Multitarget Tracking Using Virtual Measurement of Binary Sensor Networks

Transcription

1 Multitarget Tracking Using Virtual Measurement of Binary Sensor Networks Xuezhi Wang Melbourne Systems Laboratory Department of Electrical & Electronics University of Melbourne Australia Bill Moran Melbourne Systems Laboratory Department of Electrical & Electronics University of Melbourne Australia Abstract - Networks of small low-cost sensors for target tracking are becoming increasingly important for many applications. A major problem is that these small sensors usually have limited observability due to power constraints and the transition between sensor observation and target states is nonlinear. As a consequence, nonlinear filtering techniques, such as particle filtering, are often chosen by researchers in this context. We focus on a network of sensors where each sensor provides binary data at each epoch: target present or target absent. At this point it is not clear that existing approaches can effectively handle the tracking of multiple targets using such networks. In addition, algorithmic computational complexity is an issue if particle filters are used. In this paper, we present a new method, the Virtual Measurement (VM) approach, for multi-target tracking using distributed binary sensor networks. The central idea of this approach is to define a mapping between the space of binary sensor observations and the so-called VM space, such that, any point within a VM space is a transform of the target state, as if it were generated by an equivalent large sensor. With VMs, conventional multi-target tracking (MTT) algorithms can be used in a straightforward way for tracking multiple targets over the sensing field of binary sensor networks. Computer simulated examples of MTT demonstrate the effectiveness and robustness of the VM approach. Keywords: Multi-target tracking, Integrated Sensing and Processing (ISP), Binary sensor networks, Virtual Measurement (VM) Approach, Wireless Communications. 1 Introduction The application of distributed sensor networks to multitarget tracking can be seen as a benchmark in the achievement of Integrated (or Collaborative [1]) Sensing Processing (ISP). Sensor nodes equipped with wireless communication facilities (which are popularly called as smart dust or motes ), constrained by cost and size, usually have limited sensing ability, computing capability and low reliability. Research on methods and algorithms that can extract sufficient target information This work was supported in part by the Defense Advanced Research Projects Agency of the US Department of Defense and was monitored by the Office of Naval Research under Contract No. N14-4-C-437. from (distributed) sensor detections of such networks and thus estimate target states are clearly crucial to the development of these low cost sensor networks [1, 2]. One of the fundamental study areas on information processing is ISP through the class of binary sensor networks. A binary sensor network, perhaps, is the simplest prototype of sensor networks that can be used for target tracking. The sensor system we have in mind is comprised of a binary sensors as nodes in a communicating network, where each node serves as an event detector (e.g., a target enters an area or not, a target is approaching or departing), and generates and transmits one bit new information after every detection. Clearly, under the binary sensor model, individual sensors of the network have very limited observability with respect to target states apart from nonlinearity between what a sensor may observed and the target state of interest. In contrast to the use of large sensors 1, as mentioned in [1], distributed target tracking using binary sensors gives rise to many challenges to conventional target tracking techniques, in particular, to the way that target information is acquired. A number of approaches have been proposed in recent years, such as those in [3, 4, 5]. In these approaches, different ISP techniques were used to extract target information from multiple binary sensors under different assumptions. Target tracking is performed in a central structured sensor network segment, where a base station (or a dominant sensor node) collects and processes information from all sensors and provides the estimate of target state within each data sampling period. Among most existing approaches, a common theme is the particle filtering technique [6] which plays a central role for recovering information from highly compressed sensor data and thus provides an estimate of target state. It is important to bear in mind that while the use of particle filters may effectively solve the nonlinear estimation problem for small sensors, it also requires considerable computation compared to the use of linear estimation algorithms. To this end, it may not be appropriate for some applications using motes. Moreover, the use of particle filters for multi-target tracking problem is an ongoing research issue [7]. Therefore, the extension of existing approaches to handle multi-target tracking is 1 A single large sensor, such as a radar, can cover an entire surveillance region. Small sensors, such as motes, usually have significantly shorter sensing ranges and the surveillance region may only be filled by the deployment of many of them.

