprinting model is trained as a baseline model for the later fusion step with Bluetooth data. For building the Wi-Fi fingerprinting database, Device 1 (Samsung Galaxy Note 3) and Device 3 (Asus ME) are used. The database is built by using interpolation. First, one user is asked to carry the device and walk along the test path. The test path is predefined by several checkpoints (see Figure 7). Every time a checkpoint is reached, a timestamp is recorded and then used to interpolate the full moving path in a later stage. The database building process therefore does not take much time. There are six training log files in total. Given the specific testing path, all the data are collected in almost 1 hour.

Table 3 gives an overview of the collected Wi-Fi database. A time threshold of 5 s is used to group RSS values into one complete fingerprint scan. There are around 400 fingerprints in six training files. The number of completed Wi-Fi scans per user's walks varies between 50 and 100. Besides, the Cumulative distribution number of visible Wi-Fi access points also varies depending on the user location and the device in use. In our database, the average number of visible Wi-Fi access points per scan is almost 7, while the minimum is 3 and maximum is 12.

The distributions of RSS values from two devices is plotted Figure 10. A variation between the distributions of the two devices can be noticed. The variation is more significant in the range of signal strength from -90 dBm to -55 dBm. In a multiple-device context, this variation may affect the performance of fingerprinting models. To reduce the effect of device diversity, we first filter out the RSS values below -85 dBm. Second, a normalization step is carried out, so that for each participating device, it is assumed that the mean RSS value over the test area is known. The raw RSS values are then subtracted by this mean. Other alternative approaches such as finding the linear transformation or using HLF features would be suitable for improving the later step of fingerprinting model training.

For the fingerprinting model, we use Random Forest as the training model. The Random Forest is trained with 500 trees. Both the raw and the mean normalized RSS features are used in the K-fold cross validation testing with 𝐾 5. As the path contains two floors with some transient segments within stairs, the target position is treated as a 2.5D coordinate. For a triplet 𝑥, 𝑦, 𝑧 , the 𝑧 component is normalized to receive only one of three values: 0, 0.5, and 1. The values 0 and 1 represent the points in the eighth and ninth floors, respectively, while the value 0.5 indicates that the user is somewhere on the stairs. The distance error between the target point 𝑝 𝑥 , 𝑦 , 𝑧 and the output position 𝑝 𝑥, 𝑦, 𝑧 is calculated by:

𝑑𝑖𝑠𝑡 𝑝 , 𝑝 𝑥 𝑥 𝑦 𝑦 𝑘 𝑧 𝑧 , ( 24
)
where 𝑘 is a floor multiplier. In our experiment, 𝑘 is set to 10. The performance of the two preprocessing feature approaches is shown in Figure 11. The standard raw features result in a mean distance error of 4.21 m while the mean normalized one has a mean error of 3.61 m. The former has a standard deviation of 2.65 m and the latter of 2.53 m. There is a slight improvement by changing from the raw features to the preprocessed one. In terms of maximum distance error, both approaches suffer from large errors that exceed 10 m. Compared with the published dataset of IPIN 2016 [START_REF] Torres-Sospedra | The Smartphone-Based Offline Indoor Location Competition at IPIN 2016: Analysis and Future Work[END_REF], the performance of the Random Forest model with the preprocessing features is comparable. To reduce the error further, it would require a larger amount of training data.

Evaluation Setup

Three approaches are used to localize the users: Wi-Fi only, Non-temporal and Temporal. In the Wi-Fi only approach, the output of the Wi-Fi fingerprinting method is provided as the reference tracking results to evaluate the performance of the two other approaches. First, the data is collected along the designed walking path. The baseline Random Forest (RF) regressor model is used without utilizing the Bluetooth data. In the testing phase, for each incoming Wi-Fi scan from the test devices, the RF model is used to estimate the user position.

In the Non-temporal approach, the output positions from the pre-trained RF regressor model on Wi-Fi are calculated for each device. If there is any Bluetooth data available, the Bluetooth scanned information is used for adjusting the positions of two involved devices. To solve the problem of nonsimultaneous events between Wi-Fi and Bluetooth scans, we use a time window of length Δ𝑡 of 10 s for grouping successive events into the same timestamp. The resulting position is calculated as the mean value of these positions.

In the Temporal approach, a RF classifier model is built on top of the RF regressor model. To transform the real-world coordinates to a label index, we perform K-means clustering of all the available training positions from the training data. The new learning targets are the indices of the corresponding clusters. In our experiments, we use 𝐾 30 for clustering all the available points in the tested area. The radius of each cluster in this configuration is 4.0 m approximately. The probability output of the classifier model is then used to update the Particle Filter within a time window of 10 s. If there are multiple completed scans in this time window, the closest completed scan is used. The Bluetooth data have the effective time set to 2.0 s. Regarding the moving model, the average speed of each particle is set to 1 m/s. In the simulation step, the number of particles is set to 1000.

