Anytime Optimal Distributed Kalman Filtering and Smoothing

Abstract

Distributed algorithms are derived for estimation and smoothing of nonstationary dynamical processes based on correlated observations collected by ad hoc wireless sensor networks (WSNs). Specifically, distributed Kalman filtering (KF) and smoothing schemes are constructed for any-time minimum mean-square error (MMSE) optimal consensus-based state estimation using WSNs. The novel distributed filtering/smoothing approach is flexible to trade-off estimation delay for MSE reduction, while it exhibits robustness in the presence of communication noise. Numerical examples demonstrate the merits of the proposed approach with respect to existing alternatives.

Distributed Kalman filtering

“…Other DKF applications can be seen in [335], [336], [338], [339] . [38], [39], [40], [41], [42], [43], [44], [105], [106], [109], [114], [119], [156], [179], [191], [197], [213], [214], [215], [216], [221], [233], [237] , [238] and [242]. [204] • Only the estimates at each Kalman update over-head are exchanged [205] • Analyzes the number of messages to exchange between successive updates in DKF [206] • Global Optimality of DKF fusion exactly equal to the corresponding centralized optimal Kalman filtering fusion [276] • A parallel and distributed state estimation structure developed from an hierarchical estimation structure [297] • A computational procedure to transform an hierarchical Kalman filter into a partially decentralized estimation structure [298] • Optimal DKF based on a-priori determination of measurements [300] 2.3.…”

“…Diffusion Kalman filtering for every measurement and for every node, a local state estimate using the data from the neighborhood is provided in [178]. Other publications classified with diffusion-based DKF are [97], [99], [173], [174], [175], [176] and [177] respectively. …”

Distributed $H_{\infty}$ Filtering for Polynomial Nonlinear Stochastic Systems in Sensor Networks

“…In addition, the consensus-based distributed filtering technology has been developed in parallel to the rapid development of multi-agent consensus control theory, For example, a distributed filter has been introduced in [15] that allows the nodes of a sensor network to track the average of n sensor measurements using an average consensus based distributed filter called consensus filter. The distributed Kalman filtering (DKF) problem considered in [19] has also been based on the average consensus, where the node hierarchy has been used with nodes performing different types of processing and communications.…”

Diffusion distributed Kalman filtering with adaptive weights

“…Distributed Kalman filtering was proposed before in the context of diffusion estimation in [1], [2], and in the context of average consensus in [3], [4], [5]. Our focus is on diffusion Kalman filtering , where nodes communicate only with their neighbors, and no fusion center is present.…”