Kalman filter is an important technology to realize information fusion between Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS). One of the most important variables in the Kalman filter structure is the state variable, which is the basis of maintaining system stability. However, due to the inherent singularity in polar regions, the INS/GNSS integrated navigation system will not work properly in polar regions. Different coordinate systems are often used in trans-polar navigation to solve the problems in the polar regions, therefore the Kalman filter state variable transformation is inevitable in the process of entering or leaving the polar regions, which will bring instability and even failure to the system. Here, this paper proposes a Kalman filter state transformation algorithm for INS/GNSS polar integrated navigation based on Psi-angle error model to ensure the numerical stability of the Kalman filter during its state transformation. Key to this success is to establish the transformation relationship between different filter state variables as well as their covariance matrices in different navigation coordinate systems, then the state variables and the covariance matrices are transformed simultaneously. After presenting the state variable transformation algorithm and the system description, a numerical evaluation is carried out to assess the presented algorithm with regard to stability and accuracy.

Dual-axis rotational inertial navigation system (DRINS) can achieve self-calibration of error parameters to improve the navigation performance. However, the traditional self-calibration methods rely on the external reference information. This paper focuses on the dual DRINSs configuration and proposes a collaborative calibration algorithm. Considering the error parameters of redundant DRINS, the 60-D Kalman filter is established, in which the geometric constraint between systems are deployed to establish the observation equation without external reference information. A novel collaborative calibration scheme is designed based on the asynchronous rotation to make all the error states observable. Monte Carlo simulations and real system experiments are conducted to verify the effectiveness of the proposed algorithm. The result shows the algorithm works well.

The Kalman filter method plays a crucial role in enhancing the navigation accuracy of the dual-axis rotational inertial navigation system (RINS) through periodic estimation and compensation of device errors. Due to the particularity of polar geography, the traditional RINS mechanism in the local-level geographic frame loses efficacy in the polar region. This paper proposes a self-calibration Kalman filter algorithm based on the transverse ellipsoidal earth model to solve the self-calibration problem of RINS in polar region. This method firstly transforms the state of the local-level geographic frame to the transverse frame, and then constructs the prediction model and observation model of the Kalman filter based on the carrier state and error parameters in the transverse frame. In the self-calibration stage, a suitable rotation strategy is employed to stimulate the errors of RINS, and the proposed algorithm is utilized to estimate and compensate for the resulting errors. In addition, the traditional spherical earth model is improved to ellipsoidal earth model in this algorithm to avoid additional errors in the polar region. Monte Carlo experiments are carried out with simulation data at high latitudes, and then experiments at middle latitudes are carried out with ring laser gyro-based dual-axis RINS. The results demonstrate that the proposed method enables precise calibration of all error parameters, which aligns consistently with results obtained within the local-level geographic frame.