Results and Discussion

Figure 12 shows the localization output results along with the users' walking ground truth from the three approaches for different scenarios. Visually, it can be observed that in all the experiments, Wi-Fi only performs very poorly with highly disjointed spots as multiple data scans result in fixed pre-trained locations due to the nature of the fingerprinting method in use. When fusion is applied, the Wi-Fi based results are combined with Bluetooth-based ones and spread along the real path. However, for the Non-temporal approach, because of the grouping of data using time windows, the resulting locations are much more disjointed in comparison with those from the Temporal approach. It is clear in the figure that the Temporal results track the real path more continuously. A summary of the tracking results using the three mentioned approaches is presented in Table 4. In the configurations with only one user per group (i.e., number of users equals number of groups), the users are asked to move separately. In other configurations, users are asked to move with distance to each other kept under 10 m. The last scenario is with four users divided into two groups of two, which lets the system use Bluetooth data to identify both close and distant devices. The results are reported as the mean average distance errors across all the testing devices in the specific situation.

The Wi-Fi only approach reaches a stable performance of under 4.0 m in mean distance error. Both Non-temporal and Temporal approaches have better results than the Wi-Fi only one. However, the Non-temporal approach's results are not as stable as the Temporal one. In the setup where the users' distance could change within a specific time interval, the Non-temporal approach has a similar performance to the output from the Wi-Fi fingerprinting model. In this case, a difficulty is raised in measuring the distance in Equation [START_REF] Mathisen | A comparative analysis of Indoor WiFi Positioning at a large building complex[END_REF]. Meanwhile, the Temporal approach has a more consistent performance by reducing the errors from 25% to 50% depending on different scenarios. The biggest relative improvement is the scenario of three users moving in one group. In the experiments with two users, Devices 1 and 3 are used, where the results for each approach per device are given in Table 5. In the first scenario, they walk together while keeping their distance under 1 m. In the other scenario, they walk separately and keep their distance in the range of 5-10 m. As both devices are also used in collecting the training data, the Wi-Fi fingerprinting model is unaffected by the device diversity in this case. When the information from the Bluetooth scanning process is added, the distance error is reduced in both Non-temporal and Temporal approaches. The Non-temporal has a clear improvement in the one-group scenario. However, the impact of Bluetooth data when discarding the temporal relationship is insignificant in the two-group scenario. With the Temporal approach, we have stable improvements across the two scenarios.

For experiments with three users, Devices 1, 3 and 4 are used, and the results are summarized in Table 6. With the Wi-Fi only approach, the RF regressor model results in similar distance errors for Devices 1 and 3. The positioning results for Device 4 are not as good as the other two devices because the data does not contain training samples for Device 4. Compared to the Wi-Fi only approach, there is a slight improvement by using the Non-temporal one. Across all the devices and scenarios, the average improvement is around 0.5 m in mean distance error. The appearance of Device 4 with high distance error clearly affects the performance of the other two devices. The Temporal approach provides more stable improvement compared to the Wi-Fi only by outperforming the two other approaches in all scenarios. The highest improvement is with Device 1 in one-group and Device 3 in three-group settings. With the contribution of the motion model and the Bluetooth-based distance, the Temporal approach could make the effect of non-training data on Device 4 minimal.

Results for four users are shown in Table 7. Compared to the previous one-group scenarios with two or three users, it is difficult to keep a close relative distance in this step. The group is supposed to move within a circle of 2 m in radius. In the second scenario with two groups, the first group uses Devices 1 and 2 whereas the second uses Devices 3 and 4. The distance between the two groups is kept in a range of 5-10 m. Similar results for the three-user case can be seen for the Wi-Fi only approach. Both new Devices 2 and 4 have larger distance errors than the two others. Devices 1 and 3 have a similar performance to the five-fold cross validation testing. It is noticeable that the RF fingerprinting model has trouble in tracking Devices 2 and 4, which are not present in the training data. High errors from RF fingerprinting model add more noise into the later fusion step with the Bluetooth information. The Non-temporal approach can improve the results in most cases. However, its impact is quite low. There are several exceptions where using the Bluetooth data makes the results worse. For example, the results from Device 1 increase from 3.05 m to 3.46 m in the one-group setting. The Temporal approach results in lower errors than the two others. In general, good results are obtained with Devices 1 and 3, whose RSS data are present in the training phase. There is an exception for the results of Device 2 in the one-group scenario, that is the Temporal mean error is slightly higher than that of the Non-temporal. Nevertheless, it is able to reduce to errors compared with the Wi-Fi only approach. Figure 13 illustrates the distance error for three approaches over all the scenarios together. The Wi-Fi only and Non-temporal approaches perform similarly. For 75% of the time, the distance errors of two approaches are around 5 m. The Bluetooth-based relative distance is employed more efficiently in the Temporal approach. It has a significant improvement from the Wi-Fi-based tracking. For 75% and 90% of the time, the errors of the Temporal and Non-temporal approaches remain under 3.0 m and 5.0 m, respectively. Besides the Bluetooth information, employing map information and moving model constraints also help to reduce noisy output from the standard Wi-Fi fingerprinting model.

