Robust adaptive unscented kalman filters for integrated navigation with nonlinear models

Abstract

One of the key issues in navigation and kinematic positioning is to estimate state parameters from measurements and dynamics information with errors. The commonly used method for kinematic positioning and navigation is measurements from integrated Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU), and a Kalman filtering method can be used to fuse these two types of measurements with their uncertainties. The conventional Kalman filter is an optimal estimator for a linear system contaminated by Gaussian noises. In fact, most of the real-world dynamic systems tend to have a certain degree of nonlinearity, thus various filters have been proposed for dealing with nonlinear models, such as Extended Kalman filter (EKF), Unscented Kalman filter (UKF), and particle filter (PF). The optimality of these filter algorithms, however, is linked with the knowledge of the system noise and the quality of the measurements. The performance of the filters can be degraded or even diverged in the case that the stochastic model used in the estimation is largely different from the real dynamic system noise, or in the case that measurements containing outliers are used in the estimation process. This research investigates the method to improve the accuracy and robustness of state estimates in GNSS/IMU integrated navigation systems. The main contributions of the thesis are: (1) A common theoretical framework for both EKF and UKF is established by correlation inference. A common theoretical framework of the two filters is established by correlation inference. The estimator expressed by the inference only depends on measurements, approximated state, and predicted measurements as well as their covariance and cross-covariance matrices. The relationships and the performance differences between UKF and EKF are discussed in terms of theoretical foundation and algorithms, and are tested using both simulation and observation data. The results indicated the superiority of UKF for kinematic state estimation. (2) Based on the above theoretical framework established, an adaptive UKF (AUKF) method is proposed to reduce the influence of the disturbance of a dynamic system. An AUKF is rigorously derived based on the correlational inference method. The adaptive nonlinear estimator not only reduces the influence of those unpredictable dynamic disturbances, but also takes into account the effects of the nonlinear model. An adaptive mechanism is developed by using an innovation vector at the current measurement epoch, which avoids the storage of innovation sequences and is more sensitive to the discrepancy between those from the predicted system state and the measurements. Both simulation and field test have shown that the AUKF outperforms the conventional UKF in terms of accuracy of the positioning and velocity estimates in the case of dynamic disturbances. (3) M-M estimation theory is applied and a robust M-M UKF (RMUKF) is developed to further reduce the influence of measurement outliers. Since the estimate accuracy is improved by the aforementioned AUKF method in the case of dynamic disturbances. This study is then extended to further reduce the influence of measurement outliers, if any, for which the RMUKF method is proposed. The RMUKF estimator is robust and it applies the maximum likelihood (M-) principle to the errors in both functional model and measurements. The estimator of the RMUKF is also deduced and analysed. A weight matrix composed of bi-factor shrink elements is developed for the RMUKF for keeping the original correlation coefficients of predicted state elements unchanged. The RMUKF successfully attenuates both the dynamic model disturbances and the influence of measurement outliers. (4) The theory developed above is verified by using an integrated IMU/GNSS navigation system in which the nonlinear IMU error model is treated as a dynamic model. The conventional IMU error model is derived based on the assumption that a small angle exists in attitude errors only. Hence the coordinate transformation matrices in the positioning solution can be presented by approximated matrices. To illustrate the proposed nonlinear estimators, a nonlinear IMU error model derived by the Euler angle errors, is employed to integrate with GNSS in a loosely coupled integration strategy. The performance of the proposed estimators is evaluated by using both simulation and field data.