MATLAB Implementation of Enhanced RLS Algorithm

The enhanced Recursive Least Squares (RLS) algorithm represents an adaptive filtering technique widely employed in signal processing and system identification applications. Compared with conventional RLS algorithms, the improved versions typically feature optimizations in computational efficiency, numerical stability, or convergence speed. The core concept of this algorithm involves recursively updating parameter estimates by utilizing the most recent input and output data to adjust filter weights. The enhanced RLS algorithm may incorporate optimizations in several key areas: - Adaptive forgetting factor: Implementation of dynamically adjusted forgetting factors enables better adaptation to non-stationary environments through exponential weighting of historical data - Numerical stability enhancements: Utilization of matrix decomposition techniques (like Cholesky or UD factorization) or regularization methods prevents numerical issues during covariance matrix inversion - Computational complexity reduction: Employment of recursive formulations or approximation methods reduces computational overhead, improving real-time processing capabilities In MATLAB implementation, the algorithm typically involves these critical steps: initialization of the covariance matrix, calculation of the gain vector, weight update, and covariance matrix correction. The enhanced version might incorporate additional logic such as adaptive step-size control or error compensation mechanisms to further improve performance. Key MATLAB functions often include matrix operations (inv, chol), vector computations, and efficient memory management for recursive updates. This improved RLS algorithm is particularly suitable for applications requiring rapid tracking of time-varying systems, including channel equalization in communication systems, noise cancellation, and adaptive control tasks. The MATLAB implementation typically features configurable parameters for forgetting factors, regularization constants, and convergence thresholds to accommodate different operational scenarios.