A Kalman filter-based framework for real-time UPD estimation and quality control with multi-GNSS PPP-AR validation

Abstract Precise point positioning ambiguity resolution (PPP-AR) is a key technique for achieving fast convergence and high-precision positioning in real-time applications. However, the quality of uncalibrated phase delay (UPD) products remains a critical factor influencing ambiguity resolution success, particularly in multi-global navigation satellite systems (GNSS) environments. This study presents a robust real-time UPD estimation framework that integrates multi-GNSS differential code bias corrections, antenna phase center offset compensation in the Melbourne-Wübbena combination, and a Kalman filter-based strategy with rigorous initialization and quality control. Using 31 d of observations from 170 MGEX stations, the accuracy of Centre National d’Études Spatiale (CNES) real-time orbit and clock products is first assessed, revealing that BDS-3 satellites show poorer clock performance than GPS and Galileo. Relative to CNES/CLS products, the proposed method substantially improves UPD quality. For wide-lane ambiguities, the proportion of residuals within ±0.15 cycle increases from 84.0% to 89.8% for GPS, from 98.7% to 99.2% for Galileo, and from 75.2% to 89.7% for BDS-3. The narrow-lane ambiguities show even greater improvement, with GPS increasing from 75.1% to 86.6%, Galileo from 78.4% to 88.1%, and BDS-3 from 33.6% to 59.8%. In GPS + Galileo + BDS-3 PPP-AR experiments, the proposed method shortens convergence times by 8.3%, 25.0%, and 23.3% in the north, east, and up components, respectively, compared with CNES/CLS. The cumulative distribution of time to first fix also indicates a 6.8% increase in stations achieving ambiguity resolution within 3 to 18 min. These results demonstrate that the proposed framework effectively enhances real-time UPD quality, thus improving the reliability and efficiency of PPP-AR positioning in global multi-GNSS applications.