On the Distributed Estimation from Relative Measurements: a Graph-Based Convergence Analysis

TL;DR

This paper analyzes the convergence of distributed algorithms for multi-agent state estimation using relative noisy measurements, linking network topology to convergence behavior and optimizing rate through parameter tuning.

Contribution

It provides the first detailed convergence analysis connecting graph topology, stochastic matrix theory, and distributed estimation algorithms, with practical optimization methods.

Findings

Convergence depends on network topology and stochastic matrix properties.

Optimal parameter tuning improves convergence rate.

Numerical simulations validate theoretical results across different network structures.

Abstract

For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic solution to this issue and two distributed iterative schemes, which allow to establish a connection between the convergence behavior of consensus algorithm toward the optimal estimate and the theory of the stochastic matrices that describe the network system dynamics. This study on the one hand highlights the role of the topological links that define the neighborhood of agent nodes, while on the other allows to optimize the convergence rate by easy parameter tuning. The theoretical findings are validated considering different network topologies by means of numerical simulations.