Robust Adaptive Kalman Filtering And Its Application In GNSS Attitude Determination

When the observation conditions are poor or the system undergoes drastic dynamics, abnormal observation errors or kinematic model errors are often encountered. Both of them impose significant impact on the GNSS's accuracy sometimes even cause the divergence of the standard Kalman filtering. Accompanying with the development of GNSS, the demands for kinematic applications and the requirements for higher accuracy increase, thus the research on improving the reliability and stability of Kalman filtering becomes impending. This paper focuses in depth on the theory and algorithm of the adaptive robust Kalman filtering. The main work and innovative contribution of this thesis are summarized as follows:1. Key factors of the standard Kalman filtering are studied and its favourable statistical properties are proved. Based on the study of the filtering gain, the fact that the standard Kalman filtering can obtain optimum estimation is derived. All of the above content is to lay foundation of the designate of adaptive Kalman filtering.2. Abnormal observation errors and kinematic model errors are studied, the cause and inevitability of these errors are expounded, and their error functions are derived respectively. Based on the study of these errors, three statistics, including prediction residual, state discrepancy and ratio of variance components, which could sensitively reflect the errors are proposed. A numerical experiments are conducted to demonstrate the availability of these statistics in reflecting the the fact of the errors.3. An automatic modeling method based on principle component analysis (PCA) is proposed to restrain the periodic error caused by repetitive movement of the carrier. Several different automatic modeling methods used to control the periodic error are compared and their advantages and disadvantages are demonstrated. To validate the effectiveness of PCA in dealing with periodic errors which has irregular amplitude and phase, three sets of simulation test are conducted. Comparing with the result of FFT, the following conclusion is obtained that PCA can detect out the local errors and can effectively contorlling the influence of periodic errors which have irregular amplitude and phase.4. A variety of adaptive Kalman filtering are summarized and classified. Their principal theory are presented. Advantages and disadvantages of different adaptive Kalman filtering algorithms are analyzed and compared. The research shows that different algorithm has different advantages in controlling errors and adaptive robust Kalman filtering has a better effect on controlling the influence of abnormal observation error and kinematic model error.5. Robust adaptive Kalman filtering is applied in GNSS attitude determination system and an experiment is designed to test and analyze its feasibility and accuracy. The result of the experiment shows that the adaptive robust Kalman filtering is feasible and can weaken the influence of abnormal observation error effectively.