Distributed Optimal Predictor with Multi-consensus Gains for Sensor Networks

This paper presents a distributed optimal predictor (DOP) with the Kalman-like form for time-invariant system with communication noises, i.e., a prior filter, considering cross-covariance matrices between sensor nodes in sensor networks, where each sensor exchanges local estimates with its neighbor nodes. To obtain the DOP, an optimal Kalman predictor gain for each sensor node and different optimal consensus gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense. Stability and steady-state property of DOP are analyzed. An example for target tracking based on a directed topology in sensor networks demonstrates effectiveness of the proposed algorithm.