Kalman-Consensus Filter : Optimality, stability, and performance

One of the fundamental problems in sensor networks is to estimate and track the state of targets (or dynamic processes) of interest that evolve in the sensing field. Kalman filtering has been an effective algorithm for tracking dynamic processes for over four decades. Distributed Kalman Filtering (DKF) involves design of the information processing algorithm of a network of estimator agents with a two-fold objective: (1) estimate the state of the target of interest and (2) reach a consensus with neighboring estimator agents on the state estimate. We refer to this DKF algorithm as Kalman-Consensus Filter (KCF). The main contributions of this paper are as follows: (i) finding the optimal decentralized Kalman-Consensus filter and showing that its computational and communication costs are not scalable in n and (ii) introducing a scalable suboptimal Kalman-Consensus Filter and providing a formal stability and performance analysis of this distributed and cooperative filtering algorithm. Kalman-Consensus Filtering algorithm is applicable to sensor networks with variable topology including mobile sensor networks and networks with packet-loss.