Real-time PPP algorithm considering hourly discontinuous BDS-3 broadcast ephemeris with covariance-adaptive Kalman filter

Abstract Previous studies indicate that the accuracy of the BDS-3 broadcast orbit is comparable to that of the real-time precise products provided by International GNSS Service (IGS). However, the precision of both the broadcast orbit and clock remains limited by the hourly update. This characteristic enables Precise Point Positioning (PPP) implementation with broadcast ephemeris, yet introduces critical challenges, namely, hourly discontinuities and the associated ephemeris uncertainties. To address these limitations, a PPP estimation strategy incorporating covariance-adaptive Kalman filter is proposed in this paper. The strategy aims to mitigate the impact of broadcast ephemeris discontinuities and to adjust the covariance matrix to accommodate the actual uncertainties caused by these discontinuities. Specifically, the proposed approach employs a parameter-augmented state model capable of simultaneously estimating position parameters and compensating for the errors resulting from the discontinuities. Furthermore, an adaptive factor is proposed to adjust the covariance matrix according to the uncertainties induced by the periodically updated ephemeris. The proposed algorithm was rigorously evaluated with comprehensive static and kinematic tests. In the static assessments, the observations spanning one week at seven globally distributed IGS stations were utilized. The outcomes demonstrated a mean horizontal Root-Mean-Square (RMS) value of 18.04 cm and a Three-Dimensional (3D) RMS value of 24.64 cm were achieved, representing a 30.82% improvement compared with conventional broadcast ephemeris PPP algorithm. Dynamic validation was conducted using 10 h maritime experiment data in the south China sea. The results show that the horizontal, vertical, and 3D accuracies are improved by 7.32%, 45.32%, and 39.07%, respectively, confirming the effectiveness of the algorithm in both static and dynamic applications.