Approximate Distributed Kalman Filtering for Cooperative Multi-agent Localization

We consider the problem of estimating the locations of mobile agents by fusing the measurements of displacements of the agents as well as relative position measurements between pairs of agents. We propose an algorithm that computes an approximation of the centralized optimal (Kalman filter) estimates. The algorithm is distributed in the sense each agent can estimate its own position by communication only with nearby agents. The problem of distributed Kalman filtering for this application is reformulated as a parameter estimation problem. The graph structure underlying the reformulated problem makes it computable in a distributed manner using iterative methods of solving linear equations. With finite memory and limited number of iterations before new measurements are obtained, the algorithm produces an approximation of the Kalman filter estimates. As the memory of each agent and the number of iterations between each time step are increased, the approximation improves. Simulations are presented that show that even with small memory size and few iterations, the estimates are quite close to the centralized optimal. The error covariances of the location estimates produced by the proposed algorithm are significantly lower than what is possible if inter-agent relative position measurements are not available.