Research on Parameter Identification Using Least Squares Method

In this article, we explore parameter identification research using the Least Squares Method. We provide a comprehensive discussion of the least squares algorithm and conduct an in-depth study of its implementation. Additionally, we examine the applications of least squares in modern mathematics and engineering fields, and demonstrate how to apply it to solve practical problems. We detail various aspects of the algorithm including its fundamental principles, computational steps, and implementation approaches, supplemented with real-world data examples to help readers better understand the algorithm's applications. The implementation typically involves constructing a design matrix, calculating the normal equations (XᵀX)β = Xᵀy, and solving for parameters using matrix operations. Furthermore, we discuss the advantages and limitations of the least squares method, along with potential challenges that may arise in practical applications. Through this article, readers will gain thorough understanding of the least squares method and its applications, providing strong support for solving real-world engineering problems. Key programming considerations include handling ill-conditioned matrices through regularization techniques and implementing efficient matrix inversion methods for optimal performance.