Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Renyi Entropy based Target Tracking in Mobile Sensor Networks

This paper proposes an entropy based target tracking approach for mobile sensor networks. The proposed tracking algorithm runs a target state estimation stage and a motion control stage alternatively. A distributed particle filter is developed to estimate the target position in the first stage. This distributed particle filter does not require to transmit the weighted particles from one sensor node to another. Instead, a Gaussian mixture model is formulated to approximate the posterior distribution represented by the weighted particles via an EM algorithm. The EM algorithm is developed in a distributed form to compute the parameters of Gaussian mixture model via local communication, which leads to the distributed implementation of the particle filter. A flocking controller is developed to control the mobile sensor nodes to track the target in the second stage. The flocking control algorithm includes three components. Collision avoidance component is based on the design of a separation potential function. Alignment component is based on a consensus algorithm. Navigation component is based on the minimization of an quadratic Renyi entropy. The quadratic Renyi entropy of Gaussian mixture model has an analytical expression so that its optimization is feasible in mobile sensor networks. The proposed active tracking algorithm is tested in simulation. © 2011 IFAC

Distributive JPDAF for multi-target tracking in wireless sensor networks

Copyright © 2005 IEEEIn this paper we present the development of a distributive joint probabilistic data association filter (JPDAF) for multi-target tracking in wireless sensor networks. We adopt sequential Monte Carlo (SMC) method to implement the JPDAF, and use Gaussian mixture model (GMM) to develop the distributive JPDAF. Simulation results are also provided.Hui Ma, Brian W.-H. N

Likelihood Consensus and Its Application to Distributed Particle Filtering

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task---based on the past and current measurements of all sensors---using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This "likelihood consensus" method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem

Cooperative localization in mobile networks using nonparametric variants of belief propagation

Of the many state-of-the-art methods for cooperative localization in wireless sensor networks (WSN), only very few adapt well to mobile networks. The main problems of the well-known algorithms, based on nonparametric belief propagation (NBP), are the high communication cost and inefficient sampling techniques. Moreover, they either do not use smoothing or just apply it o ine. Therefore, in this article, we propose more flexible and effcient variants of NBP for cooperative localization in mobile networks. In particular, we provide: i) an optional 1-lag smoothing done almost in real-time, ii) a novel low-cost communication protocol based on package approximation and censoring, iii) higher robustness of the standard mixture importance sampling (MIS) technique, and iv) a higher amount of information in the importance densities by using the population Monte Carlo (PMC) approach, or an auxiliary variable. Through extensive simulations, we confirmed that all the proposed techniques outperform the standard NBP method

Belief Consensus Algorithms for Fast Distributed Target Tracking in Wireless Sensor Networks

In distributed target tracking for wireless sensor networks, agreement on the target state can be achieved by the construction and maintenance of a communication path, in order to exchange information regarding local likelihood functions. Such an approach lacks robustness to failures and is not easily applicable to ad-hoc networks. To address this, several methods have been proposed that allow agreement on the global likelihood through fully distributed belief consensus (BC) algorithms, operating on local likelihoods in distributed particle filtering (DPF). However, a unified comparison of the convergence speed and communication cost has not been performed. In this paper, we provide such a comparison and propose a novel BC algorithm based on belief propagation (BP). According to our study, DPF based on metropolis belief consensus (MBC) is the fastest in loopy graphs, while DPF based on BP consensus is the fastest in tree graphs. Moreover, we found that BC-based DPF methods have lower communication overhead than data flooding when the network is sufficiently sparse

