Research On Nonlinear Bayesian Filtering And Its Application For SINS/GPS Tightly Coupled Navigation

Integrated navigation system constituted by strapdown inertial navigation system (SINS)and Global Positioning System (GPS) was widely used. In complex application environments,the higher requirements for accurate and reliability were put forward. It is an important way tosolve this problem by researches on more accurate and more robust nonlinear filteringalgorithms. Taking SINS/GPS tightly coupled integrated navigation system as the background,this dissertation focused on the analysis of accuracy, complexity, robustness and improvementof nonlinear filtering algorithm, which was deduced by the Bayesian optimal filteringframework. In the end, these nonlinear filtering algorithms were applied in SINS/GPS tightlycoupled integrated navigation system. The research details were as follows:The accuracy and complexity of nonlinear Bayesian filtering algorithms were analyzed,and then the basis for selection was given. And, optimal iterative Bayesian filter was derivedbased on the Bayesian theorem. From the point of the approximation of the posteriordistribution function, the EKF, CDKF, UKF and CKF which were suited for the Gaussiandistribution system, together with the PF algorithm applicable to non-Gaussian system weresummarized and qualitatively analyzed. In order to laterally investigate the real timeperformance of various algorithms, the equivalent degree of complexity was used as theindicator. Then more accurate computational form of the filtering complexity was derived.Finally numerical simulation of the algorithms was carried to verify the correctness ofprevious analysis.The nonlinear fusion problem of SINS/GPS tightly coupled system with large inertialerrors was researched based on nonlinear Bayesian filtering. The nonlinear characteristics oftightly coupled system were presented by deriving the nonlinear error quaternion stateequations of SINS, the nonlinear pseudorange and pseudorange rate equations of GPS. Tostrongly nonlinear characteristics of SINS/GPS tightly coupled navigation system with largeinertial errors, CKF and CPF algorithms were applied to solve the problem. Numericalsimulations were carried out, which showed robustness of the adopted nonlinear filters indealing with large initial errors. Nonlinearity of the measurement model was analyzed, asequencial fusion method of tightly coupled navigation was proposed, and its performancewas proved by simulation.Variational Bayesian adaptive Kalman filter based on conjugate distribution estimationprinciple of the noise variance was analyzed. And compared with the traditional RAE adaptive method, the similarity and difference of the two methods were revealed. Whenmean and variance of measurement noise were both unknown, the Gaussian Inverse Gammadistribution was used to approximate the parameters. Based on this method, a newvariational Bayesian adaptive Kalman filter algorithm was proposed, and which couldsynchronously estimate the mean and variance. Aiming at precision reducing problemcaused by noise modeling error of GPS in the SINS/GPS tightly coupled navigation system,VB-CKF was proposed by joining variational Bayesian method and CKF. In order to obtainhigher accuracy, VB-CPF algorithm was proposed using the VB-CKF posteriori Gaussiandistribution as a recommendation of PF distribution. And then, the effectiveness of thealgorithm was proved by numerical simulation. VB-CKF and VB-CPF were applied in theadaptive nonlinear fusion algorithm of SINS/GPS tightly coupled system. And the precisionreducing problem of traditional algorithm was restrained, so the robustness was enhanced.Aiming at partly outage of visible satellites in harsh visibility environment of GPS, therobustness of SINS/GPS tightly coupled system was analyzed and verified from theperspective of system observability. Taking the state observability degree as themeasurement of system robustness, State estimation performance influenced by the variety ofGPS visible satellites number was analyzed, which explained the advantage of tightly coupledsystem.Aiming at positioning precision reducing problem caused by outage of visible satellitesin harsh visibility environment, the signal bridging algorithm based on Kalman smoother wasresearched. Statistical linearization method of the nonlinear function was realized based onCKF. Forward-backward smoothing and RTS smoothing algorithms were derived based onthe statistical linearization function. SINS/GPS precision positioning method based onstatistical linearization forward-backward smoother was proposed. Finally, simulation resultsshow that the positioning precision was improved.