2 not trivial. In this paper, we present a new method: the virtual measurement (VM) approach, for multi-target tracking using distributed binary sensor networks. As in [5], we assume that binary sensors are deployed so as to cover the entire area of interest and their sensing ranges and locations are known to the base station. At each data sampling time, activated sensors signal the base station via wireless communications. The central idea is to define a mapping between the space of binary sensor observations and a space, called VM space, such that, a point within the VM space is a transform of a target state, as if it were generated by an equivalent large sensor. With VMs, conventional MTT algorithms can be used in a straightforward manner for the tracking of multiple targets over the sensing field of binary sensor networks. We believe that one of the reasons that existing approaches have been limited to single target tracking is that the ISP has failed to extract information that can lead to identification of multiple targets from a collection of sensor detections. In the VM approach, this information is extracted by clustering the collection of activated sensors into Independently Activated Sensor Groups (IASG), which is one of the contributions of this paper. An important property of the proposed method is that the uncertainty/noise associated with sensor detections, sensing radius, sensor locations can be reflected by the uncertainties of the assigned VMs. The latter can be effectively handled by techniques of multi-target tracking in clutter. The reminder of the paper is organized as follows. The problem of multi-target tracking in binary sensor networks is formulated in Section 2. The VM approach is presented in Section 3, where some important concepts, related algorithms, practical issues and solutions are discussed. In Section 5, we demonstrate the robustness and effectiveness, and highlight some properties of the proposed VM approach with a computer simulated scenario. Section 6 concludes the paper. 2 Problem Description Consider a 2D sensor network, comprised of a set of N passive sensors (motes) and a base station and it is used to track moving targets intruding into an area of interest. The base station is essentially a sensor (or mote) node capable of performing target tracking and exchanging information with other networks (segments). The sensors, which have sensing ranges R i at locations r i, i = 1,2,,N, are distributed to cover the area of interest with overlapping sensing fields. We assume n targets with states x j [position, velocity, ], j = 1,2,,n are present. The jth target trajectory may be modeled as a Markov process, x j k+1 = f(k,xj k,uj k ) + wj k j = 1,2,,n (1) where f is the state transition function, u is an input parameter for target dynamics and w is process noise. All noises are assumed independent. Target detection of the ith of N sensors is a binary output based on the model z i k = h(k, Hx j k r i ) + v i k, j = 1,2,,n (2) where H is a transition matrix, vk i is a noise term to account for uncertainties associated with sensor location, target location, sensing range and the environment of the sensor field, etc. In particular, { zk i 1, with PD 1, if Hx j = k r i R i, otherwise j = 1,2,,n (3) If the output of the ith sensor is equal to 1, we say that the ith sensor is activated. At each time k, the base station collects sensor detection outputs Z k = {z 1 k,z2 k, } from all activated sensors. The problem is to estimate the target states, conditioned on all available prior information and sensor detections up to time k collected by the base station; that is, to find the conditional posterior densities p(x j k Z k,z k 1, ), j = 1,2,,n (4) (4) has a close form solution only in very particular cases, such as the linear-gaussian case where x is Gaussian and z is a linear transformation of x. 3 Virtual Measurement Approach Sensor observation space Z Multiple targets Target location space S IASG space 1:1 * * * * * * * * * * * * * * ** * * * * * * * * * * * VM space Figure 1: Illustration of the proposed ISP process. As illustrated in Figure 1, in the VM approach we consider the ISP process as following mapping X = Z = S = Y (5) where X is target position vector space, Z signifies the (joint) sensor observation (i.e., binary vector) space, Y X is a discrete set and S is another binary vector space which bridges Z and Y. The key idea of the VM approach is to find the mapping, i.e., Z = Y X (6) such that for a given collection of activated sensors Z k = {zk 1,z2 k, } Z we can allocate a set of points Y k = {yk 1,y2 k,, } Y, where the space Y is a transform of the target state space X and is finite and discrete (since sensor observation space is finite).

