Abstract
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.
Highlights
Kalman filtering is a recursive algorithm widely used in positioning and navigation
When the real observations do not satisfy the mathematical model or the statistical properties of the measurement noise and the dynamic state process (in particular, when signals undergo severe interference from multipath, no-line-of-sight (NLOS) and gross errors), such a recursive process of conventional Kalman filtering generates a poor solution for this epoch, and propagates poor quality solutions for subsequent epochs
This paper focuses on the detection and elimination of abnormal observations and gross errors of Kalman filtering, in order to ensure its stability and reliability
Summary
Kalman filtering is a recursive algorithm widely used in positioning and navigation. It dynamically updates the state variables of a system and recursively estimates the state variables by assigning proper weights to the observations and state predictions. When the real observations do not satisfy the mathematical model or the statistical properties of the measurement noise and the dynamic state process (in particular, when signals undergo severe interference from multipath, no-line-of-sight (NLOS) and gross errors), such a recursive process of conventional Kalman filtering generates a poor solution for this epoch, and propagates poor quality solutions for subsequent epochs To remedy such a vulnerability, scholars have proposed various methods to mitigate the impact of these abnormal situations, such as function model compensation [2], adaptive Kalman filtering [3], and robust Kalman filtering [4]. The observations represent the pseudo-range measurements from the receiver in GNSS positioning, and refer to the positioning parameters obtained by GPS, IMU, and VO in integrated navigation The validity of this model verifies that ∆χ2-based robust Kalman filtering does improve the accuracy and stability of real-time kinematic positioning, and has an advantage over the other schemes of Kalman filtering that are compared in the paper
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