Distributed Kalman Filtering Over Wireless Sensor Networks in the Presence of Data Packet Drops

We study distributed Kalman filtering over the wireless sensor network, where each sensor node is required to locally estimate the state of a linear time-invariant discrete-time 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-like protocol. We first present the stationary distributed Kalman filter (DKF) that minimizes the local average error variance in the steady state at each sensor node, based on the stabilizing solution to the corresponding modified algebraic Riccati equation (MARE). The existence of the stabilizing solution to the MARE is addressed by adopting the stability margin, which can be computed by solving a set of linear matrix inequalities. Then, the Kalman consensus filter (KCF), consisting of the stationary DKF and a consensus term of prior estimates, is studied. Finally, the performance of the stationary DKF and KCF is illustrated by a numerical example.