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

arXiv: https://arxiv.org/abs/1507.05233 · HTML: https://mlsanity.com/paper/1507.05233/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2015.

## Built on by (most cited first, 1 of 1)

- [A survey on active noise control techniques -- Part I: Linear systems](https://mlsanity.com/paper/2110.00531/) (2021)

## Abstract (arXiv)

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.