Distributed Collaborative Feedback Particle Filter: A Diffusion Map-Based Feedback Gain Approximation Approach

In this article, we consider the diffusion collaborative feedback particle filter (DFPF) for distributed nonlinear target tracking with an adaptive network consisting of geographically-distributed nodes. In the DFPF, each particle at each node is controlled by the collaborative feedback structure incorporating the innovation process and the feedback gain, which is the solution to the constrained Poisson equation. Utilizing the diffusion map (DM) approximation of the exact semigroup of the Poisson equation in the DFPF, we herein develop the feedback gain approximation, the performance of which is pertinent to the Gaussian kernel bandwidth. Further, based on the mean square error induced by the empirical approximation in the DM feedback gain, we derive the adaptive kernel bandwidth under the positive kernel bandwidth constraint. Moreover, we develop the variable integration step-size, referred to as the pseudotime step-size in the DFPF, to efficiently solve the ordinary differential equation, which is utilized to describe the gradual transition from the prior to the posterior. Illustrative simulations validate that the proposed DFPF could achieve enhanced tracking performance with preferable computational efficiency.