Individual error distribution for each test device is given in Figure 14. Both smartphones, Samsung Galaxy Note 4 (Device 1) and HTC One ME (Device 2) have a similar distribution. The Nontemporal approach gains a slight improvement from using only Wi-Fi data, and the Temporal approach can reduce the error significantly for the range under 7.5 m. However, the additional Bluetooth data does not help when the tracking error exceed 8 m, and the error of all three models are distributed similarly in the range above 10 m. It even adds more noise to the tracking results of Device 2. In the case of Device

Conclusions

In this work, a collaborative tracking framework based on the smartphone's Wi-Fi and Bluetooth scanning data is introduced. The Wi-Fi data is used as a raw positioning output, which is then improved using the relative distance from Bluetooth inquiry RSS values. Two combination approaches are introduced, namely Non-temporal and Temporal approaches. The Non-temporal approach attempts to simplify the information fusion task by ignoring the time relationship between different Wi-Fi and Bluetooth scans. The Temporal approach takes a more direct way to establish the conditions between the two types of data. Both approaches have been tested and compared with a standard Wi-Fi fingerprinting model. From the testing results, while the Non-temporal is only applicable in some specific scenarios, the Temporal approach outperforms the Wi-Fi fingerprinting models significantly. Results show that the collaborative positioning based on the Wi-Fi and Bluetooth data would be applicable in a multi-user context. Combining two types of wireless data can reduce the noise from the Wi-Fi fingerprinting model significantly.

The testing scenario is still dealing with simple contexts of multiple users. There are also some remaining issues on the technical aspects, such as the communication between the users and the server, energy impacts on the smartphones, and signal inference between multiple devices. For the Temporal, we are currently using a simplistic particle filter based on distributions with constant parameters (e.g., moving speed, heading direction), which can be targeted for further improvement. Moreover, for demonstration of the effect gained by adding Bluetooth information, a simple Wi-Fi model is used in the experiments, but can be replaced by more advanced models in reality.

Figure 1 .

 1 Figure1. A decision tree with two internal and three leaf nodes for splitting 𝑋 , 𝑋 , 𝑋 in Table1.

Figure 2 .

 2 Figure 2. Data sent from two devices to the central server and derived information at the server for estimating each devices' position.

Figure 3

 3 Figure 3 illustrates of the symmetric properties 𝑔. The pair of positions 𝑥 , 𝑦 and 𝑥 , 𝑦 can be used for finding the minimum value of 𝑔 𝑥 , 𝑦 , 𝑥 , 𝑦 . It also shows the symmetric property of 𝑔. The value of 𝑔 𝑥 , 𝑦 , 𝑥 , 𝑦 is equal to 𝑔 𝑥 , 𝑦 , 𝑥 , 𝑦 if 𝑟 is equal to 𝑟 and 𝑟 is equal to 𝑟 .

Figure 3 .

 3 Figure 3. Several ways for evaluating 𝑔 by using its symmetric property.

Figure 4 .

 4 Figure 4. A simple moving model with the black dot being the initial particle. The walls are used as a constraint to remove bad particles.

Figure 5 .

 5 Figure 5. K-means clustering process used to group nearby training points into separated clusters, and position targets transformed from coordinates into labels.

Figure 6 .

 6 Figure 6. Scoring function for particles (gray dots) with two centers 𝐶 and 𝐶 . The maximum and minimum distances are used to scale the observation probability.

Figure 7 .

 7 Figure 7. Moving path and checkpoints in two floors.

Figure 8 .

 8 Figure 8. The mean RSS and its standard deviation values for selected distances between two smartphones.

Figure 9 .

 9 Figure 9. Cumulative distance errors with the selected parameters for the LDPL model in the obstaclefree setup.

Figure 10 .

 10 Figure 10. RSS value distribution of collected dataset for training fingerprinting model.

Figure 11 .

 11 Figure 11. Comparison between the raw feature and the normalized feature in training with Random Forest model.

Figure 12 .

 12 Figure 12. Localization results for designed scenarios. (a) Two users walking together in single group. (b) To users walking separately. (c) Three users walking all together in single group. (d) Three users walking where two are in group and another separately. (e) Three users walking separately. (f) Four users walking all together in single group. (g) Four users where each two walking together in group.

  Figure13illustrates the distance error for three approaches over all the scenarios together. The Wi-Fi only and Non-temporal approaches perform similarly. For 75% of the time, the distance errors of two approaches are around 5 m. The Bluetooth-based relative distance is employed more efficiently in the Temporal approach. It has a significant improvement from the Wi-Fi-based tracking. For 75% and 90% of the time, the errors of the Temporal and Non-temporal approaches remain under 3.0 m and 5.0 m, respectively. Besides the Bluetooth information, employing map information and moving model constraints also help to reduce noisy output from the standard Wi-Fi fingerprinting model.Individual error distribution for each test device is given in Figure14. Both smartphones, Samsung Galaxy Note 4 (Device 1) and HTC One ME (Device 2) have a similar distribution. The Nontemporal approach gains a slight improvement from using only Wi-Fi data, and the Temporal approach can reduce the error significantly for the range under 7.5 m. However, the additional Bluetooth data does not help when the tracking error exceed 8 m, and the error of all three models are distributed similarly in the range above 10 m. It even adds more noise to the tracking results of Device 2. In the case of Device 3 and Device 4, both Non-temporal and Wi-Fi only have nearly identical distributions while the Temporal one outperforms the two others. The Temporal has the highest improvement with Device 4, which can overcome the issue of non-training data.

