RANSAC-based iterative data refining method for multiple outliers in GNSS positioning

Effectively dealing with multiple outliers is indispensable for achieving reliable navigation and positioning performance in GNSS. The iterative data snooping (IDS) method is commonly used to identify outliers in a forward stepwise manner. Nevertheless, its effectiveness is often compromised by masking and swamping when multiple outliers are present. Recently, the iterative data refining (IDR) method was proposed as a backward alternative to IDS, which identifies potential inliers from the initial outlying set. However, its performance depends critically on the preset maximum number of suspected outliers (qmax), as this critically affects the quality of the initial outlying set. A large qmax covers all outliers at the expense of estimation accuracy, whereas a small qmax may fail to mitigate the masking and swamping effects. To address this dilemma, a dynamic adjustment strategy for qmax is adopted. Meanwhile, random sample consensus (RANSAC) is employed to evaluate whether the resulting inliers obtained by IDR still contain outliers, which guides the adjustment of qmax. Therefore, this paper proposes a RANSAC-based IDR method that dynamically adjusts qmax in a piecewise increasing manner. Taking GNSS single-point positioning as an example, the proposed method is compared with least squares (LS), IDS, information criterion-based model selection (DIA-AICc), and IDR with fixed qmax under various gross error simulation strategies, using one day of observation data. Results indicate that the average positioning accuracies of the four methods are 97.250 m, 81.075 m, 22.500 m, and 16.224 m. In terms of solution availability, the average results are 100% for IDS, 89.29% for DIA-AICc, and 93.90% for the proposed method, while the average wrong identification rates reach 57.78%, 20.24%, and 12.72%, respectively. Overall, the proposed method consistently achieves the highest correct identification rate and the lowest wrong identification rate among all compared methods, with competitive positioning accuracy and acceptable computational time.