1 Distributive Target Tracking in Wireless Sensor Networks under Measurement Origin Uncertainty Hui Ma, Brian W.-H. Ng 1 School of Electrical and Electronic Engineering, The University of Adelaide Adelaide, SA 5005, Australia, [hma, bwng]@eleceng.adelaide.edu.au Abstract This paper addresses the problem of tracking a single target under measurement uncertainty due to clutters and missed detections in wireless sensor networks. By adopting the particles’ representation of the probability density function of target state, this paper develops a Particle filter (PF) and probabilistic data association filter (PDAF) hybrid tracking algorithm, name as PF-PDAF. PF-PDAF extends the well- known PDAF to the general nonlinear system. Based on the hierarchical sensor network architecture, the distributive PF- PDAF is also implemented. Moreover, the posterior Cramer- Rao lower bound (PCRLB) is computed to provide a theoretical bound on the tracking performance of the developed algorithms. Simulation results are provided. 1. INTRODUCTION Target tracking is one of the typical applications of wireless sensor networks: a large number of spatially deployed sensor nodes collaboratively sense, detect and infer the target state (e.g., position, velocity and heading). In contrast with tracking algorithms for traditional centralized systems (e.g., radar, sonar…etc), algorithms for wireless sensor networks need to be distributive and energy efficient [1], [3]. By adopting the Particle filter (PF) approach [2], recently several researchers proposed a number of tracking algorithms for wireless sensor networks [4]-[7]. In [4], Coates proposed a distributive PF algorithm in which each sensor node maintains a separate Particle filter. A sensor node updates partial measurement likelihood using its own measurement and the partial measurement likelihood estimated at previous sensor nodes. It then forwards the result to the next sensor node. This process will continue until the information reaches the last sensor node. The computation and communication burden of this algorithm is quite high and might not be applicable to wireless sensor networks with resource constraints. In contrast to Coates’ approach, Vercauteren, Guo, and Wang [6],[7] proposed a leader-based tracking scheme by adopting the information-driven sensor querying (IDSQ) [3]: at each time step, the single most informative sensor node is selected as the leader node, which estimates target state based on the estimation from its predecessor and its current measurement. The tracking algorithms developed in this paper differ from the above leader-based algorithms in that the estimation takes place in a sensor node cluster which consists of a number of sensor nodes. Instead of only using the measurement from one leader node, the target state is estimated based on a set of essential but non-redundant measurements from a group of sensor nodes. Sheng et al. [5] also developed distributed tracking algorithms by making use the measurements from several sensor nodes. However, their algorithms did not consider the measurement origin uncertainty. In this paper, we develop a Particle filter (PF) and the probabilistic data association filter (PDAF) hybrid tracking algorithm, named PF-PDAF for tracking a single target under measurement origin uncertainty in wireless sensor networks. The PF-PDAF adopts particles to represent the probability density function of the target state and thus extends the PDAF to the general nonlinear system. To facilitate distributive target tracking, we adopt the hierarchical sensor network architecture [8]: sensor nodes assume different roles – sensing (sensing node) and processing (leader node); and according to the geometry of the sensing nodes and the target, a portion of sensing nodes and a leader node form a sensor cluster. At every time step, only a small subset of sensing nodes located in the current active sensor cluster is invoked to provide the leader node with their measurements. The leader node then runs PF-PDAF to update the probability density function of the target state. When the target moves out of the current sensor cluster, the leader node propagates its estimation result to the next leader node. In this way, the target tracking is performed in a distributive manner. This paper is organized as follows. Section 2 formulates the problem of tracking a single target under measurement origin uncertainty in wireless sensor networks. Section 3 details the hybrid PF-PDAF algorithm. Section 4 develops distributive PF-PDAF. Section 5 calculates the PCRLB under measurement origin uncertainty. Section 5 presents the simulation results and Section 6 concludes the paper. 2. PROBLEM FORMULATION Assuming a wireless sensor network employs a set of s N sensing nodes to perform the target tracking task, the state- space model can be written as follows: k k k k v x A x + = +1 (1) ( ) s n k k n k n k t N n , ... , 1 , , = = n x h z (2)