Figure 13 .Figure 14 .

 1314 Figure 13. Cumulative distance error distribution for three approaches.

Table 1 .

 1 An example dataset with raw RSS feature for 3 access points.

	Samples	𝑨𝑷 𝟏	𝑨𝑷 𝟐	𝑨𝑷 𝟑
	𝑋	-50 dBm	-70 dBm	-75 dBm
	𝑋	-65 dBm	-80 dBm	-52 dBm
	𝑋	-70 dBm	-65 dBm	-76 dBm
	𝑋	-50 dBm	-70 dBm	-75 dBm

Table 2 .

 2 Participating devices in the testing scenarios.

	Device ID	Name	Type
	1	Samsung Galaxy Note 4 Smartphone
	2	HTC One ME	Smartphone
	3	Asus ME	Tablet
	4

Table 3 .

 3 Data for training the Wi-Fi fingerprinting model.

Table 4 .

 4 Average positioning errors for all devices together in designed scenarios.

	No. of Users	No. of Groups	Wi-Fi Only (m)	Non-Temporal (m)	Non-Temporal Improvement (%)	Temporal (m)	Temporal Improvement (%)
	2	1	3.7 ± 2.0	2.4 ± 1.6	35.1	2.2 ± 1.5	40.5
	2	2	3.4 ± 2.4	3.2 ± 2.3	5.9	2.5 ± 2.0	26.5
	3	1	4.0 ± 2.4	3.5 ± 2.2	12.5	2.1 ± 1.8	47.5
	3	2	3.4 ± 2.4	3.1 ± 2.2	9.8	2.4 ± 2.0	30.4
	3	3	3.6 ± 2.1	3.1 ± 2.2	13.9	2.2 ± 1.9	38.9
	4	1	3.8 ± 2.6	3.6 ± 2.6	5.3	2.8 ± 2.0	26.3
	4	2	3.8 ± 2.4	3.5 ± 2.3	7.9	2.6 ± 2.1	31.6

Table 5 .

 5 Average positioning errors per device for two-user experiments.

	No. of	Device	Wi-Fi Only	Non-Temporal	Temporal
	Groups	ID	(m)	(m)	(m)
	1	1	3.7 ± 2.1	2.6 ± 1.6	2.2 ± 1.6
	1	3	3.7 ± 1.8	2.3 ± 1.6	2.2 ± 1.5
	2	1	3.8 ± 2.8	3.9 ± 2.6	2.9 ± 2.2
	2	3	3.1 ± 1.9	2.7 ± 1.9	2.1 ± 1.8

Table 6 .

 6 Average positioning errors per device for three-user experiments.

	No. of	Device	Wi-Fi Only	Non-Temporal	Temporal
	Groups	ID	(m)	(m)	(m)
	1	1	3.8 ± 2.1	3.0 ± 2.2	2.2 ± 2.1
	1	3	3.5 ± 2.3	3.3 ± 2.1	2.0 ± 1.7
	1	4	4.8 ± 2.9	4.3 ± 2.2	2.2 ± 1.7
	2	1	3.0 ± 2.1	2.8 ± 1.9	2.3 ± 1.7
	2	3	3.4 ± 2.6	3.3 ± 2.3	2.8 ± 2.4
	2	4	3.9 ± 2.6	3.3 ± 2.3	2.1 ± 1.8
	3	1	3.3 ± 2.4	3.0 ± 2.4	2.2 ± 1.9
	3	3	3.5 ± 2.0	2.7 ± 1.9	2.1 ± 1.7
	3	4	3.9 ± 2.0	3.8 ± 2.4	2.4 ± 2.0

Table 7 .

 7 Average positioning errors per device for four-user experiments.

	No. of	Device	Wi-Fi Only	Non-Temporal	Temporal
	Groups	ID	(m)	(m)	(m)
	1	1	3.1 ± 1.9	3.5 ± 2.3	1.9 ± 1.5
	1	3	5.0 ± 3.6	4.3 ± 3.2	4.6 ± 3.1
	1	4	3.5 ± 2.6	3.0 ± 2.3	2.4 ± 1.8
	1	1	3.5 ± 2.6	3.3 ± 2.4	2.3 ± 1.6
	2	3	3.2 ± 2.3	2.6 ± 1.7	2.7 ± 2.0
	2	4	4.2 ± 2.5	3.5 ± 2.2	3.2 ± 2.7
	2	1	3.5 ± 2.2	3.9 ± 2.3	1.7 ± 1.6

Funding: This research is funded by the project entitled "Research and development of application for counseling students in university using artificial intelligence" funded by Vietnamese Ministry of Education and Training in the program of "Development of core technologies for establishing university model towards Industry 4.0"; and by Hanoi University of Science and Technology (HUST) under project number T2017-PC-124.

Author Contributions: All authors participated in the development of the proposed method, implementation and experimentation, as well as the preparation and revision of the article. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:

The authors declare no conflict of interest.


