Distributed Object Tracking Using a Cluster-Based Kalman Filter in Wireless Camera Networks

Local data aggregation is an effective means to save sensor node energy and prolong the lifespan of wireless sensor networks. However, when a sensor network is used to track moving objects, the task of local data aggregation in the network presents a new set of challenges, such as the necessity to estimate, usually in real time, the constantly changing state of the target based on information acquired by the nodes at different time instants. To address these issues, we propose a distributed object tracking system which employs a cluster-based Kalman filter in a network of wireless cameras. When a target is detected, cameras that can observe the same target interact with one another to form a cluster and elect a cluster head. Local measurements of the target acquired by members of the cluster are sent to the cluster head, which then estimates the target position via Kalman filtering and periodically transmits this information to a base station. The underlying clustering protocol allows the current state and uncertainty of the target position to be easily handed off among clusters as the object is being tracked. This allows Kalman filter-based object tracking to be carried out in a distributed manner. An extended Kalman filter is necessary since measurements acquired by the cameras are related to the actual position of the target by nonlinear transformations. In addition, in order to take into consideration the time uncertainty in the measurements acquired by the different cameras, it is necessary to introduce nonlinearity in the system dynamics. Our object tracking protocol requires the transmission of significantly fewer messages than a centralized tracker that naively transmits all of the local measurements to the base station. It is also more accurate than a decentralized tracker that employs linear interpolation for local data aggregation. Besides, the protocol is able to perform real-time estimation because our implementation takes into consideration the sparsit- - y of the matrices involved in the problem. The experimental results show that our distributed object tracking protocol is able to achieve tracking accuracy comparable to the centralized tracking method, while requiring a significantly smaller number of message transmissions in the network

Distributing the Kalman Filter for Large-Scale Systems

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors

Stochastic Sensor Scheduling via Distributed Convex Optimization

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last versio

Localisation of mobile nodes in wireless networks with correlated in time measurement noise.

Wireless sensor networks are an inherent part of decision making, object tracking and location awareness systems. This work is focused on simultaneous localisation of mobile nodes based on received signal strength indicators (RSSIs) with correlated in time measurement noises. Two approaches to deal with the correlated measurement noises are proposed in the framework of auxiliary particle filtering: with a noise augmented state vector and the second approach implements noise decorrelation. The performance of the two proposed multi model auxiliary particle filters (MM AUX-PFs) is validated over simulated and real RSSIs and high localisation accuracy is demonstrated