An improved approach for rapid filter convergence of GNSS satellite real-time orbit determination - Zhou, Liqin; Fan, Lei; Li, Zongnan; Fang, Xinqi; Shi, Chuang (Frontiers in Physics, 2023)
The real-time precise satellite orbit of Global Navigation Satellite System (GNSS) usually takes a long time to converge to a stable state using the filter method. The ultra-rapid orbit products are helpful to improve convergence speed by introducing them as external constraints. Reasonably determination of stochastic model of the constraint equation from the ultra-rapid products is the key for a better performance of convergence whereas it has not been well solved. We propose to establish the stochastic model by analyzing the differences between the predicted part of the ultra-rapid orbit and the filter orbit after convergence. To validate the proposed method, a month of data from 80 globally distributed stations is processed using the Square Root Information Filtering (SRIF) algorithm. Orbit results without external constraints show that the convergence time in radial direction is 13.75, 15.25 and 17.75 hours for GPS, Galileo and BDS-3 satellite, respectively. To improve the orbit accuracy during the convergence, the constant stochastic model is first determined for each system by averaging the root mean square (RMS) time-series of the differences between predicted orbit from the ultra-rapid products and the SRIF orbit after convergence in different time ranges. Using the average RMS over 6 hours, results show that there is no significant convergence phenomenon for each system in all directions. The one-dimensional (1D) RMS during the constraint period is improved by 86.5%, 84.8%, 96.8% for GPS, Galileo and BDS-3 satellites when compared to the results without external constraints. Besides, a time-dependent stochastic model is determined by analyzing the variation of the RMS time-series. Results show that the quadratic function is suitable for modeling the RMS time-series for each system, and the accuracy of results during the constraint period has a further improvement of 1.3%, 3.7% in 1D direction for GPS, BDS-3 satellites when compared to the constant stochastic model using the average RMS over 6 hours. In addition, the orbit accuracy with external orbit constraint is slightly better than those without external constraint after the constraint period. This indicates that the proposed method can significantly improve the convergence performance without damaging the orbit accuracy after convergence.