Effect of Noise Correlation Coefficient on Joint Recursive Least Squares Parameters and State Estimation of Linear Stochastic State-space System

This article addresses the joint estimation of parameters and states in linear stochastic systems with correlated process and measurement noises. We propose the Kalman Filtering with Correlated Noises based Recursive Generalized Extended Least Squares (KF-CN-RGELS) algorithm, which innovatively integrates a reformulated Kalman filter to handle noise cross-correlation via a gain matrix <i>T</i>, alongside recursive least squares for synchronous parameter-state updates. The algorithm’s key advantage lies in its ability to leverage noise correlation for improved accuracy: experimental results demonstrate that a higher correlation coefficient (<i>ρ<sub>w, v</sub></i>=0.8)reduces parameter estimation errors to 0.85% (vs. 1.81% for <i>ρ<sub>w, v</sub></i>=0) and enhances state estimation. The method’s robustness is validated under varying noise conditions, offering practical utility in systems like radar guidance and industrial control.