Person tracking for WiFi based multistatic passive radar

Transcription

1 Person tracking for WiFi based multistatic passive radar Martina Broetje Department Sensor Data and Information Fusion Fraunhofer FKIE Wachtberg, Germany Abstract In this paper the task of person tracking for WiFi based multistatic passive radar is discussed. To benefit from the localisation gain by fusing measurements from different transmitter-receiver pairs a robust association strategy is needed. We present a version of the multihypothesis tracker, which incorporates a detailed model of probability of detection (for example occlusion by walls is modelled) and a strategy for handling unresolved measurements. The algorithm is tested with simulated data. I. INTRODUCTION Passive radar exploits illuminators of opportunity (radio, TV, WiFi transmitters) to detect moving targets, see for example [], [2]. At the receiver the direct signal as well as delayed echoes from targets are collected. Signal processing at the receiver delivers measurements of the time delay of the reflected vs. direct signal path, which gives the bistatic range, and the direction of arrival and Doppler shift of the reflected signal. With the transmitted waveforms not designed for radar, passive radar systems deliver typically less precise measurements than active radar. This is compensated by using multiple illuminator-receiver pairs. This requires a strategy for tracking and fusing the multiple sensor data. Multistatic radar operation significantly improves the total probability of detection and target state estimation. However, the measurement errors depend in a complicated way on the transmitter (Tx)- receiver (Rx) geometry. Multistatic tracking of multiple targets is a key component of all passive radars if realistic scenarios are taken into account. This topic has been studied in various applications resulting in the development of a Multihypothesis tracking (MHT) based algorithm adapted to DAB/DVB-T and GSM passive radar [3], [4] and multistatic active sonar [5]. The algorithms were tested in maritime and air surveillance applications. Within the European project ATOM [6] the potential of passive radar for person tracking within the airport terminal was investigated. The use of the WiFi signal turned out to be most promising. The WiFi signal (like most passive radar signals) is continuously transmitted and a Doppler sensitive waveform. The range resolution is thereby determined by the bandwidth of the digital signal. A concept for antenna design and signal processing is developed by the University of Rome, for details we refer to [7], [8]. This paper focus on the development of an advanced tracking filter for WiFi-based passive radar. The tracking task is composed of the subtasks of target association and state estimation. The association task maps new (multiple) measurements to multiple existing tracks or ignores them as false alarms. Obviously, the association task depends critically on the magnitude of the measurement uncertainty. The MHT concept [9], [] has been proven to be robust in difficult association scenarios and is therefore chosen as the basis of the developed algorithms. For the ATOM scenarios the features of MHT have been tailored to a passive radar system based on WiFi transmitters for person tracking. As underlying tracking filter the Unscented Kalman Filter (UKF)[] was selected, which turned out to be most convenient and which can handle the emerging nonlinearities. Furthermore, specific solutions of the following problems are introduced: Inclusion of a-priori knowledge like the admissible area of target movement and the geometric distribution of detection probabilities of the system. Incorporation of the case of occlusion. Knowledge of walls and corners are used to model occlusion phenomena. This is incorporated in the MHT framework as a- priori knowledge. Inclusion of the concept of negative information, compare [2]. If a person has stopped this event implies several possible interpretations for the tracker (target in the zero Doppler notch, target has stopped, target is occluded, target miss). All these interpretations are evaluated with their likelihood and are updated as hypotheses. Resolution conflicts in multi-target situations. This is a special and highly important case for person tracking with passive radar data. It involves the problem of multiple unresolved, ambiguous targets. Unresolved measurements are considered in the MHT in form of additional hypotheses [3]. We introduce here a modified version of the track-oriented MHT to handle resolution conflicts. This work has the following structure: In Section II we describe the scenario and give an overview about the challenges concerning target tracking in Section III. In Section IV and V we address the adaptation of the tracker to model the probability of detection and to handle unresolved measurements. Simulation results will be discussed in Section VI.

