A Distributed Implementation of Steady-State Kalman Filter

This article studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer notation="LaTeX">$n$ -dimensional of a linear time-invariant Gaussian system. By lossless decomposition optimal steady-state Kalman filter, we show that problem can be reformulated as synchronization homogeneous systems. Based on such decomposition, estimator is proposed, each node runs local filter using only its own measurement, alongside with consensus algorithm fuse estimate every node. We prove average estimates from all coincides estimate, and under certain condition graph Laplacian matrix system matrix, covariance error bounded asymptotic derived. As result, stable for single further proposed has low message complexity notation="LaTeX">$\min (m,n)$ . Numerical examples provided end illustrate efficiency algorithm.