Melanie Jouaiti
email: melanie.jouaiti@loria.fr

Improving Motor Coordination in HRI with Bio-Inspired Controllers

Keywords: Human-centered computing, • Computing methodologies → Bio-inspired approaches, • Computer systems organization → Robotic control, Robotics, Motor coordination, human-robot interaction, bio-inspired controller

Gestural communication is an important aspect of HRI in social, assistance and rehabilitation robotics. Indeed, social synchrony is a key component of interpersonal interactions which affects the interaction at a behavioral level, as well as at a social level. It is therefore paramount for the robot to be able to adapt to its interaction partner, at the risk of experiencing an awkward interaction. Bio-inspired controllers endowed with plasticity mechanisms can be employed in order to make these interactions as natural and enjoyable as possible. Integrating adaptive properties can lead to the emergence of motor coordination and hence to social synchrony. A non-negligible aspect of the work consists in studying humans in HRI to understand human behavior better and design better interactions. On the long term, this could be quite useful for improved robot-assisted motor therapy.

INTRODUCTION

In rhythmic social interactions, humans experience two physical phenomena which can also be observed in oscillators: the magnet effect entrains both systems until they are coupled and synchronized; the maintenance effect is the struggle of each system to preserve its own intrinsic frequency [START_REF] Eva | The Handbook of Psycholinguistics[END_REF]. These mechanisms could play a fundamental role in interpersonal interactions [START_REF] Delaherche | Interpersonal Synchrony: A Survey of Evaluation Methods across Disciplines[END_REF].

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s). HRI '20 Social synchrony is at the root of interpersonal interactions [START_REF] Ellamil | Influences on and Measures of Unintentional Group Synchrony[END_REF][START_REF] Mathieu Gueugnon | Postural coordination during socio-motor improvisation[END_REF][START_REF] Paxton | Interpersonal Movement Synchrony Responds to High-and Low-Level Conversational Constraints[END_REF] and thus humans expect robots to adapt to them and demonstrate appropriate responses. Robot controllers with adaptive capabilities are therefore necessary for social acceptance. My work is two-fold: first, improve motor coordination in robots using a bio-inspired controller, and second, use this controller for effective motor rehabilitation with autistic children.

RELATED WORKS

Synchrony is an important aspect of interpersonal interactions which has been evidenced by numerous studies. [START_REF] Lorenz | Synchrony and Reciprocity: Key Mechanisms for Social Companion Robots in Therapy and Care[END_REF] observed that synchrony has to be bi-directional and may fail if the robot is not adaptive. [START_REF] Neil Macrae | A case of hand waving: Action synchrony and person perception[END_REF] showed that subjects attributed a greater likability to a partner waving in phase with them. Moreover, in the case of inter-limb coordination, neural synchrony has been observed between cortical areas of the brain [START_REF] Varela | The brainweb: phase synchronization and large-scale integration[END_REF] but also between two distinct brains [START_REF] Richard C Schmidt | Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people[END_REF][START_REF] Tognoli | The phi complex as a neuromarker of human social coordination[END_REF]. Neuroscientists assume that emotional and social interactions involve a coupling between individuals which is achieved thanks to neural structures with similar properties as those implicated in the neural control of movements.

The consensus that robots should be adaptive leads to the emergence of several methods. Motor coordination in robots can be achieved using Dynamic Movement Primitives [START_REF] Auke | Learning rhythmic movements by demonstration using nonlinear oscillators[END_REF], such as in [START_REF] Pongas | Rapid synchronization and accurate phase-locking of rhythmic motor primitives[END_REF] where a robotic arm was able to synchronize with an external signal and perform coordinated drum beating with a changing frequency. [START_REF] Eva Ansermin | Learning to synchronously imitate gestures using entrainment effect[END_REF] employed a reservoir of oscillators to reproduce rhythmic arm movements with the NAO robot. While the oscillator can be slightly entrained during the interaction, the oscillators do not retain the frequency, going back to their original properties right afterwards. [START_REF] Degallier | Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives[END_REF] combined a rhythmic pattern generator (Hopf [START_REF] Hopf | Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems[END_REF]) and a discrete pattern generator (VITE [START_REF] Bullock | The VITE model: a neural command circuit for generating arm and articulator trajectories[END_REF]) to achieve motor coordination.

ACHIEVING MOTOR COORDINATION USING CENTRAL PATTERN GENERATORS (CPGS)

