Nonlinear distributed state estimation on the Stiefel manifold using diffusion particle filters

Abstract

Many relevant problems in engineering demand the estimation of dynamic system states that are constrained to non-Euclidean spaces. Furthermore, it is generally advantageous to implement estimation methods in a network of cooperating nodes instead of relying on a single data fusion center. With this in mind, we propose in this paper two new distributed particle filtering methods to track the states of a dynamic system that evolves on the Stiefel manifold, which arises naturally when the states are subject to nonlinear orthogonal constraints. The proposed algorithms are based on the Random Exchange and Adapt-then-Combine diffusion techniques, and perform parametric approximations using the matrix von Mises-Fisher distribution to compress information exchanged between network nodes. Estimates of the state are then determined via an empirical averaging method that approximates the centroid (Karcher mean) of the particle set. As we verify via numerical simulations, the proposed methods show improved performance compared to previous Particle and Extended Kalman filters designed for Euclidean state variables, and compared to a non-cooperative particle filtering algorithm.