Distributed Robust Kalman Filtering with Unknown and Noisy Parameters in Sensor Networks

This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor's measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results.