RLS Adaptive Linear Prediction Algorithm in Adaptive Signal Processing

In this document, I will introduce the RLS (Recursive Least Squares) adaptive linear prediction algorithm program for adaptive signal processing. The primary objective of this algorithm is to predict future signal values by adaptively adjusting to the statistical characteristics of input signals. Through continuous updates of the prediction model parameters using a recursive approach, the RLS algorithm progressively optimizes prediction accuracy with each new data sample. The implementation features a forgetting factor mechanism that controls the influence of historical data, allowing the algorithm to track non-stationary signal statistics effectively. Key computational components include: - Recursive weight vector updates using the Kalman gain calculation - Inverse correlation matrix maintenance through the matrix inversion lemma - Efficient O(n²) complexity per iteration for n-dimensional parameters This program demonstrates practical RLS implementation for adaptive filtering applications, providing insights into real-time signal prediction techniques. The code structure includes initialization of filter coefficients, recursive parameter updates, and prediction error computation modules, making it suitable for understanding and applying adaptive signal processing technologies in various domains such as communications, audio processing, and system identification.