3 If the mapping (6) is constructed, for each collection of sensor detections Z k, we can uniquely find a set Y k as described above. Using the time sequence Y k = {Y 1,Y 2,,Y k } Y, Y k = {yk 1,y2 k,, }, the MTT is able to apply a conventional technique of MTT in clutter [8]. A point y in the space of Y X is called a virtual measurement since it is not what sensor directly observes. Next, we show that with following defined conditions and assumptions, we can determine the mapping (6), i.e., Z = Y. In particular, that mapping is unique (1:1) for single target case. In the multiple target case, it is not unique, but it does include the information of all possible target locations, while the mapping uncertainty due to the presence of multi-target and clutter may be resolved via a conventional multi-target tracker. 3.1 Preliminaries First, we make several minimal assumptions for the sensor network to permit us to establish the theory of the VM approach. These assumptions are not fundamental to the VM approach and how our method can be extended to cope with the relaxing of them is discussed later. Assumptions 1 Target within the sensing area of a sensor will always be detected; that is, the probability of detection P D = 1 for all sensors. There is no sensor failure. Assumptions 2 All sensors are stationary and their locations r i and sensing ranges R i, i = 1,2,,N are known to the base station. Assumptions 3 There are no false detections. Definition 1 Distinct Sensing Region (DSR): A DSR is a particular sensing region in the region covered by a sensor network. It is distinguished from other sensing regions in one or more of the following: 1) the particular sensor detection regions overlapped, 2) its location, and 3) its size. With respect to a target location, the DSR is the smallest resolution cell that may be achieved with the given sensor distribution. Within a DSR, a target position cannot be further resolved via sensor detections. Figure 2 shows a DSR described by 2 sensors. If the sensing region of a sensor does not overlap with sensing regions of any other sensors, the DSR is just the detection region of that sensor. Definition 2 Virtual Measurement (VM): An VM is a random variable of sample space corresponding to a DSR. The collection of all VMs in the region of interest composes VM space. In this work, we assume the distribution of a VM to be a truncate Gaussian with mean at the center and standard deviation equal to to half of the maximum span of that DSR. In the example of Figure 2, we have V M N(Y,S), Y = [x,y], S = [ V 2 x V 2 y Definition 3 Independently Activated Sensor Group (IASG): An IASG is the largest set of activated sensors (or sensor cluster) at a sampling time, in which all members share a common DSR. ]. sensing boundaries Vy Vx overlapped sensing area Y = (x, y) Figure 2: A DSR is represented by a VM. In other words, an IASG is the largest set of sensors which may be triggered by a single point target 2. Note that an IASG may contain a single sensor if part of its sensing region is not overlapped by that of any other sensors (e.g., sensors 7, 5, and 9 in Figure 3, which correspond the regions A 2,A 4 and A 5 respectively). The IASG is an important concept for the VM approach and is a key to resolving those sensor detections due to multi-target trajectories. An example is A5 A A Figure 3: Example of IASGs: presented in Figure 3, where a region covered by total 13 sensors with sensing ranges indicated by circles. At the time of data collection, sensors 5,6,7,9,1 are activated (excited). According to IASG definition, we can identify 5 IASGs in this case as shown in Table 3.1. In Table 3.1: IASGs for Figure 3 IASG Index Sensor Index DSR 1 5, 6, 9, 1 A 1 2 6, 7, 1 A A A A 5 other words, in the case in Figure 3 the IASG definition implicitly assumes that there are 5 possible (target) sources located in the regions of A 1,A 2, A 3, A 4 and A 5 respectively and sensors 5,6,7,9,1 are excited by these or part of these sources at the time of data collection. 2 If the cross section of a target is less than or equal to the sensor resolution cell, sensors can only generate a single point measurement for target detection. We assume the target as a point target in this sense. 11 A3 A2

4 Having the concepts of DSR, VM and IASG, we may state the following assertion that lay down the foundation of the VM approach. Theorem 1 For a given binary sensor network configured based on Assumptions 1, 2 and 3, the IASG space is determined. The number of different IASGs which comprise the IASG space (see Figure 1) is equal to the number of DSRs (and thus to that of VMs). The mapping between the IASG space (S) and VM space (Y) is a one-to-one mapping. Theorem 2 If that target sources are well separated 3, the space of sensor observation (Z) and the space of IASG (S) are identical. The proofs of Theorems 1 and 2 are obvious and thus we omit them. 3.2 VM Approach As we pointed out earlier, a locally centralized sensor network is assumed to cover the region of interest. In the case of tracking a single target under perfect sensing condition, at each time, the base station collects data from activated sensors and identifies the index of the IASG. A VM that correspond to that IASG is then assigned to a linear estimation algorithm for updating the underlying target state estimate. Similar process can be expected for tracking multiple well separated targets over the sensor network. For tracking multiple targets which are closely spaced, uncertainties will arise in the VM domain. From the set of activated sensors multiple IASGs may be identified as to cover all possibilities of the sensor excitement due to multiple target sources and additional VMs will be assigned. Such a situation may be explained using the example of Figure 3, where sensors 5,6,7,9 and 1 are activated. 