广东石油化工学院学报2025，Vol.35Issue(6)：61-67,73,8.DOI:10.26962/j.cnki.1991.2025.0053
相关噪声系统Kalman滤波与最小二乘的等价性
Equivalence of Kalman Filtering and Least Squares in Correlated Noise Systems
摘要
Abstract
Kalman filtering is an optimal recursive filtering method.However,its representation of model contributions is intertwined,making it less transparent.The least squares method provides a clearer decomposition of model contributions.By transforming Kalman filtering into the equivalent least squares formulation,the performance of the filter can be analyzed more intuitively.Kalman filtering and least squares methods typically assume that the process noise and measurement noise are mutually independent.However,in practical engineering applications,this assumption is often violated,as the two are frequently correlated.Under scenarios involving correlated noise,this study investigates the design of both Kalman filters and least squares estimators,proposes a noise decorrelation method along with corresponding filter design strategies,and rigorously demonstrates the equivalence of the designed filters and estimators before and after decorrelation of process noise and observation noise.It provides a theoretical foundation and methodological guidance for their application in engineering practice.关键词
线性系统/Kalman滤波器/线性最小二乘方法/噪声相关Key words
linear system/Kalman filtering/linear least squares method/noise related分类
信息技术与安全科学引用本文复制引用
黄伟昌,何舒颖,文成林..相关噪声系统Kalman滤波与最小二乘的等价性[J].广东石油化工学院学报,2025,35(6):61-67,73,8.基金项目
国家重点研发计划(2023YFB4704000) （2023YFB4704000）