CPGs are biological neural structures found in the central nervous system of vertebrates or in some ganglia of invertebrates. CPGs are the source of neural activity that controls rhythmic and stereotyped behaviors, such as locomotion, swimming, flying, breathing, swallowing. They can generate a pattern without an input and adapt to an external feedback. Mesoscopic CPGs are usually based on a pair of half-center neurons [START_REF] Grillner | Central pattern generators for locomotion, with special reference to vertebrates[END_REF], controlling the extensor and flexor muscles. Half-center oscillators are composed of two neurons which would not have the ability to oscillate individually but their coupling leads to an oscillatory behavior. The oscillator neurons (See Fig. 1) employed here are based on the Rowat-Selverston neuron which is able to generate both Figure 1: CPG architecture based on the half-center model from [START_REF] Ilya A Rybak | Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion[END_REF] for joint i. RG: rhythmic generator cells (Rowat-Selverston here) for the extensor and flexor; PF, MN, SN: layers of interneurons (Pattern Formation, Motoneurons, Sensory Neurons); ϵ: synaptic weight; W: mutual inhibition. See [START_REF] Jouaiti | Hebbian plasticity in CPG controllers facilitates self-synchronization for human-robot handshaking[END_REF] for a detailed explanation rhythmic and discrete patterns. In the rhythmic mode, the CPG can adapt its intrinsic frequency, amplitude and synaptic weight using hebbian plasticity mechanisms [START_REF] Jouaiti | Hebbian plasticity in CPG controllers facilitates self-synchronization for human-robot handshaking[END_REF]. This CPG also has a discrete mode where it behaves like a PID controller and it can adapt its parameters to match the input amplitude [START_REF] Jouaiti | CPG-based Controllers can Generate Both Discrete and Rhythmic Movements[END_REF]. The CPG controller confers several advantages: no robot model is necessary; it can take in any kind of input (position, velocity, torque...) and it can achieve coordination through multimodal information (visual, contact...).

In previous work, we compared CPG control with a direct geometric control for human imitation. In discrete mode, the CPG smooths out the signal and is thus less sensitive to noise than the direct geometric control. In rhythmic mode, the CPG adapts its parameters and is able to anticipate the signal. The direct geometric approach endlessly tries to catch up with the signal and never matches the full amplitude.

The adaptation achieved by the CPG is similar to synchronization in humans: the CPG has an adaptation period, synchronization can fail if the input frequency is too different from its own, the CPG still retains its own characteristics while adapting, the CPG can resist synchronization depending on parameters.

The CPG controller is usually coupled with a vision system [1, [START_REF] Cao | OpenPose: realtime multi-person 2D pose estimation using Part Affinity Fields[END_REF][START_REF] Martinez | A simple yet effective baseline for 3d human pose estimation[END_REF] to obtain the 3D pose estimation of the interaction partner, which is then used as an input for the controller (angular position or speed). However, the input can also be the force applied to the robot joints in a handshaking interaction or for collaborative robotics.

Each degree of freedom of the robot is controlled by one CPG and they can be coupled with each other to achieve a bio-inspired architecture.

EVALUATING MOTOR COORDINATION

Interpersonal coordination can be evaluated thanks to the Phase locking Value (PLV) which has been introduced by [START_REF] Lachaux | Measuring phase synchrony in brain signals[END_REF] to measure coordination in brain signals. It relies on the assumption that both signals are locked with a constant phase difference but the PLV allows for deviation and evaluates its spread. It ranges from 0 (no coordination) to 1 (perfect coordination).

Engagement is "the process by which two (or more) participants establish, maintain and end their perceived connection during interactions they jointly undertake" [START_REF] Sidner | Explorations in engagement for humans and robots[END_REF]. It can also be defined as "emotionally laden attention" [START_REF] Jacek P Dmochowski | Correlated components of ongoing EEG point to emotionally laden attention-a possible marker of engagement[END_REF]. Engagement is computed from EEG data [START_REF] Pope | Biocybernetic system evaluates indices of operator engagement in automated task[END_REF]:

enдaдement = SP(β) SP(α) + SP(θ ) (1)
With SP(f ) the spectral power of the frequency band f [θ (4 -8 Hz), α (8 -13 Hz) and β (13 -30 Hz)]. The higher the score, the higher the engagement.

CONCLUSION AND PERSPECTIVES

In this work, we incorporated plasticity mechanisms into CPG controllers to make them even more adaptive. Versatile control of a robot can be achieved to imitate both discrete and rhythmic movements and switch seamlessly from one to the other. We can thus achieve synchronization in rhythmic tasks but also motor imitation for discrete movements. The model in itself is also quite flexible and can be extended or modified with new plasticity rules better suited for the purpose.

We performed a user-study to evaluate the impact of adaptive controllers on human engagement and coordination. Most participants enjoyed the interaction much more when the partner was adaptive than when it was not, they were very playful and tested the limits of the controller. This experiment also confirmed that humans expect their interaction partner to be able to adapt and feel the lack of adaptation as awkward. Most subjects also declared that they felt the non-adaptive partners adapted to them, demonstrating that the subjects unconsciously coordinated.

In future work, we will perform several user studies to evaluate human perception with CPG control and geometric control in imitation or interaction with contact.

The CPG controller could also be a valuable method for robotassisted motor therapy, as it is both suited for physical interactions with (exoskeletons) and without contact (motor therapy). Besides, these controllers will be employed in a pilot study aimed at motor rehabilitation for autistic children. Motor rehabilitation in ASD is a paramount problematic since motor deficits are correlated with communication deficits [START_REF] Macdonald | Motor skills and calibrated autism severity in young children with autism spectrum disorder[END_REF]. This issue has, however, been a little neglected by the research community with few impactful studies. Combining a robot (with which autistic children more likely engage) and rhythm therapy (the most effective therapy for motor deficits) appears to be a promising idea. [START_REF] Sudha M Srinivasan | The effects of rhythm and robotic interventions on the imitation/praxis, interpersonal synchrony, and motor performance of children with autism spectrum disorder (ASD): a pilot randomized controlled trial[END_REF] compared rhythm therapy and robot-rhythm therapy with autistic children and they reported that the children grew bored with the robot limitations. Could adaptive controllers, such as CPGs, improve the interaction?