5 IASGs can be identified as in Table 3.1 to cover total 13 possibilities where targets of numbers between 2 5 may be present as listed in Table 3.2. In fact, 5 VMs that correspond to those IASGs have to be assigned although some of them may not originated from any of the unknown number of targets (i.e., they are false measurements). This is the exactly the same situation as in conventional multi-target tracking in clutter. Clearly, a data association mechanism is required to provide measurement-to-track association. Many data association techniques are available in the literature [9]. Among them, the well known probabilistic data association (PDA) technique [1] yields much better tracking performance, while it has only mildly increased computational requirements when compared to a Kalman type filter [8]. The key idea of PDA technique is to use the probabilistic average of all measurements (in side the tracking gate) to update the underlying track. A variety of algorithms for conventional multi-target tracking in clutter are based on the PDA technique [11], such as the one we used in the simulation software package. 3 In the situation where any sensor in the network can only be triggered by at most a single target source, we say, the target sources are well saperated. Table 3.2: Possibilities of Multiple Targets Index DSRs of target sources No. Targets 1 A 1,A 2 A 3,A 4,A A 1,A 3,A 2,A4 4 3 A 1,A 3,A 2,A A 1,A 3,A 4,A A 1,A 3,A A 1,A 3,A A 1,A 3,A A 1,A 3,A A 1,A 2,A A 1,A 2,A A 3,A 4,A A 1,A A 1,A 3 2 Same as conventional MTT, the PDA will treat alternative VMs as clutter (though they are not uniformly distributed in a track gate). It should be mentioned that for each given IASG, we need to work out the area and the center of its own DSR and this may be computational demanding when the number of IASGs is large. However, this work can be done offline for all VMs if sensors are stationary. In fact, we have included this process into the network initialization phase. Network Initialization Sensor Detection Collection Virtual Measurement Space Virtual Measurement Assignment Multitarget Tracking Figure 4: The idea of the proposed approach. In summary, as shown in Figure 4, the VM approach consists of following 2 processes: 1. Network Initialization obtain VM space (algorithm) based on Assumptions 1, 2 and 3. This process should be done during the network set up phase. 2. Target Tracking on line estimation of the states of all targets in the region covered by the sensor network based on the collection of binary sensor detections. At each epoch, on receiving data, the algorithm performs following 2 tasks: (a) Identify IASGs, and assign VMs accordingly; (b) Conventional multi-target tracking in clutter using the assigned VMs. 3.3 Algorithms The VM approach for target tracking requires the following algorithms: Network Initialization any method that can compute the centers and maximum spans of all DSRs for the local sensor network can be used. In our demonstration program, we implemented the network initialization using a 2D grid search. All VMs computed are stored into a database.

5 IASG Identification: Algorithm is implemented based on the Definition 3. Specifically, sensor s i and sensor s j are said to be in same IASG if and only if If r i r j (R i + R j ), i,j, i j (7) r i r j > (R i + R j ), j, i j (8) for entire or part of the sensing region of sensor s i, it will form an IASG on its own. VM Assignment For each identified IASG, assign the corresponding VM from the VM space (database) to the tracker. The VM assignment algorithm that follows from Theorem 1 is called an exact VM assignment (EVMA) algorithm. Tracker Any conventional multi-target tracking in clutter algorithms, such as, Linear Multitarget Integrated Probabilistic Data Association (LMIPDA) [12], Joint Integrated Probabilistic Data Association (JIPDA) [13], or simply the Integrated Probabilistic Data Association (IPDA) [14]. More reference can be found in [15, 16]. In our demonstration program, we implemented a LMIPDA tracker that includes automatic track formation [17] and maintenance [18] features. 4 Practical Issues and Solutions The method we described in the last section rests on the Assumptions 1, 2 and 3. In reality, sensors may fail to function or have detection probabilities 4 less than unit, i.e., P D < 1. Furthermore, both sensor locations and sensing boundaries may not be exactly known to the base station. The impact of these facts to the VM approach for target tracking and solutions are discussed in this section. 4.1 The Impact P D < 1 may lead a sensor to miss detection when a target is presented in its sensing field and thus miss a VM assignment to tracker. This is because that the IASGs identified according to the collection of activated sensors may not correspond to any VM in the VM space predefined when individual sensor P D < 1. Nevertheless, the problem of missing VMs can be handled by the tracker as if the overall detection probability of the equivalent sensor less than unit. The probability of missing target detection can be even higher if a DSR overlaps more than one sensor region. For example, if we assume identical detection probabilities, i.e., P D =.6 for all sensors, then for a DSR covered by a single sensor, the probability of missing VM assignment is 1 P D =.4; for a DSR covered by two sensors, the probability of missing VM assignment becomes 4 It may be more appropriate to model the detection probability as a function of relative distance to target. However, we will assume in this work that the detection probability of a sensor is a constant within its sensing range. 