Communication-Efficient Distributed Kalman Filtering using ADMM

TL;DR

This paper introduces a communication-efficient distributed Kalman filtering method using ADMM, which reduces communication overhead while ensuring convergence to the true state and optimal covariance estimates.

Contribution

The paper develops a novel ADMM-based distributed Kalman filtering algorithm that improves communication efficiency by eliminating dual variable exchange and provides rigorous convergence analysis.

Findings

Enhanced communication efficiency by avoiding dual variable exchange.

Convergence of state estimates to true state and covariance matrices to optimal solution.

Tighter bounds on design parameters based on network Laplacian eigenvalues.

Abstract

This paper addresses the problem of optimal linear filtering in a network of local estimators, commonly referred to as distributed Kalman filtering (DKF). The DKF problem is formulated within a distributed optimization framework, where coupling constraints require the exchange of local state and covariance updates between neighboring nodes to achieve consensus. To address these constraints, the problem is transformed into an unconstrained optimization form using the augmented Lagrangian method. The distributed alternating direction method of multipliers (ADMM) is then applied to derive update steps that achieve the desired performance while exchanging only the primal variables. Notably, the proposed method enhances communication efficiency by eliminating the need for dual variable exchange. We show that the design parameters depend on the maximum eigenvalue of the network's Laplacian matrix, yielding a significantly tighter bound compared to existing results. A rigorous convergence analysis is provided, proving that the state estimates converge to the true state and that the covariance matrices across all local estimators converge to a globally optimal solution. Numerical results are presented to validate the efficacy of the proposed approach.