System Parameter Identification Using Recursive Least Squares Method

This article presents the implementation of recursive least squares (RLS) method for system parameter identification. We utilize a 6-bit maximum-length sequence (M-sequence) as the input signal and perform 300 recursive iterations to obtain sufficient data points for accurate parameter estimation. The RLS algorithm maintains and updates a covariance matrix P and parameter vector θ at each iteration using the forgetting factor λ, typically implemented through matrix inversion lemma to avoid direct matrix inversion. This approach enables real-time parameter tracking while providing insights into system dynamics and performance characteristics. We also analyze the method's advantages in computational efficiency and convergence properties, discuss limitations such as parameter drift and sensitivity to initial conditions, and provide practical implementation guidelines for achieving optimal results in real-world applications including code examples for weight update equations and covariance matrix maintenance.