  Companion, March 23-26, 2020, Cambridge, United Kingdom © 2020 Copyright held by the owner/author(s). ACM ISBN 978-1-4503-7057-8/20/03.

https://doi.org/10.1145/3371382.3377439

ACKNOWLEDGMENTS

I thank all the subjects who willingly participated to my studies, Dominique Martinez for proof-reading this paper and Patrick Hénaff for supervision.


Arnaud ALESSANDRIN , « Transidentités : histoire d'une catégorie », Encyclopédie pour une histoire nouvelle de l'Europe [en ligne], ISSN 2677ISSN -6588, 2016, mis , mis

  en ligne le 31/01/2018, consulté le 11/01/2020. Permalien : https://ehne.fr/node/1204 Traduction : Arnaud ALESSANDRIN , « Transidentities: the History of a Category », Encyclopédie pour une histoire nouvelle de l'Europe [online], ISSN 2677-6588, 2016, published 09/07/2018, consulted 11/01/2020. Permalink : http://ehne.fr/en/node/1320 Résumé Le terme transidentités, apparu en Allemagne au début du xx e siècle, renvoie à un ensemble de pratiques d'identification à un genre différent de celui assigné à la naissance. La définition des transidentités se situe à la croisée des discours médicaux, des prescriptions juridiques et des pratiques sociales. Les avancées médicales et chirurgicales depuis le premier tiers du xx e siècle rendent possible le changement de sexe ; selon les pays, celui-ci peut comporter une occulte, jusque dans les années 1970, celui de transexualisme. Néanmoins, en 1956, le Français Jean-Marc Alby (1926-2003) soutient une thèse intitulée Contribution à l'étude du transexualisme qui s'oppose aux demandes de changement de sexe et témoigne du poids de la psychanalyse contre les propositions psychiatriques. Des révélations dans la presse, telles celle d'April Ashley (née en 1960) en Grande-Bretagne, et de Coccinelle (1931-2006) en France rendent plus visible le « transexualisme ». Les demandes des trans interpellent la médecine et la justice. Toutefois, en France, le Conseil de l'ordre des médecins refuse l'accompagnement chirurgical des opérations des trans. En 1972, les Pays-Bas et la Suède établissent des soins remboursés pour les personnes demandant des réassignations chirurgicales. S'inspirant des modèles états-uniens, on tente, en Angleterre et en France, de mettre sur pieds des gender clinics, c'est-à-dire des regroupements de médecins chargés de suivre les demandes de transition durant la seconde moitié des années 1970. La première équipe française reconnue voit le jour en 1979 à Paris, autour des professeurs Jacques Breton (psychiatre à Fernand Widal), Jean-Pierre Luton (endocrinologue à Cochin) et Bordeaux, le VIII e congrès de la HBIGDA (Harry Benjamin International Gender Dysphoria Association, actuellement World Professional Association for Transgender Health) dénonce cette situation ; en 1986, suite à des plaintes de citoyen.ne.s trans britanniques et belges, la CEDH (Cour européenne des droits de l'homme) refuse d'imposer aux États membres une procédure de changement d'état civil. À partir des années 1990, et plus encore après les années 2000, naissent dans les pays occidentaux de nombreuses associations trans, militant en faveur de la reconnaissance juridique et du changement des mentalités. Alors que la reconnaissance psychiatrique avait permis une institutionnalisation du « transsexualisme », sa définition par la psychiatrie provoque une pathologisation forte des personnes concernées. En portant des projets de lois, en fondant des groupes d'auto-support et en rédigeant des rapports sur l'état des discriminations, elles dynamisent le mouvement trans européen. En 2017, celui-ci doit toujours lutter contre toutes les formes de transphobie, il milite pour la dépsychiatrisation des parcours de changements de sexe et leur prise en charge dans l'ensemble des pays membres de l'Union. En parallèle, des évolutions juridiques sont enregistrées en faveur des droits des personnes trans. La France est condamnée en 1992 par la CEDH pour non-respect de la vie privée de la personne, puisqu'elle doit se justifier systématiquement de la différence entre son apparence et le sexe légal. La législation française est modifiée et élargit le droit au changement de sexe à l'état civil. La même année, la jurisprudence polonaise autorise des changements de sexe. En 1994, le juriste et activiste Stephen Whittle (né en 1955) réclame une loi reconnaissant les personnes trans : le Gender Recognition Act est voté en 2004. L'année précédente, l'Allemagne est, elle aussi, condamnée par le CEDH et fait évoluer son droit. L'Espagne et la Belgique suivent la même évolution, allégeant les parcours et les conditions d'obtention d'un nouvel état civil. Si certains pays sont lents à faire évoluer leur droit (Portugal, France), d'autres (Lettonie, Lituanie) ne disposent en 2017 d'aucune disposition pour accompagner les demandes des personnes trans. Actualité des trans studies, Edition des Archives Contemporaines, 2019 (à paraître). Alessandrin, Arnaud, Sociologie des transidentités, Cavalier Bleu, 2018. Foerster, Maxime, Elle ou lui ? Une histoire des transsexuels en France, Paris, La Musardine, 2012. Stryker, Susan, Whittle, Stephen, The Transgender Studies Reader, New York, Routledge, 2006. Ayoub, Philipp, Paternotte, David, LGBT Activism and the Making of Europe : a Rainbow Europe ?, Houndmills, Basingstoke, Hampshire, Palgrave Macmillan, 2014.

