An Optimal Kalman-Consensus Filter for Distributed Implementation Over a Dynamic Communication Network

With the rising number of applications for sensor networks comes a need for more accurate cooperative fusion algorithms. In this paper, a distributed and optimal state estimator is presented for implementation through a dynamically switching, yet strongly connected, directed communication network to cooperatively estimate the state of a dynamic system. The Kalman-Consensus filter approach is used to incorporate a consensus protocol of neighboring state estimates into the traditional Kalman filter. It has been known that the main difficulty associated with implementing such an optimal solution is its fully coupled covariance matrix. Presented is a distributed computation of the covariance matrix at every node achieved by taking advantage of its independence from state estimates. Reductions to the distributed covariance computations are achieved through shared processing made available by the strongly connected digraph. Should the digraph change over time, a distributed topology estimation algorithm is included to facilitate the implementation of the proposed Kalman-Consensus filters. Together, these advances render a distributed and optimal solution to the consensus-based cooperative Kalman filter design problem. Convergence and stability of the proposed algorithms are analyzed and analytically concluded with performance verified through simulation of an illustrative example.