Implementation of Recursive Least Squares Algorithm for System Identification

In this article, I will provide a detailed introduction to a MATLAB program I developed that implements the recursive least squares algorithm for system identification. The program's execution results and corresponding graphical outputs will also be presented.

First, to better understand the program's implementation, we need to review the concepts of system identification and the recursive least squares algorithm. Simply put, system identification is a methodology for constructing mathematical models of dynamic systems based on observed input-output data. The recursive least squares algorithm is an efficient method that recursively computes system parameters using sequential observation data, featuring real-time parameter updates with each new data point through matrix inversion lemma operations.

Regarding our implementation, the program executes the recursive least squares algorithm with key components including: initialization of parameter vectors and covariance matrices, recursive update equations for parameter estimation, and real-time plotting functions. The MATLAB implementation utilizes matrix operations for efficient computation and includes data visualization components using plot() functions to display parameter convergence trends and model fitting results. The program operates within the MATLAB environment and has been verified for correctness through multiple test cases.

After execution, the program generates both numerical results and graphical outputs, including convergence plots of parameter estimates and comparison graphs between actual system outputs and model predictions. These visualizations help demonstrate the algorithm's application in system identification and its parameter tracking capabilities.

For those interested in system identification and recursive estimation techniques, this program provides practical insights into algorithm implementation. I hope this article assists in understanding the program's implementation and applications, while stimulating further interest in recursive least squares methods for system identification.