Convergence analysis of leader-follower consensus Kalman filtering in sensor networks

This paper studies the consensus based Kalman filtering problem for discrete-time linear systems in sensor networks. Considering the fact that just part of sensors in the network can measure the target, the filtering algorithms of the sensors are assigned differently according to the availability to get the direct measurements. For the sensors that can directly get the measurement outputs, we call them leaders and apply Kalman filters directly; for other sensors which are called followers, weighted average strategy of neighbors' estimations is applied. The communication weights are designed on the basis of the sensors' path distances to the monitored target and one parameter. By analyzing the multiple linearly coupled discrete-time Riccati equations, sufficient parameter conditions of the convergence of the mean square estimation errors are explicitly proposed for both spanning tree and arbitrary topology, respectively. Numerical examples are given to illustrate our results.