Research On Nonlinear SPKF Filtering Algorithm And Its Application For Integrated Navigation

SINS/GPS integrated navigation system is essentially non-linear, and has model uncertainty. At present, the non-linear filtering method applied for SINS/GPS integrated navigation system is mainly extended Kalman filter (EKF). However, EKF has some shortcomings including low precision resulted from the first-order linear and calculating Jacobian matrix of non-linear function, so its estimation accuracy is poor in the integrated navigation, and EKF does not have robustness to overcome the system model uncertainty. In recent years, with the deepening demand for non-linear filtering technique, non-linear filtering theory has made remarkable progress. Especially the emerging non-linear filtering methods, such as Sigma-point Kalman filter (SPKF) and particle filter (PF) developed, making non-linear filtering theory has made considerable development.SPKF with easy implementation, high precision and good convergence, etc., is becoming the research focus and development direction of the current and future non-linear filtering technique. This paper applies SINS/GPS integrated navigation system for the application background, and for the theory limitations existing in SPKF, the theory innovation is mainly made from the following aspects:1) According to the linear minimum variance estimation criteria, the recurrence formula of the non-linear optimal filter is derived in detail.2) For this problem that filtering accuracy of the traditional SPKF reduces or even diverges when noisy priori statistics is unknown or time-varying, based on maximum a posteriori estimation principle, a kind of adaptive SPKF algorithm with noise statistics estimator is designed.3) Similar to the EKF, the traditional SPKF does not have the robustness to overcome the system model uncertainty. For this, a strong track SPKF algorithmwith suboptimal fading factor is presented. Meanwhile, the above-mentioned non-linear filtering theory innovations about SPKF is used in SINS/GPS integrated system navigation, and the following aspects were mainly studied:1) This papr establishes the non-linear model of SINS/GPS integrated navigation system based on the errors of posture, speed and location, and compares the filtering performance of EKF and SPKF. Simulation results validate the SPKF has better positioning accuracy than EKF.2) For time-varying characteristics of inertial device random noise statistics on the working environment with a slightly evil, the adaptive UKF algorithm is applied to SINS/GPS integrated system. Simulation results show that the adaptive SPKF does not require to precisely know the priori statistics of inertia device random noise before the filter, and has a adaptive capacity to response to changes in inertial random noise statistics.3) Under normal circumstances, inertial device regular random drift will be seen as part of the state variable to been estimated in fitering, and is prone to mutation caused by the uncertain factors of operation environmental. For this, the strong tracking SPKF is applied to SINS/GPS integrated system, and simulation analysis shows that strong track SPKF has a strong ability to track inertial device regular random drift when it has a mutation, and possesses a robustness to overcome model uncertainty of the integrated navigation system.