Normalized LMS algorithm and data-selective strategies for adaptive graph signal estimation

Abstract This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive filtering framework, the resulting GS estimation technique converges faster than the least-mean-squares (LMS) algorithm while being less complex than the recursive least-squares (RLS) algorithm, both recently recast as adaptive estimation strategies for the GS framework. Detailed steady-state mean-squared error and deviation analyses are provided for the proposed NLMS algorithm, and are also employed to complement previous analyses on the LMS and RLS algorithms. Additionally, two different time-domain data-selective (DS) strategies are proposed to reduce the overall computational complexity by only performing updates when the input signal brings enough innovation. The parameter setting of the algorithms is performed based on the analysis of these DS strategies, and closed formulas are derived for an accurate evaluation of the update probability when using different adaptive algorithms. The theoretical results predicted in this work are corroborated with high accuracy by numerical simulations.