Partial Diffusion Kalman Filtering

TL;DR

This paper introduces a Partial Diffusion Kalman Filter (PDKF) that reduces communication costs in distributed state estimation by sharing only subsets of estimates, maintaining stability and convergence.

Contribution

The paper proposes a novel PDKF algorithm that limits inter-node communication while ensuring stability, convergence, and predictable steady-state performance.

Findings

PDKF reduces communication load significantly.

The algorithm remains stable and convergent in mean and mean-square senses.

Steady-state MSD can be accurately predicted with a closed-form expression.

Abstract

In conventional distributed Kalman filtering, employing diffusion strategies, each node transmits its state estimate to all its direct neighbors in each iteration. In this paper we propose a partial diffusion Kalman filter (PDKF) for state estimation of linear dynamic systems. In the PDKF algorithm every node (agent) is allowed to share only a subset of its intermediate estimate vectors at each iteration among its neighbors, which reduces the amount of internode communications. We study the stability of the PDKF algorithm where our analysis reveals that the algorithm is stable and convergent in both mean and mean-square senses. We also investigate the steady-state mean-square deviation (MSD) of the PDKF algorithm and derive a closed-form expression that describes how the algorithm performs at the steady-state. Experimental results validate the effectiveness of PDKF algorithm and demonstrate that the proposed algorithm provides a trade-off between communication cost and estimation performance that is extremely profitable.