2 II. MULTISTATIC SCENARIO A bistatic radar system consists of a single transmitter and a single receiver placed at different locations. A signal is emitted by the transmitter at s = (s x, s y ) and is reflected by the target at q = (x, y) (see Fig. ) producing an echo of the original signal. By comparing at the receiver at o = (o x, o y ) the q s Target q = (x, y) o q ϕ north Rx Tx o = (o x, o y ) s = (s x, s y ) east Figure : Bistatic Setup; signal from transmitter at s is reflected by the target at q and received at the observer o. emitted signal with the target echo, the target state parameters can be estimated. One parameter is the Time Difference of Arrival (TDoA) τ between the arrival of the direct signal and the delayed signal at the receiver. From the known distance between illuminator and receiver o s the bistatic range is calculated by r = τ c+ o s, where c is the speed of light. In dependency on the Cartesian position of the target the bistatic range equation is given by r = q o + q s. () The observed phase difference between successive echoes can be used to determine the Doppler shift, which value depends on the bistatic geometry. To describe the Doppler shift f d as a function of the target state we use the bistatic range-rate equation given by ṙ = f d λ = ( q o q o + q s ) T v, (2) q s where λ is the wavelength of the signal. The angle of the incoming echo can be determined by an array of receiving antennas. We consider here the angle of incidence in the x-y plane (azimuth). It is related to the geometry by the fourquadrant inverse tangent ) ϕ = atan2 (x o x, y o y ( π, π]. (3) When defining the 2D-target state vector by x k = (q, v) = (x, y, ẋ, ẏ) the functional relationship between target state and measurements can be expressed by the non-linear measurement equations h(x, s, o) = (r, ṙ, ϕ). The development of the target state is usually modelled by a discrete-time Markov chain {x k } k N, where the index k corresponds to t k and t k < t k+ for each k N. The observations of the target states (measurements) describe a second stochastic process {z k } k N over times t k. The target motion model is typically modelled by a deterministic and a random part (process noise), i.e. x k = f(x k ) + v k, with v k N (, Q), (4) with process noise matrix Q. We use here the model of nearly constant velocity, which yields the linear dependency according to x k = F x k + v k. (5) The process noise matrix is used to compensate deviations from the linear model. The technical equipment (consisting of the sensors with subsequent signal processing) delivers measurements of r, ṙ and/or ϕ with certain accuracy. For simplification we model the measurement noise to be unbiased and Gaussian distributed random variables. Strictly speaking, the Gaussian model is violated in real applications. For example, all measured values have only a limited range. However, it is a reasonable approximation in many tracking applications. Following these assumptions the measurement z k is modelled by z k = h(x k, s, o) + w k, with w k N (, R k ), (6) where R k denotes the positive definite η z η z measurement covariance matrix, R = diag(σ 2 r, σ 2 ṙ, σ2 ϕ). The bistatic measurements are nonlinear functions of the target state. Several approximation techniques like the EKF [4] and UKF [5] exist and fit into the framework of the MHT: only the measurement update component of the MHT is affected. Due to our experiences with multistatic measurements, the UKF component was chosen here, because of better performance with respect to handling strong nonlinearities, see [5] for a detailed simulation study. III. CHALLENGES OF TARGET TRACKING IN THE ATOM SCENARIO The ATOM project addresses the enhancement of the airport security level by a multisensor concept consisting of several imaging radars as well as distributed tracking sensors. The imaging radars aims to the identification of passengers wearing suspicious items like weapons, see for example [6]. The imaging sensors scan the person at a given position or region, to keep track of suspicious persons additional tracking sensors are needed. They shall guarantee that the person is checked by the security staff without interrupting the passenger flow. In particular the use of passive tracking sensors is explored within ATOM, which uses transmitters that are already available at the airport and needs no additional radiation. A potential scenario with six receivers and one WiFi transmitter is depicted in Fig. 2. The imaging sensors are positioned inside a corridor (coordinates (m,m) here). If a suspicious person is detected the tracking process is initiated. The task of target tracking is to keep track of this person

