Distributed Moving Horizon Estimation Over Wireless Sensor Networks: A Matrix-Weighted Consensus Approach

This brief proposes a novel approach to distributed moving horizon estimation for linear discrete-time systems over a wireless sensor network. A distributed moving horizon estimator is presented by minimizing a cost function involving consensus steps on the prediction. A matrix-weighted rule for the consensus steps is designed by combining an orthogonal matrix with a stochastic matrix, where the orthogonal matrix is obtained from the observability decomposition rule. The proposed estimator only requires that each node transmits one state vector over the network, which reduces the communication burden. The estimation error of the proposed estimator is bounded by choosing an appropriate scalar parameter and a sufficiently large consensus step. Finally, a distributed target tracking example is presented to verify the performance of the developed results.