The covariance matrix transformation method in all-earth integrated navigation considering coordinate frame conversion

In the exploration of polar regions, navigation is one of the most important issues to be resolved. To avoid the limitations of a single navigation coordinate frame, navigation systems usually use different navigation coordinate frames in polar and nonpolar regions, such as the north-oriented geographic frame and the grid frame. However, the error states and covariance matrix are related to the definition of the navigation coordinate frame, since coordinate frame conversion will cause overshoot of the integrated navigation Kalman filter and error discontinuity. To solve this problem, the transformation relationship of error states defined in different frames is deduced, whereby the covariance matrix transformation relationship is also analyzed. On this basis, covariance transformation-based open-loop and closed-loop Kalman filter integrated navigation algorithms are proposed. The effectiveness of the algorithms is verified by flight tests with a rotational strapdown inertial navigation system/global navigation satellite system integrated navigation system.