Comparative Research on Least Squares Series Algorithms in Multi-Field Engineering

Abstract

Least square is a fundamental mathematical optimization tool widely applied in data fitting and parameter estimation. Traditional error calculation methods have inherent defects, while minimizing the sum of squared residuals can avoid error offset and facilitate mathematical derivation. This paper systematically elaborates the basic principle of ordinary linear least squares, its matrix general expression, Gauss-Markov assumptions, model evaluation metrics including SSE and , as well as extended algorithms such as weighted least squares, recursive least squares and ridge regression. Three typical engineering applications are analyzed to verify its practical performance. For LEO satellite navigation simulator calibration, least squares fitting of continuous time-frequency sampling data effectively suppresses the measurement noise and the systematic timing errors, with fitting  approaching 0.9999. A multi-forgetting-factor recursive least squares algorithm achieves robust online identification of tractor-semitrailer dynamic parameters under varying loads and road conditions. However, standard OLS shows poor performance in PM2.5 concentration prediction due to severe multicollinearity of air quality variables, with an extremely low  of 0.069. The results demonstrate that least squares series algorithms deliver stable and accurate estimation for linear dynamic systems, but cannot handle strongly nonlinear, collinear environmental data. Future research can combine machine learning regression models to improve prediction accuracy for complex environmental monitoring tasks.