Diffusion LMS Strategies in Sensor Networks With Noisy Input Data

• Published in: IEEE/ACM transactions on networking Vol. 24; no. 1; pp. 3 - 14
• Main Authors: Abdolee, Reza, Champagne, Benoit
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-02-2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Bias-compensated least-mean square (LMS); diffusion adaptation; distributed parameter estimation; Estimation; Least squares approximations; network optimization; Noise; Noise measurement; Parameter estimation; Signal processing algorithms; Vectors
• ISSN: 1063-6692; 1558-2566
• DOI: 10.1109/TNET.2014.2350013

We investigate the performance of distributed least-mean square (LMS) algorithms for parameter estimation over sensor networks where the regression data of each node are corrupted by white measurement noise. Under this condition, we show that the estimates produced by distributed LMS algorithms will be biased if the regression noise is excluded from consideration. We propose a bias-elimination technique and develop a novel class of diffusion LMS algorithms that can mitigate the effect of regression noise and obtain an unbiased estimate of the unknown parameter vector over the network. In our development, we first assume that the variances of the regression noises are known a priori. Later, we relax this assumption by estimating these variances in real time. We analyze the stability and convergence of the proposed algorithms and derive closed-form expressions to characterize their mean-square error performance in transient and steady-state regimes. We further provide computer experiment results that illustrate the efficiency of the proposed algorithms and support the analytical findings.