	Les « transidentités » recouvrent diverses pratiques d'identification à un genre différent de celui assigné à la naissance. Elles ne se résument pas au seul terme de « transsexualisme », qui renvoie à un trouble, une pathologie, souvent associés à un dégoût de son sexe anatomique et à une volonté d'opération. Situées entre questions juridiques, mouvements sociaux et questions médicales, les transidentités sont en 2017 devenues, un enjeu majeur dans la lutte contre les discriminations. Le berceau des transidentités se trouve en Allemagne : en 1910, en effet, le médecin Magnus Hirschfeld (1868-1935) décrit des personnes exprimant le sentiment que leur sexe anatomique ne correspond pas à celui auquel elles ont l'impression d'appartenir. Les avancées théoriques et médicales et les progrès de la chirurgie (vaginoplasties, phalloplasties, mammectomies, Ces associations s'européanisent rapidement autour de structures comme l'« ILGA » (International Lesbian, Gay, Bisexual, Trans and Intersex Association, fondée dès 1978) ou « Transgender Europe » (2005) ; elles entérinent un triple mouvement, caractéristique de nombreuses associations nationales : l'expertisation (notamment juridique), la professionnalisation (sur les questions de santé par exemple) et l'internationalisation. Bibliographie Alessandrin, Arnaud,

dimension thérapeutique et s'accompagner d'une modification de l'état civil. À partir de la décennie 1960, les transidentités deviennent plus visibles et à des rythmes différents selon le contexte politique national ; des mesures médicales et juridiques sont adoptées pour prendre en compte les demandes des « trans », souvent sous la pression des nouvelles normes internationales. Durant les années 1990, des associations voient le jour et s'européanisent pour dépsychiatriser la transidentité ; elles trouvent dans la Cour européenne des droits de l'homme une alliée pour faire évoluer les législations nationales. etc.) se combinent alors pour accompagner pleinement les avancées techniques du changement de sexe. Ainsi, selon Hirschfeld, une première mammectomie dans le cadre d'une transition aurait eu lieu en 1912.

Et en 1930, à Dresde, Félix Abraham (1901-1937)

, son disciple, procède à la première vaginoplastie sur Dora, patiente ayant déjà subie une castration et une pénectomie.

Dans le même temps, au Danemark, des opérations de changement de sexe, sans reconnaissance de sa dimension thérapeutique, s'accompagnent d'un changement de prénom ; les patientes, telle Lili Elbe

, dont s'inspire Danish Girl de Tom Hooper (2015), sont acceptées comme des « homosexuels demandant une stérilisation ». L'arrivée au pouvoir des Nazis en 1933 suspend les recherches sur les transidentités menées par Hirschfeld et ses disciples, elles se prolongent alors outre-Atlantique. En 1953 l'endocrinologue états-unien d'origine allemande Harry

Benjamin (1885Benjamin ( -1986) )

définit le transexualisme comme « le sentiment d'appartenir au sexe opposé et le désir corrélatif d'une transformation corporelle », et distingue le « transsexualisme » de l'homosexualité. La réception européenne de ce concept est lente : en Allemagne on lui préfère le terme de « travestite », et en France, celui d'homosexualité Pierre Banzet (chirurgien plasticien à Saint-Louis). Si la médecine avance timidement vers une prise en charge des demandes de changement de sexe, c'est en partie sous la pression de nouvelles normes internationales, comme le Diagnostic and Statistical Manual (DSM) établi par l'Association américaine de psychiatrie (APA), référent majeur en ce domaine, mais objet aussi de critiquesqui tendent à reconnaître la « dysphorie de genre » comme une maladie mentale. Dans ce contexte, le droit autorise aléatoirement des changements d'état civil. La Belgique ouvre cette possibilité dès 1973, des tribunaux français

(Toulouse, 1977)

autorisent des opérations si l'objectif « thérapeutique » est avéré, tandis que d'autres

(Saint-Étienne, 1978)

valident même des changements d'état civil. Faute de témoignages, la situation dans nombre de pays est peu connue ; on sait que l'Espagne franquiste criminalise les changements de sexe quand l'URSS les passe sous silence : en Lettonie, le professeur Kalnberz opère en 1970 une patiente, Inna. Dans d'autres États, les opérations de réassignations tardent à être autorisées (Allemagne de l

'Ouest, 1981 -Italie, 1982)

et y sont conditionnées au changement d'état civil, et non l'inverse. Le couple « psychiatrie-droit » entérine alors, sous des formes variées, une reconnaissance des personnes trans, à la condition d'un diagnostic psychiatrique attestant de la demande. Ces conditions strictes privent de nombreuses personnes des opérations.

En 1983, à