Distributed Kalman filtering over wireless sensor networks in the presence of data packet drops

Abstract

We study distributed Kalman filtering over the wireless sensor network, where each sensor node is required to locally estimate the state of a discrete-time linear time-invariant system, using its own observations and those transmitted from its neighbors in the presence of data packet drops. This is an optimal one-step prediction problem under the framework of distributed estimation, assuming the TCP protocol. We first study the stationary distributed Kalman filter (DKF) in the presence of packet drops. The optimal estimation gain is derived based on the stabilizing solution to the modified algebraic Riccati equation (MARE) associated with the DKF. The MARE admits the stabilizing solution, if the stability margin, which can be computed by solving a set of linear matrix inequalities, is greater than or equal to one. Then the Kalman consensus filter (KCF), consisting of the stationary DKF and a consensus term of prior estimates, is proposed, followed by the stability analysis. Finally the performance of stationary DKF and KCF is illustrated by a numerical example.