Parameter Estimation Using Unweighted Recursive Least Squares Method

This article discusses the implementation of unweighted recursive least squares (RLS) method for parameter estimation to enhance system adaptation and simulation accuracy. The algorithm recursively updates parameter estimates using a covariance matrix update formula: P(k) = P(k-1) - P(k-1)φ(k)[I + φ'(k)P(k-1)φ(k)]^(-1)φ'(k)P(k-1), where φ(k) represents the regression vector at time step k. Key implementation aspects include proper initialization of the covariance matrix (typically as P(0)=αI with large α) and handling of potential numerical instability through regularization techniques. We examine the method's advantages in computational efficiency and real-time applications, while addressing limitations such as sensitivity to initial conditions and potential covariance wind-up. Practical implementation considerations include MATLAB code structure using matrix operations for efficient computation and integration with system identification toolbox functions. Finally, we demonstrate application examples with code snippets showing parameter convergence analysis and validation techniques for ensuring estimation accuracy in dynamic systems.