Distributed Estimation for Sensor Networks with Arbitrary Topologies

This paper addresses the problem of distributed recursive estimation of the state of a dynamical system, using measurements obtained by a network of locally-communicating sensors. Prior work on this problem has mostly focused on the development of methods suitable for very large networks, where multiple iterations of communication between neigh- boring sensors are used to obtain good asymptotic estimation accuracy. By contrast, we here focus on the case of medium- sized networks (consisting of up to a few tens of nodes), where limited communication is the primary constraint. We propose a distributed estimation method that uses knowledge of the network topology to explicitly model the accuracy of different nodes estimates, as well as the correlations between them. As a result, the proposed method is able to optimally utilize the measurements and state estimates communicated between neighboring nodes. This method does not require iterations, imposes no assumptions on the structure of the communication graph, and can provide an accurate representation of the accuracy of the produced estimates. We provide Monte-Carlo simulation results that demonstrate that the proposed method outperforms existing algorithms, when all methods use the same amount of inter-node communication.