A Proximal Point Approach for Distributed System State Estimation

TL;DR

This paper introduces a distributed Proximal Point-based iterative method for system state estimation in multi-agent systems, highlighting the relationship between system dynamics and convergence, with detailed analysis of the approach and its parameters.

Contribution

It proposes a novel distributed Proximal Point algorithm for state estimation, connecting system structure with convergence properties and analyzing parameter effects.

Findings

The method converges to the optimal state estimate.

Structural properties influence convergence behavior.

Parameter tuning affects estimation accuracy and speed.

Abstract

System state estimation constitutes a key problem in several applications involving multi-agent system architectures. This rests upon the estimation of the state of each agent in the group, which is supposed to access only relative measurements w.r.t. some neighbors state. Exploiting the standard least-squares paradigm, the system state estimation task is faced in this work by deriving a distributed Proximal Point-based iterative scheme. This solution entails the emergence of interesting connections between the structural properties of the stochastic matrices describing the system dynamics and the convergence behavior toward the optimal estimate. A deep analysis of such relations is provided, jointly with a further discussion on the penalty parameter that characterizes the Proximal Point approach.