2(1 P D )P D + (1 P D ) 2 =.64. Higher probability of missing target measurements will lead to correspondingly higher probability of track loss. In the VM approach, we model the uncertainties of both sensor location r i and sensing boundary R i, i = 1,2,,N as zero-mean Gaussian noise. In particular, the measured location ˆr i and sensing range ˆRi of sensor s i are given by ˆr i = r i + r i r i N (, σ ri ) (9) ˆR i = R i + R i Ri N (, σ Ri ) (1) where r i and R i represent the exact sensor location and sensing range of sensor s i. As with the case of P D < 1, the existence of uncertainties both for sensor location and sensing range may lead to missed VM assignments. Because an IASG identified via (7) using ˆr i and ˆR i may not correspond to any VM in the VM space generated using r i and R i. Sensor failure can be seen as a special case of PD < 1. (When a large amount of sensor faults occurs, network should be re-initialized.) 4.2 Solution We assume that a target with state position component x k has entered into a DSR, denoted as DSR yj which corresponds to the jth VM, denoted as y j, at time k. If the detection probabilities of individual sensors, i.e., P D1,P D2,,P DN, are known, we may compute the following two conditional probabilities: the probability that the target will be detected, and the probability that a VM is assigned given that x k DSR yj, i.e., and P(y j x k DSR yj ) (11) P(the target will be detected x k DSR yj ) (12) Figure 5 is a plot of these two probabilities versus sensor P D for a DSR overlapped by 1,2,3,4 and 5 sensors respectively and we assume an identical P D for all sensors. Note that the probabilities (11) and (12) are equal to 1 if the P Di 1, i = 1,2,,N and this requires Assumptions 1, 2 and 3 to be hold. It is interesting that these two probabilities fall at different rates as sensor detection probability P D decreases and the DSR is overlapped by more than one sensor. The probability that a VM which corresponds to the DSR is assigned falls rapidly. In other words, the probability that the tracker is missing a VM rises quickly, while the probability that the target is detected (within a DSR) declines more slowly. As more sensors are involved, the difference between these two rates becomes larger. As a benefit of ISP, there will be a higher probability that a target is detected when the target is in a DSR covered by multiple sensors, even if the detection probabilities of these sensors are low. Motivated by this observation, we have developed another VM assignment algorithm, called the mixed VM Assignment (MVMA) algorithm, to reduce the probability of track loss when P D < 1.

6 IASG2 IASG3 the sensing range noise. We assume that the detection probability P D of these passive sensors is constant over sensing field (although it can be modeled as a function of the distance between sensor and target). IASG4.6 IASG5.5 P(target is detected x DSA yi ) P(y i x DSA yi ) Sensor PD Figure 5: The probability of a target is detected and the probability that a VM is assigned given x k DSR yj versus sensor P D. IASG Identification Figure 7: 1 motes distributed over m 2, where circles indicate the sensing boundaries. Is this IASG Registered? Yes VM Assignment No Pseudo VM Assignment The computed VM space that corresponds to the sensor network of Figure 7 is shown in Figure 8 (light blue stars). MTT Tracker Figure 6: Flowchart of the Mixed VM Assignment Algorithm. As illustrated in Figure 6, the MVMA will perform EVMA if a VM that corresponds to the identified IASG is found in the database (established during the network initialization phase), otherwise, it performs a pseudo- VM assignment algorithm. The pseudo-vm assignment algorithm computes the average location of those sensors in the IASG and treat it as a VM with standard deviation R m, where R m = max R i and R i,i = 1,2, are the sensing ranges of those sensors in the IASG. Clearly, the EVMA is a special case of MVMA. In general, MVMA algorithm can be used for all situation to replace EVMA algorithm. However, in some cases, such as tracking crossing targets, MVMA may assign unnecessary VMs, which may generate additional ambiguities for measurement-to-track association, to a tracker. 5 Demonstrative Results In this section, we present some statistical results from the target tracking perspective to demonstrate the effectiveness of the VM method. The results are based on the scenario described below. 1 motes are equally spaced over the area of m 2 with location offset uniformly distributed in [,2] m (see Figure 7). The sensing radius of individual sensors is 1 meters with boundary noise N(,B 2 ), where B is the standard deviation of Figure 8: Illustration of the set of VMs (VM space) after network initialization (light blue starts). Target motion is described by x k+1 = Fx k + Gw(k) (13) and the state of target can be observed according to y k = Hx k + v k (14) where x k is the target state, a 4 components vector that includes target position and velocity in a 2D Cartesian coordinate system, at time k, y k is the VM assigned at time k, F, H and G are known transition matrices given in [15] with sampling interval being T = 1 (sec). As in [8], the system process noise and observation noise are assumed to be Gaussian, i.e., w k N(, Q k ) and v k N(, S k ), Q k = GG q 2, q =.5 and S k is determined by VM assigned at k. A multi-target tracker based on the linear multitarget integrated probabilistic data association (LMIPDA) algorithm [12] is implemented for the simulation.

