Robust Bias Compensation LMS Algorithms Under Colored Gaussian Input Noise and Impulse Observation Noise Environments

Ying-Ren Chien, Han-En Hsieh and Guobing Qian ()
Additional contact information
Ying-Ren Chien: Department of Electronic Engineering, National Taipei University of Technology, Taipei 10608, Taiwan
Han-En Hsieh: Department of Electrical Engineering, National Ilan University, Yilan 26047, Taiwan
Guobing Qian: College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China

Mathematics, 2025, vol. 13, issue 20, 1-18

Abstract: Adaptive filtering algorithms often suffer from biased parameter estimation and performance degradation in the presence of colored input noise and impulsive observation noise, both of which are common in practical sensor and communication systems. Existing bias-compensated least mean square (LMS) algorithms generally assume white Gaussian input noise, thereby limiting their applicability in real-world scenarios. This paper introduces a robust convex combination bias-compensated LMS (CC-BC-LMS) algorithm designed to address both colored Gaussian input noise and impulsive observation noise. The proposed algorithm achieves bias compensation through robust estimation of the input noise autocorrelation matrix and employs a modified Huber function to mitigate the influence of impulsive noise. A convex combination of fast and slow adaptive filters enables variable step-size adaptation, effectively balancing rapid convergence and low steady-state error. Extensive simulation results demonstrate that the proposed CC-BC-LMS algorithm provides substantial improvements in normalized mean square deviation (NMSD), surpassing state-of-the-art bias-compensated and robust adaptive filtering techniques by 4.48 dB to 11.4 dB under various noise conditions. These results confirm the effectiveness of the proposed approach for reliable adaptive filtering in challenging noisy environments.

Keywords: bias compensation; colored Gaussian input noise; impulse noise; least mean square (LMS); convex combination; variable step-size; process innovation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/20/3348/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/20/3348/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:20:p:3348-:d:1776133

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().