M Faganello

F Califano

F Pegoraro

A Retinò

Kelvin-Helmholtz Vortices and Double Mid-Latitude Reconnection at the Earth's Magnetopause: comparison between observations and simulations

Keywords: 94, 30, cp - 52, 35, Mw - 52, 65, Kj -

Observational signatures of Kelvin-Helmholtz (K-H) vortices and of double midlatitude reconnection are highlighted in satellite data of the THEMIS mission. It is shown that the plasma fluid quantities at the low-latitude flank of the Earth's magnetosphere are compatible with K-H vortices, as described by three-dimensional simulations. At the same time it is shown that the particle fluxes are compatible with the presence of magnetic field lines, embedded in the K-H vortices, that close on Earth but are connected to the solar wind at low-latitude. These field lines are generated during the K-H evolution by magnetic reconnection proceeding spontaneously in both hemispheres at mid-latitudes, allowing the solar wind plasma to enter the Earth's magnetosphere directly.

Accounting for the particle transport properties in dilute space or hot laboratory plasmas remains a difficult and open physics problem due to the low collisionality of such media that makes the plasma dynamics nonlocal. In particular, in quasi-collisionless magnetized systems such as the Earth's magnetosphere, the particle orbits are strongly related to the magnetic field lines. Or, from a fluid point of view, the large-scale magnetic field obeys a nearly ideal MagnetoHydroDynamic evolution maintaining its original connectivity to the different plasma regions. In such systems collisional cross field diffusion is usually negligible and anomalous diffusion related to wave activity can be too weak to explain the efficient mixing between "unconnected" plasma regions, that is observed in the case of the Earth's magnetosphere and the solar wind [1]. More specifically it is not straightforward to identify unequivocally the physical mechanisms underlining the efficient transport of solar wind plasma inside the magnetosphere when the magnetic field advected by the solar wind is mainly parallel to the Earth's dipole axis (northward periods) and the related formation of a cold and dense plasma sheet in the near-earth magnetotail [2,3]. From a hydrodynamic point of view the anomalous diffu-sivity associated with Kelvin-Helmholtz vortices, growing along the flank of the magnetosphere during these periods [4], could explain the efficient transport properties of this boundary. However in an ideal MHD magnetized system, vortex development represents only a folding of the original boundary and a source for momentum transport [5], but cannot actually allow the solar wind plasma to penetrate the magnetosphere. For these reasons magnetic reconnection [6,7] has been invoked as one of the few mechanisms able to explain the actual particle transport by changing the global magnetic field topology and thus creating flux tubes associated to magnetic field lines closed on Earth but partially populated by solar wind particles. At the same time Kinetic Alfvén Waves, which can be excited by surface waves, such as K-H vortices [8], or by compressional waves [9,10], can, if they have a sufficiently large amplitude, enhance the cross-field diffusion.

During northward periods magnetic reconnection can occur in the lobe regions [1,11] and it has been proposed as a mechanism for the formation of the observed mixing layer [12,13]. In particular the fact that particle fluxes parallel and anti-parallel to the local magnetic field were, or were not, balanced was used [13][14][15][16][17] as an indicator of the field line topology, showing the transition from interplanetary "open" lines to lines connected to the Earth at only one pole and finally to lines "closed" by reconnection occurred in both lobes. In addition, in simplified 2D configurations that are not able to describe the actual topology of the magnetosphere-solar wind system, it has been shown that non-ideal effects such as anomalous resistivity or electron inertia can trigger magnetic reconnection during the evolution of K-H vortices [18][19][20][21]. However the former mechanism is strongly dependent on the northsouth symmetry of the magnetospheric system and thus it may not always occur in the actual magnetospheric geometry. Concerning the latter mechanism, it has been shown that the evolution of K-H vortices and of the magnetic topology can be totally different in a 3D geometry where the system is stable against the K-H instability at high latitudes.

In order to overcome these problems and to explain the observed mixing, a new mechanism, namely the onset of double mid-latitude reconnection (DMLR), has been investigated in numerical simulations. DMLR [22] is related to the intrinsic 3D behaviour of the K-H instability at the flank of the magnetosphere, in particular to the differential advection of magnetic lines, driven by the development of K-H vortices in the equatorial region [22][23][24][25][26]. This process creates current sheets at mid-latitudes where reconnection naturally occurs almost simultaneously. In this way DMLR is able to close solar wind field lines on Earth and to populate the magnetosphere with cold and dense plasma. The main advantage of this mechanism is the fact that the occurrence of two different reconnection processes is a direct result of the dynamics of the magnetic field lines. Moreover its predicted efficiency appears to be able to account for the observed plasma transport [22,27]. Finally, signatures of K-H vortices at low latitude has recently been reported [28] and the observed particle fluxes are not compatible with magnetic reconnection acting locally but with reconnection occurring far away from the equatorial plane. Indeed the location of reconnection sites can be inferred looking at particle fluxes for different energies and angles with respect to the magnetic line direction [29].

