Adaptive Recursive Least Squares (RLS) Algorithm Implementation

This document presents the Adaptive Recursive Least Squares (RLS) algorithm implemented using MATLAB M-files. The Adaptive RLS algorithm is a sophisticated signal processing technique that dynamically adjusts its internal parameters in response to changing input signals, enabling more accurate future signal predictions. The RLS component refers to the Recursive Least Squares method, which is a prediction algorithm based on the least squares principle that determines optimal prediction coefficients by minimizing the sum of squared errors. The MATLAB implementation utilizes key functions and computational approaches including: - Matrix inversion lemma for efficient computation of the inverse correlation matrix - Forgetting factor implementation for tracking time-varying systems - Real-time parameter updates using recursive weight adjustment equations - Efficient memory management through recursive computation that avoids storing entire data history The M-file structure typically includes: 1. Initialization of parameters (filter order, forgetting factor, initial weights) 2. Real-time processing loop with sample-by-sample updates 3. Covariance matrix recursion and gain vector calculation 4. Error computation and coefficient adaptation 5. Performance monitoring and convergence tracking Using MATLAB M-files provides significant advantages for algorithm development, including easy debugging through MATLAB's built-in tools, straightforward parameter optimization, and comprehensive visualization capabilities for analyzing algorithm performance and convergence behavior.