Distributed Least Squares Algorithm for Continuous-time Stochastic Systems Under Cooperative Excitation Condition

TL;DR

This paper introduces a distributed least squares algorithm for continuous-time stochastic systems that enables sensor networks to cooperatively estimate unknown parameters without requiring persistent excitation, using martingale theory and Ito calculus.

Contribution

It presents a novel diffusion-based distributed LS algorithm that converges under cooperative excitation, removing the need for boundedness or PE conditions of signals.

Findings

Sensors can cooperatively estimate parameters without individual observability.

The algorithm achieves convergence under cooperative excitation conditions.

Simulation confirms effective cooperative estimation even with limited individual information.

Abstract

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS) algorithm based on diffusion strategy is proposed such that the sensors can cooperatively estimate the unknown time-invariant parameter vector from continuous-time noisy signals. By using the martingal estimation theory and Ito formula, we provide upper bounds for the estimation error of the proposed distributed LS algorithm, and further obtain the convergence results under a cooperative excitation condition. Compared with the existing results, our results are established without using the boundedness or persistent excitation (PE) conditions of regression signals. We provide simulation examples to show that multiple sensors can cooperatively accomplish the estimation task even if any individual can not.