The Research And Application Of Functional Models In GPS Navigation Data Processing

This dissertation mainly studies functional models and their computation algorithms in GPS kinematic data processing. The main works and contributions are summarized as follows:1. The key problems of functional models in GPS navigation and positioning are analyzed based on the actual vehicle movements. It is shown by analysis that it is necessary to select the reasonable functional models in kinematic positioning.2. The algorithms in fitting the systematic errors and covariance matrices in GPS navigation are mainly researched. Using Kalman filtering for kinematic positioning, the functional models may contain systematic errors or local systematic errors. If they exist some systematic errors, the standard Kalman filtering cannot resist the influences of the systematic errors on the estimated states of navigation. Thus a reasonable functional model should be constructed to improve the accuracy of estimated states.3. Some kinematic models of the vehicle movements are introduced and the adaptive factors based on variance components estimation are investigated, then a linear adaptively robust Kalman filter based on the current statistical model and variance components estimation is set up.4. In order to avoid estimating the covariance matrices Σ_w of thefunctional model errors and Σ_Δ of the observational errors respectively,a robust Self-Tuning Kalman filtering is introduced based on the modern time series analysis. An equivalent weight based on robust M-estimator is applied in the process of Self-Tuning Kalman filtering to resist the influences of outliers on modeling parameters, and then the robust Self-Tuning Kalman filtering is proposed. This method not only adaptively estimates the state vector, but also guarantees the reliability of thekinematic state estimates.5. Finally, the nonlinear Kalman filter is analyzed in GPS navigation. The global nonlinear LS closed arithmetic—Bancroft numerical algorithm is introduced and the shortcoming of GPS two-stage filter is analyzed, then an adaptively robust filter based on Bancroft algorithm in GPS navigation is developed. It is shown that the new algorithm not only resists the influences of omitted high-order items on the estimated states of navigation, but also controls the outlying kinematic model errors and measurement outliers.