In this letter we report clear signatures of K-H vortices at the low-latitude flank of the Earth's magnetosphere observed by the THEMIS C spacecraft crossing the boundary between the magnetosphere and the magnetosheath during a northward period. We show that the observed fluid plasma quantities are compatible with the characteristic profiles of K-H vortices, as predicted by 3D numerical simulations able to retain the expected high-latitude stabilization of K-H instability. Furthermore the particle fluxes are compatible with reconnection occurring at midlatitude in both hemispheres and with the generation of double-reconnected field lines. We infer that these lines are created dynamically by DMLR acting during the nonlinear evolution of K-H vortices as described by 3D simulations and represent a direct path in for the solar wind into the magnetosphere. Finally, we discuss the competition between magnetic reconnection and KAWs for the generation of the observed fluxes and conclude that, for the considered period, reconnection must be considered as the most efficient mechanism.

The same THEMIS data were recently analyzed and similar conclusions on the K-H vortices were suggested [30]. On the contrary it was proposed a different scenario for the magnetic dynamics based on a "local" description of the equatorial region, that cannot account for the complex 3D dynamics we propose.

On 15 April 2008, the THEMIS C spacecraft [31], following its nearly equatorial orbit, was at the magnetosphere boundary for more than 2 hours, at X GSM -7, Y GSM 18 and Z GSM 0. In particular between 07:40 and 09:25 UT THEMIS C detected quasi-periodical oscillations of the plasma and of the electromagnetic fields at the magnetopause. During this period the interplanetary magnetic field was mostly northward, as reported by THEMIS B lying in the magnetosheath and by the ACE spacecraft lying in the solar wind (not shown). The observed quasi-periodical oscillations have a period that is roughly equal to 3-5min, as expected for K-H vortices at the magnetopause [4,18,20], and are characterized by alternating cold-dense and hot-tenuous structures, a bipolar velocity field and strong magnetic oscillations. Furthermore the variations of the total (magnetic + thermal) pressure are of the order of 0.15nP a, as expected for rolled-up K-H vortices [32]. Note that these variations are larger than the difference between the "unperturbed" pressure values inside the Magnetosphere and the magnetosheath and thus are generated by the vortex compression/decompression and cannot be simple attributed to spatial displacements of the magnetospheric boundary.

In order to associate the observed oscillations to K-H vortices we compare the THEMIS C data to the numerical simulations of the flank magnetopause. In these numerical simulations we adopt a simplified 3D slab geometry, with the open inhomogeneity direction perpendicular to the magnetopause along the y axis, the northward direction along the z axis and the -x direction aligned along the solar wind direction, as in the GSM coordinate system. We consider an ideal MHD equilibrium configuration that is able to model the highlatitude stabilization of the K-H instability. In this configuration all physical quantities are functions of the xcomponent of the vector potential, given by A eq,x (y, z) = [4/3 y + L z / 3π sinh(2πy/L z ) cos(2πz/L z )] /2 (all quantities are normalized to the ion skip depth d i , the ion cyclotron frequency Ω ci and the ion mass m i ) and are constant along x. In particular the equilibrium shear velocity and the density are given by U eq (y, z) = U 0 /2 {1 + tanh[A eq,x (y, z)/L u ]} x, n eq (y, z) = 1 -∆n/2 {1tanh[A eq,x (y, z)/L u ]}. Setting the box dimensions as L x = 24π, L y = 60 and L z = 120π and the half-width L u = 3 we obtain a nearly northward magnetic field lying in the y, z plane and a velocity gradient stronger in the equatorial region than at high-latitudes. In this way the K-H instability grows much faster in the equatorial plane than at high latitudes [22,33] which can thus be considered as stable during the development of the instability at low latitude. In our simulations the Fast Growing Mode at the equator [34,35] corresponds to m x = 2 with m x the wave number along the periodic x-direction. The reference values of the sound and Alfvén Mach numbers are set equal to M s = U 0 /C s = 1.3, M A = U 0 /U A 1.0, with U 0 = 1.0 and U A the +y asymptotic (magnetosheath) value of the equilibrium Alfvén velocity in the equatorial plane. The density jump between the two different regions (y ≷ 0) is set equal to ∆n = 0.8, reproducing the typical factor ∼ 5 between the magnetosheath and the magnetospheric density and temperature (we assume a homogeneous thermal pressure for the equilibrium configuration). Note that the physical values considered here are not strictly equal to the observed values in the two different regions, indeed our 3D system represents only a modeling of the magnetospheric flank. Nevertheless the 3D model evolution is able to provide clear qualitative signatures of the K-H vortices that cannot be predicted by 2D models.

