Data Prediction Using RLS Algorithm and MATLAB Implementation

In data processing, the Recursive Least Squares (RLS) algorithm serves as a widely adopted methodology. This approach was initially formulated by the eminent scholar Gauss in 1795. Gauss postulated that when deducing unknown parameters from acquired observational data, the most probable value for these parameters is one that minimizes the sum of squared differences between actual observations and computed values, multiplied by their precision measurement weights. This principle constitutes the renowned least squares foundation. The RLS algorithm finds extensive applications in adaptive signal filtering analysis, featuring advantages such as fast convergence rates and insensitivity to eigenvalue dispersion in autocorrelation matrices. Nevertheless, its substantial computational requirements present implementation challenges. This chapter concentrates on RLS-based data prediction methodologies and provides comprehensive MATLAB implementation approaches, including detailed algorithm explanations and practical coding techniques. Key implementation aspects cover: - RLS weight update equations using gain vector calculations - Forgetting factor implementation for tracking non-stationary signals - MATLAB code structure for efficient matrix operations - Performance comparison with other adaptive filtering algorithms - Practical considerations for real-time data prediction scenarios The MATLAB implementation typically involves initializing parameters, designing appropriate filter structures, and implementing recursive updates through matrix inversion lemma applications to enhance computational efficiency.