Comparing satellite orbit determination by batch processing and extended Kalman filtering using inter-satellite link measurements of the next-generation BeiDou satellites

The next-generation BeiDou satellites are equipped with inter-satellite link (ISL) payloads to realize the ability of autonomous navigation (Auto-Nav). We focus on the application of batch processing and extended Kalman filtering (EKF) algorithm on Auto-Nav of BeiDou satellite system (BDS). The mathematical model of dual one-way measurements and principle of batch mode and EKF are introduced. Using real ISL measurements, Auto-Nav experiments are conducted with batch processing and EKF, respectively. For the sub-constellation, the EKF with a priori equipment delay constraints is proposed. The result shows that (1) with three ISLs and only one anchor station, the ISL measurements are sparsely distributed and the coverage of the whole arc is about 31%. The observations and dynamic models per epoch contribute more to satellite position and velocity parameters than to equipment delay parameters. (2) For batch processing, the overlap precision of precise orbit determination (POD) with ISLs and ground-satellite links (GSLs) is about 0.1 m in the radial direction and is better than 1 m three-dimensionally. The variation of the estimated equipment delays is within $$\pm \,0.6$$±0.6 ns. The observation residuals of ISLs behave such as a normal distribution, while the residual of GSLs show periodical variation due to uncorrected troposphere delay. (3) For the EKF, the ISL-only orbit determination is sensitive to the accuracy of the initial state. Compared with batch result, the precision of ISL-only orbit determination using EKF is better than 2 m given accurate initial states. The filtering does not show constellation drift or rotation within 8 days. However, with approximate initial states which position accuracy is 100 m, the precision of POD decreases to dozens of meters. (4) For the EKF, the accuracy of POD improves to 1.5 m in three dimensions with the support of an anchor station. The period for equipment delay parameters to converge is about 24 h. However, the convergence rate of equipment delay parameters is much slower than that of satellite state parameters. The possible reason is the unbalanced contribution of observation and dynamic model information on the estimated parameters. Thus, it is better to constrain the equipment delay parameters with a priori information while filtering.