Unknown biases or perturbations in the INS/GNSS integrated navigation system may produce unforeseeable negative effects when the navigation states are estimated by using the Kalman filtering and its variants. To mitigate these undesirable effects in the INS/GNSS integrated navigation, a novel partially strong tracking extended consider Kalman filtering (PSTECKF) is proposed. In the presented PSTECKF algorithm, the biases are not estimated, but their covariance and co-covariance are incorporated into the state estimation covariance by using a nonlinear ‘‘consider’’ approach. Based on the above, the PSTECKF also partially introduces an adaptive fading factor into the predicted covariance of the states, which excludes the co-covariance between the states and biases, to compensate the nonlinear approximation errors and navigation system covariance uncertainties. Simulation results demonstrate the performance of the proposed PSTECKF for INS/GNSS integrated navigation is superior to that of the EKF and ECKF when the biases or perturbations happen in a navigation system.

Introduction

The inertial navigation system (INS) and global navigation satellite system (GNSS) integrated navigation system organically merge advantages of two sensors, which are the high short-term navigation accuracy of INS and high long-term navigation accuracy of GNSS, and have a widely application in navigation and positioning field [1]–[۵]. The INS/GNSS integrated navigation system overcomes the limitations of using INS or GNSS navigation systems alone and can work well in all weather conditions around the world. When the states of the INS/GNSS integrated navigation system are estimated by using the Kalman filtering and its variants, there are two methods can be selected, which are the direct method and the indirect method [6]. The indirect method obtains the optimal estimations of the navigation errors of the INS and GNSS by utilizing the navigation errors as the system states. The direct method directly gives the optimal estimations of the integrated navigation parameters by using filtering algorithm, and its states are the output navigation parameters of the navigation system. Comparing to the indirect method, the direct method has two advantages: one is more accurately propagating the navigation states and another is avoiding double counting by using mechanical calibration equation of the INS [7]–[۹].