We describe the system evolution by adopting a Hall-MHD model that includes an adiabatic closure for the ion and electron temperatures, a small but finite resistivity (η = 10 -3 in normalized units) in the generalized Ohm's law [22] together with the diamagnetic term.

In Fig. 1 we zoom in on three oscillations between 09:12 and 09:24 UT as a representative case. We show (left col- umn) the observed values of the ion density, ion temperature, ion bulk velocity and of the magnetic field in GSM coordinates. The density and temperature exhibit the typical step-like structures associated with the cold-dense and hot-tenuous arms of the travelling vortices. The X GSMcomponent of the ion velocity is tailward inside the high density arms and nearly zero inside the low density arms. The Y GSM -component, roughly perpendicular to the magnetopause unperturbed surface, shows bipolar signatures inside the low density arms. These "fluid" profiles can be recognized in the numerical data (right column, upper frame) in a cut of the simulation box at y = -5, z = -15 and t = 396, corresponding to what would be seen by a synthetic spacecraft surveying the tailward propagating vortices. Furthermore the observed strong magnetic perturbations (left column, bottom frame) show a distinctive character, peculiar to the 3D evolution of K-H vortices. At each sharp transition between hot and cold regions (at 09:13:15, 09:17:20 and 09:21:00 UT) corresponding to the compressed transition region between different vortices close to the hyperbolic point of K-H instability, THEMIS C observes bipolar signatures of the X GSM , Y GSM components of the magnetic field. These special signatures are predicted by our 3D simulations (right column, second frame) and can be explained by the differential advection of initially northward directed magnetic field lines. In Fig. 2, left frame, we show the plasma density together with the magnetic field lines at t = 396. The field lines are embedded into vortex structures grown in the lowlatitude region and are advected at the vortex phase velocity, roughly one half the magnetosheath velocity. On the contrary, the feet of the blue magnetospheric and red magnetosheath field lines at high-latitudes are advected at the unperturbed velocity , i.e. in the magnetosheath they are advected by the flowing red plasma while in the stagnant blue magnetospheric plasma they are anchored. This differential advection bends and arches the magnetospheric and magnetosheath lines in opposite directions. From the point of view of a spacecraft surveying plasma and magnetic structures below the equatorial plane (plane at z = -15 in Fig. 2), as in the case of THEMIS C, opposite arched blue and red field lines correspond to the detection of bipolar structures of the x, y magnetic components at the ribbons. The observed amplitudes of these structures are larger than the predicted ones. Nevertheless we must bear in mind that the dipolar structure of the global magnetospheric field and the draping of magnetosheath lines around the magnetopause [36], not included in our model, could enhance the arching effect at the near-tail flanks (X GSM -7).

The differential line advection creates current sheets in both hemispheres at mid latitude (light green regions in Fig. 2, left frame) where reconnection can develop. In fact reconnection occurs almost simultaneously in the northern and in the southern sheets and creates "newly closed" yellow lines that are connected to the blue magnetospheric plasma at high latitude, and thus to Earth, and to the red magnetosheath arm of K-H vortex at low-latitude. At the same time reconnection creates "opened" green lines, connected to the solar wind at high latitudes and to the magnetospheric plasma at low latitude.

We can find observational signatures of this magnetic dynamics by looking at the electron fluxes given as a function of the pitch angle with respect to the local magnetic field. For different energies, and corresponding parallel velocities, we compare the transit time τ transit taken by electrons in order to escape/fill the segments D red & D blue (as defined in Fig. 2, right frame) and the delay ∆t rec 10sec between the two different reconnection processes along the same field line, as given by numerical simulations. We estimate the distance between the two reconnection sites as ∼ 1/6 times (±30 • ) the length of a circular line crossing the equator at the satellite position. Thus we obtain L D red/blue 60000Km and the transit times, for different energies, given in Fig. 2. This length is compatible with the distance between the stable planes in our simulations (at z = ±180) that we suppose to be ∼ 100000Km (±50 • ).

