Recursive Least Squares Algorithm Identification

In this program, we utilize the recursive least squares (RLS) algorithm for system identification. The algorithm processes input signal u and output signal y to estimate system parameters. The output matrix c contains the parameter estimates in its last column. The RLS algorithm is a widely-used identification method that minimizes the sum of squared prediction errors to estimate system parameters. During implementation, the algorithm updates parameters recursively using a gain vector and covariance matrix, which allows for efficient real-time computation. Data preprocessing techniques such as outlier removal or normalization may be applied to improve algorithm accuracy. Therefore, when employing the RLS algorithm for identification, factors like data quality management, covariance matrix initialization, forgetting factor selection, and parameter convergence monitoring should be carefully considered to ensure estimation accuracy. The core implementation typically involves initializing parameter vectors, calculating the innovation term, updating the gain matrix, and recursively adjusting parameters based on prediction errors.