Abstract:
Objectives: To address the reliability deficiency of undifferenced integer ambiguity validation in short-arc precise point positioning (PPP), an extreme gradient boosting (XGBoost) validation model is developed. The average number of observed satellites (NOBS) is introduced to enhance the discriminative capability of ambiguity dimension and satellite observation count, especially under varying observation geometry across different satellite systems and arc lengths in post-processed PPP-AR scenarios.
Methods: Observation data are post-processed using the PRIDE PPP-AR software to construct a multi-dimensional feature dataset. The extracted features include NOBS, R-ratio, W-ratio, Difference, Projector, ambiguity dilution of precision (ADOP), penalty factor λ, and ambiguity dimension. For data labeling, daily PPP-AR solutions are used as reference values, and short-arc candidates are classified as successful or failed by comparing their ambiguity values. The training dataset consists of one month of observations from 130 IGS stations in 2023, while the testing dataset includes one week of observations from 150 independent stations in 2022 and 2024. The model performance is evaluated under different satellite systems and arc lengths, and compared with both the conventional R-ratio (c = 3) test and a reduced-feature model without the NOBS feature to quantify its contribution.
Results: The results show that the proposed model achieves an accuracy of 89% on the training dataset and 86% on the independent testing dataset, indicating good generalization across different stations and time periods. In the PPP-Ambiguity Resolution (PPP-AR) test, the accuracy improves by about 5 percentage points compared with the conventional R-ratio test, and by about 2 percentage points relative to the model without the NOBS feature, confirming the effectiveness of incorporating observation geometry information. The improvement is more significant under short arcs (20-30 min) and single BDS scenarios, as well as long arcs with multi-GNSS combinations, reaching about 10 percentage points. In addition, the inclusion of NOBS enhances the model’s robustness against variations in satellite availability and observation redundancy. Kinematic positioning tests show that the mean 3D positioning error of fixed solutions decreases from 14.3 cm with the R-ratio test to 9.1 cm when using the XGBoost model, representing an improvement of approximately 36%, demonstrating its effectiveness in reducing incorrect fixed solutions.
Conclusions: These results demonstrate that the proposed XGBoost-based validation model effectively integrates statistical indicators and observation geometry features to improve ambiguity validation reliability. The introduction of NOBS enhances the model’s ability to characterize observation conditions, compensating for the limited discriminative capability of ambiguity dimension across different systems and arc lengths. As a result, the model achieves more stable and accurate ambiguity validation performance under varying satellite configurations and observation environments. The improved identification of unreliable fixed solutions contributes directly to higher positioning accuracy in PPP-AR. Overall, incorporating geometry-related features such as NOBS can effectively enhance the reliability of undifferenced PPP-AR and improve positioning accuracy in short-arc.