Transient Error Analysis of the LMS and RLS Algorithm for Graph Signal Estimation

TL;DR

This paper provides a theoretical analysis of the transient errors in LMS and RLS algorithms for graph signal estimation, supported by simulations on temperature data.

Contribution

It derives formulas for transient errors of GSP LMS and RLS algorithms, advancing understanding of their dynamic performance in graph signal processing.

Findings

Transient error expressions are derived mathematically.

Simulations on temperature data validate the theoretical results.

The analysis enhances performance evaluation during transient states.

Abstract

Recently, the proposal of the least mean square (LMS) and recursive least squares (RLS) algorithm for graph signal processing (GSP) provides excellent solutions for processing signals defined on irregular structures such as sensor networks. The existing work has completed the steady state error analysis of the GSP LMS algorithm and GSP RLS algorithm in Gaussian noise scenarios, and a range of values for the step size of the GSP LMS algorithm has also been given. Meanwhile, the transient error analysis of the GSP LMS algorithm and GSP RLS algorithm is also important and challenging. Completing the above work will help to quantitatively analyze the performance of the graph signal adaptive estimation algorithm at transient moments, which is what this paper is working on. By using formula derivation and mathematical induction, the transient errors expressions of the GSP LMS and GSP RLS algorithm are given in this paper. Based on the Brazilian temperature datasets, the related simulation experiments are executed, which strongly demonstrate the correctness of our proposed theoretical analysis