7 Table 5: Tracking Performance Statistics P D B (m) Track Loss (%) Algorithm.9 EVMA.9 MVMA.9 3 EVMA.9 3 MVMA.5 75 EVMA.5 21 MVMA EVMA MVMA RMS Position Error RMS Performance with MVMA Algorithm PD =.9, B = PD =.5, B = PD =.5, B = 3 PD =.9, B = Scan 1 Monte Carlo runs were carried out for a single target tracking case. Table 5 listed the tracking performance statistics in terms of percentage of track loss in different cases and using different VM assignment algorithms. Figure 9 is the distribution of VMs assigned versus target true position. The root-mean-squared (RMS) errors of confirmed track in different cases are shown in Figure 1. Note that, a track is confirmed only if the value of its probability of target existence exceeds the track confirmation threshold. A track will be terminated if the value of its probability of target existence is below this threshold. We claim a track loss if a track has been terminated or has not been updated for 1 consecutive scans. It is evident that in multi-target tracking environments, tracking performance is dependend on the measurement-to-track association method used, and this varies across tracking algorithms. (While the performance of measurement-to-track association really depends on what MTT algorithm is used.) Figure 11 illustrates an example of tracking 2 crossing targets based on LMIPDA tracker. Figure 1: RMS position error performance comparison under diverse noise conditions. Tracking 2 Crossing Target Using a Sensor Network of 1 Motes T 5 (a) Half Way of Tracks T2 and T5 at 17 th Scan. T 2 T 116 T 2 T 5 (b) Tracks T2 and T5 after Crossing at 4 Scans. 18 Measurements X 18 Measurements Y Figure 11: Example of tracking 2 crossing targets: (a) Before crossing. (b) after crossing. Confirmed track thick line, tentative track thin line, VM circle Figure 9: Statistical distribution of VMs versus ground truth. Result discussion: The effectiveness of the VM approach is multi-fold. Firstly, it solves multi-target tracking problem over a binary sensor network of wireless motes which are constrained with power and bandwidth. Secondly, for stationary sensors, the most significant computations required by the VM approach can be allocated into the network initialization stage while the computational complexity for on-line tracking varies according to the choice of MTT algorithm, the number of targets involved, etc. Usually a satisfactory compromise for mote application can be achieved. Thirdly, the method takes into account uncertainties that related to sensor location, sensing radius and detection probability. The statistical distribution of the time sequence of VMs to target truth approximates a (zero-mean) Gaussian distribution (see Figure 9). The MVMA algorithm outperforms EVMA both in low P D and more densely distributed motes. In particular, MVMA will be identical to EVMA when perfect detection condition (P D = 1 and no sensor failure) is present. Nevertheless, when closely spaced multiple targets are present, MVMA may yield additional ambiguities by assigning additional VMs, which sometime can lead to track-swap. While advanced MTT algorithms such as multiple hypotheses tracker (MHT) [19], joint IPDA [13] may improve tracking performance (at the cost of yielding additional computational complexity), the tracking error of the VM approach will also depends

8 on the quality of VMs which in turn depend on the size of the associated DSRs. The more motes deployed (uniformly) into an area, the smaller the size of the DSRs will be and the smaller the tracking error can be achieved. Track loss may be reduced by increasing the process noise level of the tracker at the cost of larger tracking errors. In our simulation statistics of the examples, the average target-originated track confirmation requires 4 consecutive (target supporting) measurements as seen in Figure 1. This renders an indication for network design on the minimum number of motes needed to cover a region of interest for this case. 6 Conclusion In this paper, we