In Fig. 3, first and second frames, we show the ion and electron flux as a function of the particle energy. The cold-dense and the hot-tenuous regions map the different magnetospheric and magnetosheath arms of two close vortices accurately. In the following frames we show the electron fluxes in different energy ranges as a function of their pitch angle with respect to the local magnetic field. 20 -100eV electrons are detected only inside the densecold region. On the contrary faster 100 -500eV elec- trons, mainly coming from the magnetosphere, start to populate the cold region and show a dominant antiparallel component. Higher energy electrons are also present in the cold region but do not exhibit this anisotropy. These fluxes are compatible with DMLR that occurred first in the northern hemisphere some 15sec before their detection. In this case low energy electrons are too slow in order to escape from the magnetosheath segment D red from where they originate or in order to populate the D blue segment that crosses the hot-tenuous region. At intermediate energies electrons have enough time to fill the segment D red , starting from the northern hemisphere where reconnection occurs first and therefore have unbalanced fluxes.

Note that no strahl population is present in the magnetosheath during the considered period and thus cannot account for the observed fluxes. This anisotropy disappears at higher energies since these electrons are fast enough in order to populate D red also from the southern hemisphere (τ transit becomes smaller and smaller compared to t detection -t northern,rec -∆t rec , i.e. τ transit < t detection -t southern,rec ). Looking at the hot-tenuous region, we observe a partial depletion of parallel/antiparallel electrons with energy larger ≥ 300eV . In fact these electrons have enough time to escape from the D blue segment of "opened" tubes before their detection. Even more relevant is the observation of several parallel/antiparallel beams (the most visible is shown at 09:16:20 UT). The density in these beams is larger than the magnetospheric density in each energy range (100eV up to 1000eV ). Thus we can suppose that these beams are composed of a magnetosheath dense population that is accelerated along field lines at the northern and southern reconnection sites. Indeed, once accelerated, these electrons have energies large enough to reach the satellite location in time to be detected.

In principle, bunch of accelerated electrons can also be produced along field lines by the parallel electric field of KAWs with long parallel wavelength. However, for the considered period, the KAW activity appears too weak to account for such an electron acceleration, as indicated by the observed magnetic wave amplitude at different frequencies (see Fig.ffig:waves). Indeed, the observed spectrum at 09:16:20 UT does not correspond to what would be obtained by KAW. For example, the dominant mode is detected at 48Hz, that would correspond to a dopplershifted KAW with a too small wavelength, of the order of the electron skin depth. Instead, a KAW spectrum should be dominated by much larger wavelengths of the order of the ion Larmor radius [8][9][10]. Furthermore the observed wave activity at the beam location, or inside the magnetospheric arm (between 09:15:30 and 09:17:00 UT in Fig. 4) or at the transition region between the magnetosphere and the magnetosheath, is too weak as compared to that typically reported when KAWs are recorded [8][9][10]. Finally, we do not observe on the data an enhancement of ion perpendicular temperature which would be a clear signature of KAWs. All these aspects lead us to conclude that, for the considered period, KAWs should be not responsible for the generation of the observed particle fluxes.

We also note that electron fluxes in the 20 -100eV range differ from those usually observed inside the magnetosheath (that have a dominant perpendicular flux). Since the DMLR occurred too recently to affect these fluxes, we can suppose that the observed well-balanced parallel/antiparallel fluxes are related to the previous dynamics of the magnetopause (KAW activity or other phenomena). The same "lack of reaction" holds for ions: THEMIS C does not report any ion jet. This is expected in the case of recent reconnection at mid-latitude, since the accelerated ions are too slow to be observed at the satellite location. This fact is also confirmed by the lack of mixing between cold-dense and hot-tenuous ion populations inside the magnetospheric or magnetosheath arms, as shown in Fig.ffig:fluxes. Mixed ion populations are observed only at each transition region between the two different arms, where plasma density increases/decreases. These observations are consistent with the picture of vortices that grow on a pre-existing transition region (day-side magnetopause) and that, during their evolution, have folded the original boundary but, for the moment, not yet allowing an enhancement in the ion transport. The temporal width of these transition regions (20-60sec), that could be compressed near the hyperbolic point or decompressed inside each vortex during the K-H evolution, is compatible with the observed periods of K-H vortices (3 -5min) [4].

