Estimation of Space-Time Varying Parameters Using a Diffusion LMS Algorithm

TL;DR

This paper introduces a diffusion LMS algorithm for distributed estimation of space-time varying parameters, analyzing its stability, convergence, and steady-state performance in networked systems.

Contribution

It proposes a novel diffusion LMS strategy that effectively estimates space-time varying parameters and overcomes rank-deficiency issues through network cooperation.

Findings

The algorithm converges stably under certain conditions.

It predicts mean-square error performance accurately.

Network cooperation mitigates data rank-deficiency problems.

Abstract

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying nature of the parameters and propose a diffusion least mean-squares (LMS) strategy to recover these parameters from successive time measurements. We analyze the stability and convergence of the proposed algorithm, and derive closed-form expressions to predict its learning behavior and steady-state performance in terms of mean-square error. We find that in the estimation of the space-varying parameters using distributed approaches, the covariance matrix of the regression data at each node becomes rank-deficient. Our analysis reveals that the proposed algorithm can overcome this difficulty to a large extent by benefiting from the network stochastic matrices that are used to combine exchanged information between nodes. We provide computer experiments to illustrate and support the theoretical findings.