Robust GNSS Positioning Algorithm for High Orbit with Orbit Propagator Assistance

‍ ‍Traditional methods of high-orbit determination relied on ground-based radio and laser measurements， which have significant limitations such as the delay in measurement processing and the logistical challenges of establishing measurement stations globally. Owing to the increasing number of space missions， the autonomy of satellite orbit determination has attracted considerable attention. The use of global navigation satellite systems （GNSSs） for orbit determination presents a promising solution by facilitating autonomous operations in orbit. However， high-orbit satellites， because of their distant positions， encounter specific challenges when using GNSS， with the primary challenge being that these satellites need to receive signals from navigation satellites positioned on the opposite side of the Earth. This requirement significantly weakens the received signal strength， reduces the number of available satellites， and results in poor geometric dilution precision， thereby complicating the orbit determination process. This study specifically addresses the susceptibility of high-orbit GNSS users' received signals to contamination， which could introduce gross errors into observation data， undermining the robustness and accuracy of positioning solutions. To address this issue， we propose an innovative high-orbit GNSS-robust positioning algorithm that leverages an orbit propagator （OP） for assistance. This algorithm is built upon the traditional GNSS and OP combined positioning method but introduces a novel approach to robustly address gross errors in the observation data of high-orbit users. The proposed technique involved normalizing the residual vector and residuals within the positioning algorithm based on predictions from the orbit propagator. The efficacy of this proposed algorithm was rigorously evaluated through a series of simulations. In scenarios devoid of intentional gross errors， where GNSS signals were only influenced by thermal noise， the traditional GNSS/OP combined positioning algorithm achieved a positioning accuracy of 41.92 m， whereas the robust GNSS positioning algorithm for high orbit with orbit propagator assistance demonstrated an accuracy of 42.14 m. The simulation further explored the performance under conditions where gross errors of 300 m were artificially introduced into the observation data. Under these conditions， the traditional GNSS/OP algorithm exhibited deteriorating positioning accuracies of 69.55 m. By contrast， the robust GNSS positioning algorithm for high orbit with orbit propagator assistance achieved accuracies of 42.17 m. The simulation results indicate that， when different magnitudes of gross errors are added to the observations， the larger the gross error added， the stronger the ability of the robust GNSS positioning algorithm for high orbit with orbit propagator assistance to eliminate gross errors. Remarkably， when a 300 m gross error was added， the robust GNSS positioning algorithm for high orbit with orbit propagator assistance achieved a positioning accuracy similar to that without the addition of gross errors. The observations with gross errors were eliminated， resulting in significantly improved positioning accuracy compared with that of the traditional GNSS/OP algorithm. Consequently， this advanced algorithm significantly enhances the robustness and reliability of high-orbit satellite positioning， marking a substantial improvement over the traditional method. Thus， the robust GNSS positioning algorithm for high orbit with OP assistance provides a modern solution to the challenges faced in high-orbit satellite navigation. By effectively addressing the issues of signal contamination and gross errors， the algorithm ensures enhanced positioning accuracy and operational reliability for high-orbit satellites. This result is crucial for the expanding landscape of space missions and the increasing demand for satellite autonomy.