3 y [m] Figure 2: Scenario: The target starts at the left and walks through a corridor into a bigger hall. The passive radar system consists of one Tx (triangle) at (2 m, m) and 6 Rx (circle) marked by numbers. Position of Rx 6 is identical to transmitter position (quasi monostatic). while walking through the corridor into a larger hall. This is done by combining the measurements from different bistatic transmitter-receiver pairs. Not every transmitter-receiver pair delivers a measurement of the target. Reasons for missed detections are for example shadowing or low signal attitude of the echo signal. Also, if the target is not moving, measurements are missed due to Doppler cancellation [7]. In this case no transmitter-receiver pair will provide detection. Incorporation of a model of probability of detection (P D ) for individual transmitter-receiver pairs is needed in target tracking for the ATOM setup and is addressed in Section IV. The presence of multiple persons has influence on the choice of the tracking filter. If multiple targets are well separated the individuals tracks can be built up in parallel. Separation is guaranteed if measurements of the one target are not associated with an other target. If two tracks compete for the same measurement a multi-target conflict appears in the tracking sense. Separation of targets depends therefore on the distance in position and velocity space, but also on the measurement error and bistatic geometry; this makes the analysis of multitarget scenarios important in the passive radar context. One solution is to introduce the multi-target state, which is the combination of the individual target states. As a consequence the dimension of the target state increases proportional to the number of targets. The track-oriented approach to MHT [9] allows consideration of the multi-target scenario without regard to the full multi-target state vector. In a first step tracks are generated for individual targets. Targets are assumed to be separated, which means that a measurement can be associated with more than one target. The second step uses multi-target association to resolve competing measurement associations. This is often coupled to the n-scan pruning [9] technique, which is applied on a batch of measurements to generate an unambiguous interpretation history. N-scan pruning pursues the hard data association logic by enforcing a unique association decision over a given time interval. The concept of track oriented MHT is well suited to solve association conflicts but contradicts the concept of unresolved measurements. This appears if two targets are within the same resolution cell, as a consequence only a single measurement is generated representing both targets. The size of the resolution cell depends on the resolution of the bistatic measurements, which is for WiFi passive radar 5 m in bistatic range and 2 Hz in Doppler (corresponding to about.2 m/s in rangerate) (compare [7]). In the ATOM application, where persons are possibly walking close to each other, resolution conflicts can not be ignored. In Section V we will present an approach to incorporate the model of unresolved measurements into the concept of track-oriented MHT. IV. MODEL OF PROBABILITY OF DETECTION For the design of the tracking algorithm a model of the probability of detection (P D ) is needed. Besides the dependency on the sensor characteristics, the P D depends on the target state and the transmitter-receiver geometry. A. Modeling the clutter notch For example Doppler blindness occurs if the bistatic radial velocities of the target as well as the velocity of the surrounding mainlobe clutter return are nearly identical. The P D is small in a certain region around the clutter notch characterized by the minimum detection velocity (MDV). This defines the location of the bistatic clutter notch in the state space of the target and, as such, reflects a fundamental physical fact without implying any further modeling assumptions. In close analogy to the discussion in [2] we write the detection probability as a sum of Gaussian-type functions reflecting the current sensor-to-target geometry which describes the basic underlying physical facts: PD CN (x k ) = p D ( MDV N (; n C (x k ), MDV2 ln(2)/π 2 ln(2) )), (7) where n C (x k ) = ṙ t ṙ C with ṙ t the range-rate of the target, ṙ C the range-rate of the corresponding background and p D describes a fixed factor, which is independent on the range-rate. Negative sensor evidence [7], i.e. the lack of an expected sensor measurement, is equivalent to a fictitious measurement (here: the distance between two range-rates is small), which provides additional information. For a set of incoming measurements Z k = (zk, z2 k,, zm k k ) the following interpretation possibilities exist: case : target detection by one of the m k measurements case 2: target detection by one of the m k measurements, even though the target is near to the clutter notch case 3: no target detection, since it is in the clutter notch case 4: no target detection due to other reasons ( p D ) The tracking update is driven by the likelihood function, which proves to be proportional to a sum of Gaussians. Let G f = N(; n C (x k ), MDV2 2 ln(2) ) be the Gaussian density w.r.t. the

