Diffusion Strategies for Distributed Kalman Filtering and Smoothing

TLDR

We study distributed Kalman filtering and smoothing, where nodes collaboratively estimate the state of a linear dynamic system, focusing on diffusion strategies that communicate only with direct neighbors and diffuse information across the network through Kalman iterations and data aggregation. The authors aim to develop diffusion algorithms for Kalman filtering, fixed‑lag smoothing, and fixed‑point smoothing. They analyze the mean and mean‑square performance of the algorithms, derive steady‑state mean‑square expressions, examine convergence of the diffusion Kalman filter recursions, and apply the methods to estimate and track a projectile’s position. Simulation results confirm that the proposed diffusion approach outperforms existing techniques.

Abstract

We study the problem of distributed Kalman filtering and smoothing, where a set of nodes is required to estimate the state of a linear dynamic system from in a collaborative manner. Our focus is on diffusion strategies, where nodes communicate with their direct neighbors only, and the information is diffused across the network through a sequence of Kalman iterations and data-aggregation. We study the problems of Kalman filtering, fixed-lag smoothing and fixed-point smoothing, and propose diffusion algorithms to solve each one of these problems. We analyze the mean and mean-square performance of the proposed algorithms, provide expressions for their steady-state mean-square performance, and analyze the convergence of the diffusion Kalman filter recursions. Finally, we apply the proposed algorithms to the problem of estimating and tracking the position of a projectile. We compare our simulation results with the theoretical expressions, and note that the proposed approach outperforms existing techniques.