propose a new method: the VM approach for multi-target tracking using energy and cost constrained, distributed binary sensor networks. A simple sensor model is assumed; that is, each sensor of the network will transmit a 1 if a target is entering its sensing region. At each sampling time, a set of sensor detections are mapped into a set VMs that correspond to target states. The mapping process fundamentally involves no information loss under perfect sensing conditions and may generate uncertainties in the VM domain if noise is present. Consequently, the technique of conventional multi-target tracking in clutter can be straightforwardly used to update tracks using these VMs. The VM concepts, the ISP technique used, the effectiveness and robustness of the proposed method are demonstrated via simulated examples of target tracking using motes. References [1] C. -Y. Chong, and S. P. Kumar. Sensor Networks: Evolution, Opportunities, and Challenges, Proc. of the IEEE, vol. 91, no. 8, pp , August 23. [2] I. F. Akyildiz, W. Su. Y. Sankarasubramaniam and E. Cayirci. A Survey on Sensor Networks, IEEE Communications Magazine, pp , August 22. [3] J. Aslam, Z. Butler, F. Constantin, V.Crespi, G.Cybenko, and D. Rus. Tracking a moving object with a binary sensor network, in the Proceedings of the First International Conference on Embeded Networked Sensor Systems, Los Angeles, CA, USA, 23, pp [4] K. Mechitov, S. Sundresh, Y. Kwon, and G. Agha. Cooperative tracking with binary-detection sensor networks, Technical Report UIUCDCS-R , University of Illinois at Urbana-Champaign, September 23. [5] P. M. Djuric, M. Vemula, and M. F. Bugallo. Signal processing by particle filtering for binary sensor networks, Proceedings of the 24 IEEE 11th Digital Signal Processing Workshop & IEEE Signal Processing Education Workshop, pp , 24. [6] A. Doucet, N. J. Gordon, and V.Krishnamurthy. Particle Filter for State Estimation of Jump Markov Linear Systems, Proceedings of Signal Processing, vol. 49, no. 3, pp , March 21. [7] M.R. Morelande and S.Challa. Maneuvering target tracking in clutter using particle filters, IEEE Trans. on AES, vol. 41, no. 1, pp , 25. [8] Y. Bar-Shalom, and T. E. Fortmann. Tracking and Data Association, Academic Press, [9] X. Wang, and D. Musǐcki. A Literature Review of Data Association Techniques for Target Tracking, Technical report to MOD,DSTO, University of Melbourne, Australia, March 25. [1] Y. Bar-Shalom, and E. Tse. Tracking in a Cluttered Environment With Probabilistic Data Association, Automatica, vol. 11, pp , [11] T.Kirubarajan, and Y. Bar-Shalom. Probabilistic data association techniques for target tracking in clutter, Proceedings of the IEEE, Vol. 92, No. 3 pp , March 24. [12] Darko Mušicki, Barbara La Scala, and Robin Evans. Multi-target tracking in clutter without measurement assignment. In 43rd IEEE Conference on Decision and Control, CDC 24, Atlantis, Paradise Island, Bahamas, December 24. [13] Mušicki, Darko and Evans, Robin. Joint integrated probabilistic data association - JIPDA, IEEE Trans. Aerospace Electronic Systems, vol. 4, no. 3, pp , July, 24. [14] D. Mušicki, R. J. Evans, and S. Stanković. Integrated Probabilistic Data Association, IEEE Trans. Auto. Control, Vol. 39, no. 6, pp , June [15] Y. Bar-Shalom, and X.-R. Li. Multitarget- Multisensor Tracking: Principles and Techniques, ISSN , YBS Publishing, [16] Y. Bar-Shalom, and W. D. Blair. Multitarget- Multisensor Tracking: Applications and Advances, Volume III Ed, Artech House, 2. [17] Y. Bar-Shalom, K. C. Chang, and H. A. P. Blom. Automatic Track Formation in Clutter with a Recursive Algorithm, in Multitarget- Multisensor Tracking: Advanced Applications, pp , Artech House, MA., 199. [18] X. Wang, and D. Mušicki. Low Elevation Sea- Surface Target Tracking Using IPDA Type Filters, in Proceedings of Radar 23 International Conference, Adelaide, Australia, September, 23, pp [19] S. Blackman. Multiple hypothesis tracking for multiple target tracking, IEEE AES Magazine, vol. 19, no. 1, pp. 5 18, January 24.