4 fictitious measurement and G n U = N(zn k ; h(x k), R) then: m p(z k, m x k ) ( PD CN (x k ))ρ F + PD CN (x k ) n= G n U = ( p D )ρ F + p D ρ F MDV (ln(2)/π) G f (8) y [m] m (p D G n MDV U p D sqrt(ln(2)/π) Gn U G f ), n= where ρ F is the value of the (assumed uniformly distributed) false alarm intensity. From this and the predicted density p(x k Z k ) the updated density is calculated by p(x k Z k ) p(z k, m x k )p(x k Z k ). (9) The derivation of the update formulas leads to the standard Kalman update formulas by using the fictitious measurement in the cases 2 and 3, see also [2], [8]. B. Modeling shadowing Since the WiFi signal is not able to fully penetrate walls, P D is further decreased by occlusion effects. We use the following model: if one of the two rays, either Tx-target or Rx-target is disturbed by a wall the target is declared as not detected. We sample the position of potential target in the observation area and decide if the target could be detected by a given transmitter-receiver combination. Fig. 3 (upper) shows samples of P D equal zero. We use these samples to approximate P OC D by a Gaussian mixture (GM), see Fig. 3 (lower). Red corresponds to low and blue to high values of P D. For generating the GM approximation we use the EM algorithm [9] followed by a smoothing step based on the Gibbs Sampling method. Thus, P D can be expressed as PD OC (x k ) = i N (x k ; µ i, P i ). () As in the previous subsection the modeling of P D can be used as a pseudo-measurement. If there is no detection of the target this might be due to event that the target is in the occluded area. If there is a detection of the target, the probability of being in a region of high P D increases. This can help to overcome a passage of low detection rate by some sensorcombinations. Total P D is a combination of different models: we choose a constant parameter p D as the maximal P D taking into account random fluctuations and P OC D phenomena and transmission loss and PD CN clutter notch. We obtain: modeling occlusion modeling the P D (x k ) = PD CN (x k )PD OC (x k ). () In analogy to (8) P D (x k ) can be used to calculate the Likelihood function, which is the first step in the calculation of the posterior density (9). Different hypotheses are evaluated, e.g. target is occluded but not in the clutter notch, target is not occluded and not in the clutter notch, target is occluded and in the clutter notch, and so on.... Moment matching is applied after filtering to reduce the number of total hypotheses. y [m] Figure 3: Modeling occlusion for single pair of Tx (triangle) and Rx (circle): (upper) samples of P D, (lower) Gaussian Mixture approximation The Gaussian mixture model additionally incorporates a model of signal-to-noise dependent P D [3]. V. HANDLING OF UNRESOLVED MEASUREMENTS IN TRACK-ORIENTED MHT If two targets lie in the same resolution cell only a single measurement is generated. The typical tracking assumption that a measurement is only used with one track is no longer fulfilled. Furthermore, an unresolved measurement is a group measurement, which might fit not very well with each target. This means that for correctly updating the track state according to this measurement we need to regard the multi-target state instead of the single-target state. The first step is to model the probability that the measurements of two targets are unresolved. Following the approach described in [3] we define r = r r 2, ṙ = ṙ ṙ 2 and ϕ = ϕ ϕ 2 as the distance of the noise free measurements of the two targets in bistatic range, bistatic range-rate and azimuth. Further, let α r, αṙ and α ϕ describe the sensor resolution. Two targets are unresolved if m/α m for one of the measurements. The probability that a measurement is unresolved is modeled by P u ( r, ṙ, ϕ) = exp( log(2)( r/α r ) 2 ) (2) exp( log(2)( ṙ/αṙ) 2 ) exp( log(2)( ϕ/α ϕ ) 2 ). P u ( r, r, ϕ) becomes small if one of the measurements is resolved.

