Performance Improvement in Kalman Filters Due to Cooperation for Multi-agent Systems Under Identical Noise

In this paper, we consider cooperative Kalman filtering with information exchange between agents for a discrete-time multi-agent system. The aim of the paper is to evaluate efficacy of the cooperation through comparing precision of the cooperative Kalman filtering with that of Kalman filtering without information exchange, an existing estimation method. The precision of these Kalman filters is mainly evaluated by the traces of a priori error covariance matrices, which are solutions to the associated matrix Riccati difference equations. We show that when an identical process noise is added to each agent, the information exchange improves the precision of Kalman filtering, and the precision improvement increases as the number of agents increases.