It is worth noting that the generation of doublereconnected lines as a pairs of "opened" and "newly closed" lines is not only suggested by the simulations. This mechanism is strongly supported by physical arguments: once reconnection occurred in the northern hemisphere the resulting lines become braided at mid-latitude in the southern hemisphere. Reconnection must thus take place a second time between the same lines in order to unbraid them and reduce the line stretching [22].

In conclusion observational data are in agreement with a scenario where DMLR started to "close" interplanetary field lines on Earth several seconds before the detection of the particle fluxes.

We can thus expect that this new magnetic topology allows thermal solar wind ions and electrons to enter the magnetosphere since they can move along the "newly closed" field lines. In particular the redistribution of these low-energy and dense particle populations is expected to happen slightly tailward with respect to the satellite location and can account for the formation of a cold and dense plasma sheet in the near-earth magnetotail.

Fig. 1 :

 1 Fig. 1: Left column: ion density, temperature, bulk velocity and magnetic field as detected by THEMIS C. Right column: ion density, temperature and x, y components of the ion velocity and magnetic field obtained from a cut of the simulation box at y = -5, z = -15 and t = 396, corresponding to what would be seen by a stationary synthetic spacecraft surveying the tailward propagating vortices (yellow line in the third frame).

Fig. 2 :

 2 Fig. 2: Left frame: ion density, represented in blue (tenuous) and red (dense), in the x, y-planes at z = -180, -15, +180, light green: current sheet isosurfaces defined by |J| = 0.8, blue/red: pristine magnetospheric/magnetosheath field lines, green/yellow: "opened" and "newly closed" double reconnected field lines. Right frame: a schematic representation of DMLR and the values of τtransit as a function of the electron energy.

Fig. 3 :

 3 Fig. 3: First and second frames: ion and electron fluxes respectively, detected by THEMIS C, as a function of energy (eV) and time. Following frames: electron fluxes for different energy ranges, as a function of the pitch angle with respect to the local magnetic field. White ellipse shows the dense electron beams observed inside a magnetospheric arm at 09:16:20 UT.

Fig. 4 :

 4 Fig. 4: Magnetic oscillation amplitudes for different frequencies, as reported by the Filter Bank.

The research leading to these results received funding from the European Commission's Seventh Framework Programme (FP7/2007-2013) under the grant agreement SWIFF (project n. 263340, www.swiff.eu). This work was supported by the Italian Supercomputing Center -CINECA under the ISCRA initiative. We acknowledge NASA contract NAS5-02099 and V. Angelopoulos for use of data from the THEMIS Mission, O. LeContel and P. Henri for valuable suggestions for the treatment of electron fluxes. Part of data analysis was done with the AMDA science analysis system (http://amda.cdpp.eu/). We acknowledge the access to supermuc machine at LRZ made available within the PRACE initiative receiving funding from the European Commission's Seventh Framework Programme (FP7/2007-2013) under, Grant Agreement No. RI-283493, Project n. 2012071282.


Mohamed-Hédi Amri
email: mohamed-hedi.amri@inria.fr

Tania Jimenez
email: tania.jimenez@univ-avignon.fr

Yves Papegay
email: yves.papegay@inria.fr

Odile Pourtallier
email: odile.pourtallier@inria.fr

Valérie Roy
email: valerie.roy@mines-paristech.fr

Minimal information sensor system for indoor tracking of several persons

In this paper, we introduce an on-going experimentation in our laboratory for indoor tracking of several persons with a minimal set of informations, based on photoelectric beam barrier sensors. Incremental design, data analysis and acceptance concerns are discussed.

I. INTRODUCTION

Population ageing becomes an important problem in our societies as it incurs both financial and social costs. Although human care and interaction for the frail and the elderly cannot be replaced by technological approaches and tools, at least for ethical reasons, these approaches may bring some relief to medical staffs and families. General objective of our laboratory is to bring technological services for the care of frail and elderly persons. A long-term focus is the design of continuous indoor monitoring devices for answering questions related to gait and activity analysis as expressed by medical staff.

In addition to the relief brought to medical staff, continuous monitoring brings several advantages compared to classical monitoring during medical examination: Continuous monitoring may help early detection of changes in the gait of a person that may show physical or mental alteration; It may also prevent the "examination" effect where a patient may be prone not to adopt his/her usual gait during the examination.

Our scenarii are residential care or nursing home where several persons, potentially belonging to several groups (staff, residents) can evolve. Hence the first step toward our objectives is to be able to track each person and determine to which group he/she belongs. We need therefore to localize him/her whenever necessary and to retrieve his/her daily trajectory.

