A Fast Robust Recursive Least-Squares Algorithm

• Published in: IEEE transactions on signal processing Vol. 57; no. 3; pp. 1209 - 1216
• Main Authors: Vega, L.R., Rey, H., Benesty, J., Tressens, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acoustic applications; Acoustic echo cancellation; Acoustic testing; Adaptive filters; Algorithm design and analysis; Algorithms; Applied sciences; Approximation; Asymptotic properties; Closed-form solution; Cost function; Detection, estimation, filtering, equalization, prediction; Echo cancellers; Exact sciences and technology; Exact solutions; impulsive noise; Information, signal and communications theory; Least squares method; Mathematical analysis; Miscellaneous; Recursive; recursive least-squares algorithm; robust filtering; Robustness; Signal and communications theory; Signal processing; Signal, noise; System identification; System testing; Telecommunications and information theory; Acoustic echo cancellation; Noise reduction; Asymptotic behavior; Theoretical study; Updating; Adaptive filter; Acoustic signal processing; Echo suppression; Recursive algorithm; Temporal constraint; Exact solution; robust filtering; Robust control; Time dependence; Pulse noise; Acoustic noise; Least squares method; Recursive method; Signal processing; Cost function; impulsive noise; System identification; Approximate solution; recursive least-squares algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.2010643

We present a fast robust recursive least-squares (FRRLS) algorithm based on a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing a cost function subject to a time-dependent constraint on the norm of the filter update. Although the characteristics of the exact solution to this problem are known, there is no closed-form solution in general. However, the approximate solution we propose is very close to the optimal one. We also present some theoretical results regarding the asymptotic behavior of the algorithm. The FRRLS is then tested in different environments for system identification and acoustic echo cancellation applications.