5 H H 2 H 3 track measurements track 2 H Figure 4: measurement update of two multi-hypotheses tracks We further define the function H 2 H 3 H 4 ( r, r, ϕ) = h u (x k, x 2 k) and (3) R u = 2log(2) diag[α2 r, αṙ2, αϕ]. 2 (4) Thus we can express the probability that two targets are unresolved by [3]: P u (x k, x 2 k) = 2πR u N (; h u (x k, x 2 k), R u ) (5) The event that two targets are unresolved can therefore be interpreted as a pseudo-measurement (compare Section V). A. Multi-target hypotheses for unresolved measurments In track-oriented MHT for each predicted hypothesis and each measurement that falls into the gate of the track a new hypothesis is generated. This is done under the assumption that all measurements are resolved. If we consider unresolved measurements we need to look at the multi-target state to correctly exploit the group measurement. For example in Fig. 4 a constellation of two tracks is shown. Track contains 3, track 2 contains 4 hypotheses. Each combination of predicted single-target hypotheses from track and track 2 forms a multi-target hypothesis, i.e. (H, H ), (H, H 2 ), (H, H 3 ), (H, H 4 ), (H 2, H ), (H 2, H 2 ), (H 2, H 3 ), (H 2, H 4 ), (H 3, H ), (H 3, H 2 ), (H 3, H 3 ), (H 3, H 4 ) For each of these states we need to consider the possibility that the two targets are either resolved or unresolved. If there would be two measurements as in the example for each multi-target hypothesis this would result in the following new hypotheses: Case : targets are unresolved 3 new hypotheses Update with group meas. or 2, miss-detection Case 2: targets are resolved 6 new hypotheses Update with the following combinations of measurements: (meas., meas. 2), (meas. 2, meas. ), (meas., miss), (meas. 2, miss), (miss, meas. ), (miss, meas. 2) Thus, after the update we would have 2 x 9 = 8 (multitarget) hypotheses. Following the idea of track-oriented MHT we use this to re-generate single-target hypotheses. For each single-target hypothesis and each measurement two new hypotheses are generated: Measurement is resolved Measurement is unresolved Single target hypotheses result from multi-target hypotheses by merging the respective single target components. For example, to update hypotheses H with measurement in case of the assumption of an unresolved measurement, we merge: (H, H ), (H, H 2 ), (H, H 3 ), (H, H 4 ) + update with group meas. This procedure results in 3 x 3 x 2 new hypotheses for track and 4 x 3 x 2 hypotheses for track 2, so at all we consider 42 hypotheses in contrast to 8 multi-target hypotheses. This procedure starts in every update step. B. N-scan pruning with unresolved measurements For application of n-scan pruning techniques the best multitarget hypothesis over a fixed time window needs to be found. To do this we use the / integer programming technique [2], where each single-target hypothesis is displayed as a vector containing zeros and ones. We assume that at each time scan i the number of collected measurements is m i. If we look at a window of n T time scans, we get the total number of measurements by m = k s=k n T + m s. A hypothesis H l can be displayed as an m-dimensional vector v l, where { association of z j v l (j) = target is not detected. When forming multi-target hypotheses it can easily be checked if the combination of single-target hypotheses is admissible. By calculating the sum of the corresponding vectors v l. If one entry is larger than the multi-target hypotheses is not valid. The / integer programming technique combines the reordering of hypotheses for efficient enumeration and a fast rejection criterion to find the best multi-target hypothesis. The single-target hypotheses contained in the best multitarget hypothesis will be used for n-scan pruning. In case of resolution conflicts we append this technique by introducing values smaller than, this means: association of z j (resolved) v l (j) =.5 association of z j (unresolved) target is not detected. Resolution conflicts with more than two targets can be solved in the same way, however spanning up multi-target hypotheses gets more and more complex. In [2] an approach is presented to handle multi-target resolution conflicts with more than two targets by representation by a resolution path. VI. RESULTS FOR SIMULATED PASSIVE RADAR DATA Simulated data for ATOM scenario was provided by university of Rome (DIET) [7]. This data reflect the specific

6 characteristics of the signal and the signal processing. The simulation takes into account: SNR dependent measurement error (in bistatic range, bistatic range-rate and azimuth) SNR dependent probability of detection (P D ) Doppler dependent P D occlusion phenomena Resolution conflicts in case of multiple targets Six receivers and one transmitter Measurements together with estimated measurement errors was provided. We compare different versions of the MHT tracker for the simulated data sets. We use the following abbreviations: OC : Taking into account occlusion phenomena CN: Taking into account the clutter notch phenomena OC-CN : Taking into account occlusion and the clutter notch phenomena standard: using a fixed P D This always corresponds to the modeling in the tracker and is independent from what was simulated in the data. The geometry of scenario is displayed in Fig. 5(upper). The input probability of detection (P D ) was calculated over a sliding window and is displayed lower for every transmitter-receiver configurations. Also shown is the expected Doppler value calculated according to the given target-receiver-transmitter geometry. A