Robust Kalman Filtering Based on Chi-square Increment and Its Application

In Global Navigation Satellite System (GNSS) positioning, gross errors seriously limit the validity of Kalman filtering and make the final positioning solutions untrustworthy. Thus, the detection and correction of gross errors have become indispensable parts of Kalman filtering. Starting by defining an incremental Chi-square method of recursive least squares, this paper extends this definition to Kalman filtering to detect gross errors, explains its nature and its relation with the currently adopted Chi-square variables of Kalman filtering in model and data spaces, and compares them with the predictive residual statistics. Two robust Kalman filtering models based on an incremental Chi-square method (CI-RKF) were established, and the one with a better incremental Chi-square component was selected based on a static accuracy evaluation experiment. We applied the selected robust model to the GNSS positioning and the GNSS/inertial measurement unit (IMU) / visual odometry (VO) integrated navigation experiment in an occluded urban area at the East China Normal University. We compared the results for conventional Kalman filtering (CKF) with a robust Kalman filtering constructed using predictive residual statistics and an Institute of Geodesy and Geophysics (IGGШ) weight factor, abbreviated as “PRS-IGG-RKF”. The results show that the overall accuracy of CI-RKF in GNSS positioning was improved by 22.68%, 54.33%, and 72.45% in the static experiment, and 12.30%, 7.50%, and 16.15% in the kinematic experiment. The integrated navigation results indicate that the CI-RKF fusion method increased the system positioning accuracy by 66.73%, 59.59%, and 59.62% in one of the severe occlusion areas, and 42.04%, 59.04%, and 52.41% in the other.

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