USING PROBABILISTIC GRAPHICAL MODELS TO DRAW INFERENCES IN SENSOR NETWORKS WITH TRACKING APPLICATIONS

Sensor networks have been an active research area in the past decade due to the variety of their applications. Many research studies have been conducted to solve the problems underlying the middleware services of sensor networks, such as self-deployment, self-localization, and synchronization. With the provided middleware services, sensor networks have grown into a mature technology to be used as a detection and surveillance paradigm for many real-world applications. The individual sensors are small in size. Thus, they can be deployed in areas with limited space to make unobstructed measurements in locations where the traditional centralized systems would have trouble to reach. However, there are a few physical limitations to sensor networks, which can prevent sensors from performing at their maximum potential. Individual sensors have limited power supply, the wireless band can get very cluttered when multiple sensors try to transmit at the same time. Furthermore, the individual sensors have limited communication range, so the network may not have a 1-hop communication topology and routing can be a problem in many cases. Carefully designed algorithms can alleviate the physical limitations of sensor networks, and allow them to be utilized to their full potential. Graphical models are an intuitive choice for designing sensor network algorithms. This thesis focuses on a classic application in sensor networks, detecting and tracking of targets. It develops feasible inference techniques for sensor networks using statistical graphical model inference, binary sensor detection, events isolation and dynamic clustering. The main strategy is to use only binary data for rough global inferences, and then dynamically form small scale clusters around the target for detailed computations. This framework is then extended to network topology manipulation, so that the framework developed can be applied to tracking in different network topology settings. Finally the system was tested in both simulation and real-world environments. The simulations were performed on various network topologies, from regularly distributed networks to randomly distributed networks. The results show that the algorithm performs well in randomly distributed networks, and hence requires minimum deployment effort. The experiments were carried out in both corridor and open space settings. A in-home falling detection system was simulated with real-world settings, it was setup with 30 bumblebee radars and 30 ultrasonic sensors driven by TI EZ430-RF2500 boards scanning a typical 800 sqft apartment. Bumblebee radars are calibrated to detect the falling of human body, and the two-tier tracking algorithm is used on the ultrasonic sensors to track the location of the elderly people

Conditional Posterior Cramer-Rao Lower Bound and Distributed Target Tracking in Sensor Networks

Sequential Bayesian estimation is the process of recursively estimating the state of a dynamical system observed in the presence of noise. Posterior Cramer-Rao lower bound (PCRLB) sets a performance limit onany Bayesian estimator for the given dynamical system. The PCRLBdoes not fully utilize the existing measurement information to give anindication of the mean squared error (MSE) of the estimator in the future. In many practical applications, we are more concerned with the value of the bound in the future than in the past. PCRLB is an offline bound, because it averages out the very useful measurement information, which makes it an off-line bound determined only by the system dynamical model, system measurement model and the prior knowledge of the system state at the initial time. This dissertation studies the sequential Bayesian estimation problem and then introduces the notation of conditional PCRLB, which utilizes the existing measurement information up to the current time, and sets the limit on the MSE of any Bayesian estimators at the next time step. This work has two emphases: firstly, we give the mathematically rigorous formulation of the conditional PCRLB as well as the approximate recursive version of conditional PCRLB for nonlinear, possibly non-Gaussian dynamical systems. Secondly, we apply particle filter techniques to compute the numerical values of the conditional PCRLB approximately, which overcomes the integration problems introduced by nonlinear/non-Gaussian systems. Further, we explore several possible applications of the proposed bound to find algorithms that provide improved performance. The primary problem of interest is the sensor selection problem for target tracking in sensor networks. Comparisons are also made between the performance of sensor selection algorithm based on the proposed bound and the existing approaches, such as information driven, nearest neighbor, and PCRLB with renewal strategy, to demonstrate the superior performances of the proposed approach. This dissertation also presents a bandwidth-efficient algorithm for tracking a target in sensor networks using distributed particle filters. This algorithm distributes the computation burden for target tracking over the sensor nodes. Each sensor node transmits a compressed local tracking result to the fusion center by a modified expectationmaximization (EM) algorithm to save the communication bandwidth. The fusion center incorporates the compressed tracking results to give the estimate of the target state. Finally, the target tracking problem in heterogeneous sensor networks is investigated extensively. Extended Kalman Filter and particle filter techniques are implemented and compared for tracking a maneuvering