Distributed linear estimation of dynamic random fields

In this paper we address the distributed estimation of a dynamic (time varying) random field. The dynamic field is globally observable (by the entire sensor network), but not locally observable (at each sensor). We present a distributed Kalman-type estimator such that the estimate at each sensor is unbiased with bounded mean-squared estimation error. The challenges with distributed estimation by a network of sensors lie in the estimation of fields with unstable dynamics. Our distributed Kalman filter type estimator, which includes a consensus step on the pseudo-innovations, a modified version of the filter innovations, is able to track arbitrary unstable dynamics, as long as the sensor network connectivity is above a threshold determined by the degree of instability of the field dynamics, regardless of the specifics of the local observations.