Distributed estimation based on LQG control over homogeneous sensor networks

Motivated by navigation and tracking applications within sensor networks, we consider the distributed estimation problem over wireless sensor network. We propose a consensus based Kalman filtering algorithm based on optimal Linear Quadratic Gaussian control, in which each sensor can observe the dynamical system state, process the information data individually and communicate with each other within a sensing range. We provide a sufficient condition for the convergence of the proposed algorithm, and also give an upper bound for the estimation error covariance. Further, we find an optimal consensus gain for minimizing the network estimation error. Considering the occasional sensor fault and limited sensor energy, we investigate the proposed algorithm using only a subset of sensors to observe the dynamical system. With the assistance of the simulations, we verify the effectiveness of the proposed algorithms and present some interesting examples.