Abstract

The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This paper addresses the DKF problem by reducing it to two separate dynamic consensus problems in terms of weighted measurements and inverse-covariance matrices. These to data fusion problems are solved is a distributed way using lowpass and band-pass consensus filters. Consensus filters are distributed algorithms that allow calculation of average-consensus of time-varying signals. The stability properties of consensus filters is discussed in a companion CDC ’۰۵ paper [24]. We show that a central Kalman filter for sensor networks can be decomposed into n micro-Kalman filters with inputs that are provided by two types of consensus filters. This network of micro-Kalman filters collectively are capable to provide an estimate of the state of the process (under observation) that is identical to the estimate obtained by a central Kalman filter given that all nodes agree on two central sums. Later, we demonstrate that our consensus filters can approximate these sums and that gives an approximate distributed Kalman filtering algorithm. A detailed account of the computational and communication architecture of the algorithm is provided. Simulation results are presented for a sensor network with 200 nodes and more than 1000 links.

Introduction

Sensor networks and intelligent arrays of micro-sensors have broad range of applications including information gathering and data fusion for modeling an environment, surveillance, active monitoring of forests & agricultural lands, health-care applications, collaborative information processing, and control of smart materials with embedded sensors [7], [13], [16], [4], [1], [9], [5], [19], [15], [3], [33], [22], [8].

The most fundamental distributed estimation problem for sensor networks is to develop a distributed algorithm [14] for Kalman filtering [2]. A scheme for approximate distributed Kalman filtering (DKF) was proposed in [30] based on reaching an average-consensus [23], [27], [21]. The work in [30] only suggests a scalable scheme to tackle the DKF problem in a special case of full-information and does not contain the sufficient analytical results and distributed algorithms necessary to implement a distributed Kalman filter.