Adaptive nonlinear Kalman filters based on credibility theory with noise correlation

To solve the divergence problem and overcome the difficulty in guaranteeing filtering accuracy during estimation of the process noise covariance or the measurement noise covariance with traditional new information-based nonlinear filtering methods, we design a new method for estimating noise statistical characteristics of nonlinear systems based on the credibility Kalman Filter(KF) theory considering noise correlation. This method first extends credibility to the Unscented Kalman Filter(UKF) and Extended Kalman Filter(EKF) based on the credibility theory. Further,an optimization model for nonlinear credibility under noise related conditions is established considering noise correlation. A combination of filtering smoothing and credibility iteration formula is used to improve the real-time performance of the nonlinear adaptive credibility KF algorithm, further expanding its application scenarios, and the derivation process of the formula theory is provided. Finally, the performance of the nonlinear credibility filtering algorithm is simulated and analyzed from multiple perspectives, and a comparative analysis conducted on specific experimental data. The simulation and experimental results show that the proposed credibility EKF and credibility UKF algorithms can estimate the noise covariance more accurately and effectively with lower average estimation time than traditional methods, indicating that the proposed algorithm has stable estimation performance and good real-time performance.