Diffusion LMS filter for distributed estimation of systems with stochastic state transition and observation matrices

We study the problem of distributed state estimation where a set of nodes are required to estimate the state of a system with stochastic state transition matrix based on their observations which have themselves measurement matrices evolving stochastically. We extend previous work on distributed diffusion Kalman filtering to the stochastic case, and propose a diffusion algorithm for linear least mean square (LMS) filtering. As a particular case, we also derive a diffusion LMS algorithm for a linear system under a network of intermittent observations. Convergence of the estimation error covariance is proved under assumption of mean square stability of the plant. The resulting algorithms are robust to node and link failure, scalable, and fully distributed, in the sense that no fusion center is required, and nodes communicate with their neighbors only. We apply the algorithms to the problem of estimating the position of a rotating object in an ad-hoc network. Simulation results illustrate the performance of the proposed algorithms.