Tracking persons with the aim to have statistical measures or indicators on gait does not require, in general, high precision or high reliability. From a medical point of view, qualitative results and evolution trends on physical activity are sufficient. Collecting information and data on daily activities may collide with feeling of privacy, which may yield a strict refusal of adopting such kind of technologies [START_REF] Ziefle | Information Quality in e-Health: 7th Conference of the Workgroup Human-Computer Interaction and Usability Engineering of the Austrian Computer Society[END_REF]. There is a tradeoff between collected data, needs as expressed by medical staff and privacy. Namely, this drove us not to use camera nor wearable devices, as low acceptability has been reported.

To reach our goal, a monitoring system has to be designed by paying careful attention to the geometry of the site under consideration as well as the use of residents. We promote an incremental design of the system. A first coarse system is designed and installed on the basis of the building geometry and then it is refined based on the analysis of the first collected datasets.

To summarize our objective is to design multi person/group indoor localization and tracking systems strictly fitted to answer identified monitoring objectives of medical staffs. They have to be flexible in order to adapt to evolving needs of medical staffs, easily installed, sufficiently robust, and of reasonable cost.

Related Work

Sensors for healthcare have been used since years ago. In [START_REF] Alemdar | Wireless sensor networks for healthcare: A survey[END_REF] a survey on wireless sensor networks with application to healthcare have been dressed till 2010. Many works have been carried out on Smart Homes as well, where sensors are central, another interesting and thorough survey on this subject was done by Chan et al. in 2008 [3]. In 2013 Barath and Anithapriya present a brief survey on health care for aged people based on sensor network [START_REF] Barath | A survey on healthcare for aged people based on sensor network[END_REF]. Health care with sensor detection for elder person is precisely our target application.

Authors of [START_REF] Zhang | Design of an unobtrusive wireless sensor network for nighttime falls detection[END_REF] demonstrate a proof-of-principle that night-time falls detection might be achieved using a low complexity and completely unobtrusive wireless sensor network in the home. Recently, researchers make a survey to know the interest of people on senior fall prevention. Eighty-one percent (over 1900 respondents) "expressed an interest in sensor technology that can anticipate and prevent falls" [START_REF] Hall | Survey: Consumer interest high in fall-detection sensor technology[END_REF]. Our idea follows this proof-of principle, while trying to identify more than falls, but even a change on behaviour, and not only one person but multiple people.

In [START_REF] Wahl | A green autonomous self-sustaining sensor node for counting people in office environments[END_REF] authors used PIR sensors to count people in a office building in order to save energy. For tracking many people entering or exit the offices they installed PIR sensors on both sides of each office door. This system is useful to detect empty rooms. Our model differs from this system because we are interested in residents tracking and counting persons in each room.

In [START_REF] Yun | Human movement detection and identification using pyroelectric infrared sensors[END_REF] an empirical study of human movement detection and identification using a set of PIR sensors is presented. The authors use an experimental design close to ours, but they uses three PIRbased modules: one module on the ceiling and two modules on opposite walls facing each other. Their results based on machine learning algorithms for classification analysis are encouraging for us. They could achieve more than 92% accuracy in classifying the direction and speed of movement, the distance interval and identifying subjects.

We describe in this paper an ongoing experiment conducted in our laboratory and a few preliminary results obtained. A similar experiment involving more persons split in distinct groups is also under development in an EHPAD (retirement home).

Our paper is organized as follows: in section II we describe our experimental platform. Section III outlines our first results and IV presents our first conclusions and our perspectives.

II. EXPERIMENT DESCRIPTION

The primary goal of our experimental platform is to determine the minimal set of data to acquire to localize multiple persons moving in our indoor environment. In a first version, a network of infrared barriers is installed taking roughly into account the topology of the environment. Then, we will refine the hardware configuration according to our data analysis results. Such an iterative approach allows us to take into account, beside the topology of the environment itself, the use of the residents in terms of locations and trajectories. A zone intensively used will need more sensors and we want our incremental design to exhibit and quantify this need.

