On the Tracking Performance of Adaptive Filters and Their Combinations

• Published in: IEEE transactions on signal processing Vol. 69; pp. 3104 - 3116
• Main Authors: Claser, Raffaello, Nascimento, Vitor H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Adaptive filter; Adaptive filters; Autoregressive models; Autoregressive processes; Computational modeling; convex combination; Covariance matrices; Kalman filter; Kalman filters; Mathematical model; Mean square error methods; Optimization; Parameter estimation; Steady-state; Tracking
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2021.3081045

Combinations of adaptive filters have attracted attention as a simple solution to improve filter performance, including tracking properties. In this paper, we consider combinations of LMS and RLS filters, and study their performance for tracking time-varying solutions. Modeling the variation of the parameter vector to be estimated as a first order autoregressive (AR) model, we show that a convex combination between one LMS and one RLS filters with their optimum settings may have a tracking performance close to the optimal excess mean-square error (EMSE) and mean-square deviation (MSD) obtained via Kalman filter, but with lower computational complexity (linear in the filter length instead of quadratic - in the case of diagonal matrices in the Kalman model - or cubic, for general Kalman models).