Research On Unscented Transform-Based Nonlinear Gaussian Filter And Its Application To Integrated Navigation

With the rapid progress of computer science,the nonlinear system theory and technology achieve significant improvement,and have been widely applied in engineering practice.The nonlinear filtering technology is to obtain the optimal estimation of system state for nonlinear stochastic systems.This technology has been widely used in numerous areas such as integrated navigation,target tracking,image processing,fault diagnosis and automatic control,and has become the research focus for the scholars in these areas.Because of the nonlinear characteristics of dynamic systems and the complexity of the application circumstance in practical engineering,the performance of nonlinear filtering is often affected by the system model uncertainties such as parameter mutation,temporary interference and unknown system noise statistics,leading to the degraded or divergent filtering results.In order to address this problem,based on the theory of unscented Kalman filter(UKF),this paper presents a maximum likelihood principle and moving horizon estimation based adaptive UKF(MMAUKF),a refined MMAUKF and an interacting multiple model(IMM)estimation-based adaptive robust UKF to enhance the adaptability and robustness for the state estimation of nonlinear systems.Moreover,a multi-sensor optimal data fusion methodology based on the modified UKFs is designed to improve the data fusion accuracy for the multi-sensor nonlinear systems.The main research work and innovative contributions of the paper are as follows:(1)A MMAUKF is presented to address the problem that the filtering performance of classical UKF will be degraded or even divergent due to the system noise statistics uncertainty.This method constructs an estimation model of system noise statistics according to the maximum likelihood principle.Subsequently,it further establishes a moving horizon strategy to optimize the above model,and the sequential quadratic programming is applied to calculate the estimation of noise statistics.Eventually,the proposed adaptive UKF is applied to the inertial navigation system/global navigation satellite system(INS/GNSS)integrated navigation system for the simulation and experimental verification.The results demonstrate that the proposed method can enhance the adaptability and robustness of the classical UKF through the online estimation of system noise statistics.(2)A refined MMAUKF is designed to improve the computational efficiency and enhance the real-time performance of the MMAUKF.Different to the MMAUKF,this method constructs an optimization model of system noise statistics according to maximum likelihood principle.Subsequently,it further establishes a moving horizon strategy to improve the computational efficiency of the maximum likelihood principle based optimization model.Based on the above,a new expectation maximization technique is developed to iteratively compute the system noise statistic estimation by replacing complex smoothed estimates with filtering estimates for further improvement of the computational efficiency.The results show that the filtering accuracy of the refined filter is equivalent to the MMAUKF,while it effectively improves the computational efficiency and enhances the real-time performance of the MMAUKF.(3)An IMM estimation-based adaptive robust UKF is presented to overcome the limitation of the classical UKF in requirement of accurate system model.Based on the principle of innovation orthogonality,this method establishes an adaptive fading UKF(AFUKF)for the case of process model uncertainty and a robust UKF(RUKF)for the case of measurement model uncertainty.Subsequently,an IMM estimation is developed to fuse the AFUKF and RUKF as sub-filters according to the mode probability.The overall system state estimation is achieved as a probabilistic weighted sum of the estimation results from the two subfilters.The proposed method is applied to the INS/GNSS integrated navigation system for the experimental verification.The results indicate that the proposed method not only overcomes the limitation of the classical UKF in requirement of accurate system model,but it also absorbs the merits and discards the demerits of the AFUKF and RUKF,leading to the improved adaptability and robustness.(4)An unscented transformation(UT)based nonlinear multi-sensor optimal data fusion approach is derived to address the problem that the fusion performance of federated Kalman filter will be seriously influenced by the covariance upper bound technique.The proposed approach can provide the optimal fusion results without requiring the local state estimations to be mutually independent since it is directly derived according to the minimum variance principle,leading to the improved fusion performance for the multi-sensor nonlinear systems.(5)By combining the modified UKFs with the multi-sensor optimal data fusion approach,a multi-sensor optimal data fusion methodolody based on the modified UKFs is designed to enhance the adaptability and robustness of the data fusion for the multi-sensor nonlinear systems.This methodology is of a bottom-up structure: at the bottom level,the modified UKFs are served as local filters to generate the local state estimates for the improvement of robustness against the system model uncertainty;and at the top level,the UT based multi-sensor optimal data fusion approach is applied to fuse the local state estimates for obtaining the global optimal state estimation.The proposed method is applied to the INS/GNSS/celestial navigation system(INS/GNSS/CNS)integrated navigation system,and the results verify that the proposed methodology can effectively refrain from the influence of covariance upper bound technique on data fusion accuracy,and improve the adaptability and robustness against the system model uncertainty.The research work of this paper has considerable contribution to the nonlinear filtering and multi-source information fusion technologies.The research results can be used for the navigation and positioning of the vehicles in the fields of aviation,aerospace and traffic transportation.By the promotion,they also can be applied to the dynamic systems in the areas such as target tracking,fault diagnosis and automatic control.