consecutive number of missed detections are observed for receiver 4-5 at the start of the scenario. This is when the direct path between target and receiver is blocked by a wall (occlusion (OC) phenomena). A similar effect is observed for receiver 6 but here it is mainly caused by transmission loss, i.e. due to large distance between target and receiver and target and transmitter. In addition we see the effect of Doppler cancellation, which causes P D = in the region of zero Doppler. The target geometry with respect to receivers -3 delivers zero Doppler for a long period of the scenario (even through the target is not stopping) resulting in low P D.We observe a period of 25 seconds (seconds 57-72) of no detections for any receiver combination. In Fig. 6 tracking results in terms of the position error is shown for the four different versions of the MHT. In the initial phase we observe an improvement in terms of the position error when the OC modeling is used, this is due to implicitly modeling the corridor in the occlusion model. We observe an increase in estimation error during the period of missed detections for all Tx/Rx pairs. The use of the models OC and CN further increases errors compared to the standard approach. This is due to taking into account different (also misleading) interpretation possibilities. Simple prediction (as in the standard approach) gives the best result, because the target is moving with constant velocity. However, when new measurements are provided all approaches are able to recover quickly, i.e. the correct hypothesis is selected. In scenario 2 Fig. 7 we look at a very similar geometry. This time the person stops for 2 s (at time s). As shown in terms of the input P D the stopping event looks similar to y [m] PD clutter notch TL occlusion and TL Doppler Figure 5: Scenario : (upper) geometry of target (blue trajectory), six receivers (circle) and the transmitter (triangle). (lower) the input P D for the two data sets and the expected Doppler of the target is shown. position error [m] 5 5 standard OC CN OC-CN Figure 6: Scenario : tracking results for different variants of the MHT

7 y [m] target stops position error [m] standard OC CN OC-CN PD target stops Doppler Figure 7: Scenario 2: (upper) geometry of target (blue trajectory), six receivers (circle) and the transmitter (triangle). (lower) the input P D for the two data sets and the expected Doppler of the target is shown. the period of missed detection before, which is caused by the combination of the different phenomena. Tracking results are shown in Fig. 8. The first period of missed detections is again won by the standard approach. For the stopping event the CN model works best, which means that the person stopping is detected. If we only model the effects of occlusion the tracker tends to missinterpret the data. This even results in divergence of the track. If we use the occlusion model together with the clutter notch, the tracker correctly identifies the missed detections at the beginning, however after some time also occlusion seems to be likely, which results in an increase in position error compared to the case when the clutter notch is the only alternative. In scenario 3 we consider two targets (Fig. 9). P D and the Doppler are shown for both targets in blue and red color. Target Figure 8: Scenario 2: tracking results for different variants of the MHT 2 (red) enters the scene 3 s after target (blue), but since it is moving with larger velocity the targets cross after entering the hall. Resolution conflicts appear when the measurements of the two targets are in the same Doppler resolution cell. In (Fig. 9) the expected Doppler value of a group measurement (provided the measurement would be unresolved) is displayed in black color. Unresolved measurements are indicated by a blue x. Tracking results are shown in Figure. The best results (obtained from direct comparison of tracks and groundtruth) was obtained for the combination of OC and CN model. For OC and CN a track switch appears, which could be prevented in OC-CN. Generally, maintaining track identity can not always be guarantied. VII. CONCLUSION In this paper a version of the track-oriented MHT for person tracking in a passive radar application was presented. In particular, methods for modelling the probability of detection and handling of resolution conflicts was discussed. From analysis with simulated data we found that realistic modelling according to forming different hypotheses (target is occluded, target is in clutter notch) does not necessary result in improved performance, because the probability of a wrong decision does increase. In real application the choice of receiver positions is important in terms of avoiding interpretation ambiguity. ACKNOWLEDMENTS The research leading to these results has received funding from the European TRANSPORT (including AERO- NAUTICS) Communitys Seventh Framework Programme AAT under agreement of n We would like to thank Paolo Falcone from University of Rome for providing simulated passive radar data. REFERENCES [] P. Howland, D. Maksimiuk, and G. Reitsma, FM radio based bistatic radar, IEE Proceedings - Radar, Sonar and Navigation, vol. 52, no. 3, pp. 7 5, Jun. 25. [2] H. Kuschel, J. Heckenbach, J. Schell, and D. O Hagan, Passive radar for homeland defence, in International Radar Symposium (IRS), September 29, pp [3] M. Daun, U. Nickel, and W. Koch, Tracking in multistatic passive radar systems using DAB/DVB-T illumination, Signal Processing, 2.

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