MATLAB Implementation of Adaptive Filter Using RLS Algorithm

This article presents a MATLAB implementation of an adaptive filter utilizing the Recursive Least Squares (RLS) algorithm. Adaptive filters are widely used signal processing tools that automatically adjust their filter parameters based on input signal characteristics to enhance filtering performance. The RLS algorithm, a popular adaptive filtering approach, operates on the principle of minimum mean-square error criterion. Through iterative updates of filter weights, it progressively converges toward the optimal solution. The MATLAB implementation will demonstrate key aspects including: - Initialization of filter parameters such as forgetting factor and regularization parameter - Implementation of the weight update recursion: w(n) = w(n-1) + gain*error - Calculation of the Kalman gain vector using matrix inversion lemma - Real-time adaptation of filter coefficients through recursive computations We will develop a complete MATLAB program that implements the RLS-based adaptive filter and illustrate its practical applications in signal processing scenarios such as system identification, noise cancellation, and channel equalization. The code will include proper initialization routines, main iteration loops, and performance monitoring mechanisms. Through this article, you will gain comprehensive understanding of RLS-based adaptive filters and acquire practical skills to apply them in solving real-world engineering problems. The implementation will emphasize algorithmic efficiency and numerical stability considerations essential for practical deployments.