A. Experiment Area

The sensor network has been installed to completely monitor a part of our lab, the first floor of the KAHN building of the INRIA Research Centre Sophia-Antipolis Méditerrannée. The experimental location (Fig. 1) consists of a hallway, offices, facilities and common spaces. This topology is more or less similar to a typical floor configuration of a retirement home which consists of a hallway, rooms and shared areas such as reading hall or dining room. Localization of persons can be defined in terms of precise location (2-D or 3-D coordinates), position on a trajectory (one coordinates), or appartenance to a geometric zone (discrete information). For our purpose of monitoring the third one is sufficient. We divided the experiment area into seven zones and hence equipped with 8 infrared barrier sensors discriminating the offices area and the common spaces, as depicted in Fig. 2. In this figure, the bold red lines refer to infrared barriers delimiting a zone. It is our choice not to have any barrier at the entries of the offices, as it has been reported as an intrusive set-up by our medical partner.

During the data records of this experiment, our staff was composed of 8 persons. The group is homogeneous in terms of gait ability. Occasional visitors have also been present during that period.

Another experimentation will take place in the retirement home of Valrose in Nice (France), where the monitoring area consists of a corridor with 6 rooms, 4 staff offices, an external stairs and an elevator. Six residents, their relatives and a tenth of staff members are subject to be in this area as well as visitors. The different groups (staff, residents, visitors) are not homogeneous in terms of gait Fig. 2. The zoning area ability. Therefore, the interest will be focused on residents tracking characterized by a slow gait speed, or the use of rollator or a wheel chair.

B. Hardware configuration

Hardware configuration of our initial experimental platform is quite simple and inexpensive. It consists of commercially available readyto-use photoelectric beam detectors -an infra-red light transmitter and a photoelectric receiver, Fig. 3 -interfaced with a Phidget microcontroller card, Fig. 4.

Photoelectric beam detectors provide an accurate information and offer a long sensing range ensuring a reliable data, quite robust to inaccuracy of alignment during installation. On the other hand, these devices do not provide the direction of motion of a people crossing the beam, and they suffer a 1 second latency, that prevents us to detect when several people are crossing or moving very closely. The Phidget microcontroller provides us a synchronized and timestamped sequence of event data from the inputs connected to the sensors. It is connected to a tiny fanless PC under Linux, which is programmed using shell scripts and C-code in order to store the occurence time of event data and the ID of the given sensors triggered into a data files.

These data files follow a very basic XML dialect specification recording a rough description of the hardware configuration and the sequence of events.

III. ONGOING EXPERIMENT IN OUR LAB AND FIRST RESULTS

The system described above is on use in the lab since mid-January 2016. Between January 14th and April 29th, 166 data files have been stored, one for day-time, one for night-time each day. Histograms on Fig. 5 displayed the number of files for a given range of sensor events. As already noticed our sensor system constitutes the first step toward a full system. The aim of this first analysis is to get insight of the quality of results we can obtain from this coarse installation and to explore directions to follows for improving our system.

We analyzed the data with two perspectives: In the first one the objective is to study the occupancy of each zone. In the second one the aim is to trace each person and to reconstruct her/his trajectory.

In the first perspective the main difficulty ensues from the fact that our sensors do not give information on the direction of the barrier crossing. In the second perspective, the challenge is the multi-person context, because an ambiguity arises whenever more than one person are in the same zone.

A. Occupancy analysis

We implemented a simple finite automata. Each sensor event triggers the change of occupation of the adjacent zones. Results are given in terms of occupancy configuration, we provide the minimal number of person and the maximal number of person per zone compatible with the list of events. The difference between this maximum and this minimum is interpreted as the accuracy of the method.

For some cases, the algorithm detected inconsistencies in the sequence of events. An analyze of these inconsistencies allowed us to identify and find a workaround for two types of inconsistencies. The first one is related with the initial condition of the system. Each day, the data recording starts at some time were the building is supposed to be empty, it is our initial condition. Nevertheless, for some cases this assumption turns out to not to be true. We modified our algorithm in order to set up automatically a new initial condition compatible with the few first sensor events of the sequence.

The second inconsistency is related with a latency of the sensor. Our sensors have a one second latency after it triggers. During this latency they are unable to detect a new event. It may hence result inconsistent sequence of events if a person brushes past a barrier : only one sensor event is detected instead of two. The algorithm has been modified accordingly.

1) Night and weekend experiment: As expected the system worked fine for the night and weekend data, provided that we control the global number of people in the system -this may be an a priori information or may comes from additional information from extreme sensors, as discussed further. Fig. 6 show the ratio of experiments producing a given uncertainty in terms of number of possible occupancy configuration.

