The rapid development of multi-satellite formations requires inter-satellite radio frequency (RF) measurement to be both precise and scalable. The navigation estimation of multi-satellite formations using a unified time reference demands the simultaneous RF measurement of the inter-satellite range and time difference. However, high-precision inter-satellite RF ranging and time difference measurements are investigated separately in existing studies. Different from the conventional two-way ranging (TWR) method, which is limited by its reliance on a high-performance atomic clock and navigation ephemeris, asymmetric double-sided two-way ranging (ADS-TWR)-based inter-satellite measurement schemes can eliminate such reliance while ensuring measurement precision and scalability. However, ADS-TWR was originally proposed for ranging-only applications. In this study, by fully exploiting the time-division non-coherent measurement characteristic of ADS-TWR, a joint RF measurement method is proposed to obtain the inter-satellite range and time difference simultaneously. Moreover, a multi-satellite clock synchronization scheme is proposed based on the joint measurement method. The experimental results show that when inter-satellite ranges are hundreds of kilometers, the joint measurement system has a centimeter-level accuracy for ranging and a hundred-picosecond-level accuracy for time difference measurement, and the maximum clock synchronization error was only about 1 ns.

Low-performing GPS receivers, often used in challenging scenarios such as attitude maneuver and attitude rotation, are frequently encountered for micro–nano satellites. To address these challenges, this paper proposes a modified robust adaptive hierarchical filtering algorithm (named IARKF). This algorithm leverages robust adaptive filtering to dynamically adjust the distribution of innovation vectors and employs a fading memory weighted method to estimate measurement noise in real time, thereby enhancing the filter’s adaptability to dynamic environments. A segmented adaptive filtering strategy is introduced, allowing for flexible parameter adjustment in different dynamic scenarios. A micro–nano satellite equipped with a miniaturized dual-frequency GPS receiver is employed to demonstrate precise orbit determination capabilities. On-orbit GPS data from the satellite, collected in two specific scenarios—slow rotation and Earth-pointing stabilization—are analyzed to evaluate the proposed algorithm’s ability to cope with weak GPS signals and satellite attitude instability as well as to assess the achievable orbit determination accuracy. The results show that, compared to traditional Extended Kalman Filters (EKF) and other improved filtering algorithms, the IARKF performs better in reducing post-fit residuals and improving orbit prediction accuracy, demonstrating its superior robustness. The three-axes orbit determination internal consistency precision can reach the millimeter level. This work explores a feasible approach for achieving high-performance orbit determination in micro–nano satellites.

Extended Kalman Filter (EKF) is extensively employed in Global Navigation Satellite System (GNSS)-based real-time orbit determination (RTOD) for microsatellites due to its low complexity. However, the performance of EKF-RTOD is markedly degraded when the microsatellite deviates from a stable Earth-pointing attitude and employs a low-cost receiver. Factor graph optimization (FGO), which addresses nonlinear problems through multiple iterations and re-linearization, has demonstrated superior accuracy and robustness compared to EKF in challenging environments such as urban canyons. In this study, we introduce a novel FGO-based RTOD (FGO-RTOD) approach, which integrates state transfer factors to establish temporal connections between state nodes across multiple epochs. Real-time processing is achieved through a sliding window mechanism combined with marginalization. This paper evaluates the performance of the proposed algorithm in a regular scenario using data from GRACE-FO-A, which maintains the Earth-pointing attitude and employs a high-performance receiver. The positioning results of GRACE-FO-A indicate that FGO-RTOD marginally outperforms EKF-RTOD in accuracy. Furthermore, the performance of FGO-RTOD is assessed in challenging scenarios using simulation data and on-orbit data from Tianping-2B microsatellite, which is not in an Earth-pointing attitude and employs a low-cost receiver. The simulation results reveal that FGO-RTOD reduces the Root Mean Square (RMS) of positioning error by 79.0% relative to EKF-RTOD and exhibits significantly enhanced smoothing. In the Tianping-2B experiments, FGO-RTOD reduces the RMS of carrier-phase ionosphere-free combination residuals from 2 cm to 1 cm relative to EKF-RTOD, alongside a substantial improvement in the ratio of valid observations. These findings underscore the effectiveness of FGO-RTOD in managing outlier measurements in challenging scenarios.