Generalized Least Squares Identification with MATLAB Implementation

This article provides an in-depth exploration of generalized least squares identification concepts and demonstrates their implementation in MATLAB. Generalized least squares identification serves as a powerful technique for estimating parameters in linear systems, delivering more accurate results compared to standard least squares methods. We will detail the theoretical foundation of this approach, accompanied by practical MATLAB code examples that illustrate key implementation aspects. The implementation typically involves creating a weighted residual function and solving the optimization problem using MATLAB's lsqnonlin function or formulating it as a weighted least squares problem with the backslash operator. The article covers parameter tuning strategies to enhance method performance, along with practical tips for effective implementation. Finally, we demonstrate real-world application scenarios and discuss the method's potential in engineering and scientific research, including system identification and parameter estimation tasks where noise characteristics require special consideration.