This results mainly covers the case of single occupancy of the building, even in the case where the motion of that person is non standard as is the case of the cleaning person in the morning whom have backwards and forwards motion. 2) Weekday experiment: Our algorithm presents some problems when handling the full week day data. The results show high uncertainty (large range of compatible occupancy per zone). If the sensor between two non empty adjacent zone triggers, there are two compatible possibilities, yielding, in the worst case, a 2 n complexity, n being the number of sensor events. In the experimental case, number of possibilities generally exceed 1000 after less than 150 sensor events.

B. Trajectories reconstruction

In this perspective the aim is to trace each person and to be able to reproduce its trajectory (in terms of successive zone occupied by the person). This will enable us to adapt the monitoring individually.

We implemented an algorithm that built the tree of possible states. At each step (i.e. each sensor event time), a list of compatible states with prior sensor event is provided. Each compatible states keep in memory its parent.

Each time one of the entrance sensors triggers a potential new comer is introduced and his/her trajectory initiated. For each sensor event, the algorithm determines the compatible states and remove the incompatible ones. The compatible states at the new step are determined by browsing all the compatible moving of the persons in the monitored area.

The complexity is worst than the complexity of the occupancy problem since we have to consider in addition the identity of the person. Furthermore, we faced memory problems since we have to store all the intermediate compatible states. We manage to handle the night and weekend datasets but we were unable to handle weekday data sets.

IV. CONCLUSION AND PERSPECTIVES

As shown in the previous section, in the current state of the system it is not possible to solve neither the counting problem or the tracking problem.

Several directions can be followed to improve these preliminary results. We split these directions on three types : hardware improvement, use of a priori knowledge, software improvement.

A. Hardware improvements 1) Best coverage of the monitoring area: A closer observation of the data shows us that one of the extreme barrier (between zone 1 and zone K100) was too often crossed. Each time this barrier was crossed, provided that zone 1 is not empty, two possibilities had to be considered : either a person initially in zone 1 is leaving the observed area, either a new person is entering in the observed area. Note that this behavior is not observed with the other extreme barriere (between zone 7 and stairs).

The fact that the first extreme barrier is often triggered suggest that the observed area is not sufficiently well defined and bounded. Whenever possible, one has to define the monitored area so as to avoid areas with too much traffic of people.

Our sensor system has to be extended in that direction. This could have been anticipated in that case since zone K100 is often used as a meeting room and is part of a frequent path to go to the lavatories. This raises the question of a priori knowledge that we will briefly discuss latter on.

2) Improving the barrier: The barriers we are using undergo two main drawbacks : they cannot detect the direction in which they are crossed, they suffer from a big latency delay (1 second).

We are currently testing a multi-sensor barrier made up of two distance sensors and two PIR sensors, as shown on Figure 7. In Fig. 7. New multi-sensor barrier addition to detect the passage, this barrier is able to detect the direction. The latency of the sensors used in this composed barrier are smaller. Having both distance sensor and PIR introduces some redundancy that may be useful.

B. Use of a priori knowledge

As mentioned above the use of a priori information about the system is useful for the analysis of the data.

A priori information may covers several aspects. We have mentioned earlier the a priori knowledge of the use of some area that may give bounds on the number of person that may use that room, and on the identity of these persons.

For the occupancy problem, we have added a constraint on the maximal number of persons into some zone. Zone 1 to 6, excepted zone 3, are made up with a single use office plus a portion of hallway, zone 3 is a short portion of hallway. We introduced in our algorithm the constraint that zone 1 to 6 cannot support more than a certain number of person. This allowed us to run the full weekday datasets.

The drawback of incorporating a priori information on the algorithm is that it cannot be easily generalised to other places. A phase of analysis and adaptation of the new place would be needed.

C. Software improvement

For the tracking problem, our algorithm suffers from the combinatorial curse. It is hence essential to strictly contain the number of possible new state after a barrier triggers. In addition to software improvement and consideration of a priori knowledge already mentioned, we plan to optimize our software using new coding techniques and more adapted data structures. For example, up to now each person entering or reentering the monitored area is individually taken into account. One way we are exploring is to use group instead of individuals. Whenever there is unsolved ambiguity on several people we do not track them individually but instead the group they form as long as the ambiguity cannot be solved.

Fig. 1 .

 1 Fig. 1. The Experiment location

Fig. 3 Fig. 4 .

 34 Fig. 3. Photoelectric beam detector

Fig. 5 .

 5 Fig. 5. Numbers of sensor events

Fig. 6 .

 6 Fig. 6. Uncertainties without and with control of global occupancy