Stepwise Autonomous Orbit Determination of Large LEO Constellations by GNSS Observations with Partial Inter-Satellite Ranging

Large constellations composed of a great amount of Low Earth Orbit (LEO) satellites are widely applied in satellite communication, remote sensing, augmented satellite navigation, environment monitoring, and so on. The satellite Orbit Determination (OD) is critical for the various function realization of the large constellation. Three different stepwise autonomous OD strategies for the large constellation of LEO satellites are proposed based on the spaceborne Global Navigation Satellite System (GNSS) observations and Inter-Satellite Link (ISL) range measurements, including the stepwise OD with both GNSS and ISL range measurements, stepwise OD with ISL range constraints, and an adaptive stepwise OD with both kinds of measurements. All of the three proposed stepwise autonomous OD approaches first estimate the initial orbit parameters for each satellite utilizing the spaceborne GNSS observations based on either a kinematic or dynamic OD strategy. The correction vector for the orbit parameters of each satellite is then individually calculated using the partial ISL range observations or ISL range constraints. The difference of the adaptive stepwise OD algorithm is that the covariance matrix of the predicted orbit parameters based on the dynamic model is modified by an adaptive factor. The LEO satellite parameters estimated with the stepwise OD strategies are equivalent to those obtained with the related integrated OD strategies. The main advantages of the proposed stepwise OD estimators are: (1) the orbit parameters of each satellite can be estimated in parallel, reducing the OD computational load for a large LEO constellation; (2) the spaceborne GNSS observations and the ILS range measurements in the three proposed approaches can be separately joined the OD procedures, making the parameter estimation flexible; (3) the adaptive stepwise OD mode with an adaptive factor acting on the covariance matrix of the predicted orbit parameters can effectively control the effects of the abnormal dynamic model information on the orbit parameter estimates. The simulation results for different OD strategies are analyzed. It is shown that the Root Mean Square Error (RMSE) of the estimated positions of the LEO satellites using the kinematic OD method is 60.527 cm, assuming the GNSS pseudorange noise of 30 cm. In contrast, the RMSE for the stepwise strategy, which considers only four adjacent ISL range measurements with an accuracy of 5 cm, is 18.287 cm. When the dynamic models for the LEO satellites are adopted, the RMSE of the estimated satellite positions using the stepwise orbit determination is further reduced to 11.340 cm. If the ISI ranging accuracy is better than 5 cm, the results remain nearly the same disregarding the ISL ranges are employed as observations or as constraints in the stepwise OD approaches. If the dynamic model information contains a few outliers, the adaptive stepwise OD can effectively control their effects on the orbit parameter estimates.