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Concerns for the collision risk involving Starlink satellites have motivated the interest in obtaining their accurate orbit knowledge. However, accurate orbit determination (OD) and prediction (OP) of Starlink satellites confront two main challenges: mismatching or missed matching of sparse tracklets to maneuvering satellites, and unknown or unmodeled orbit maneuvers. How to exactly associate a tracklet to the right satellite is the primary issue, since a maneuvering satellite does not follow the naturally evolving orbit during the maneuvering, while more tracklets are needed for developing an accurate orbit maneuver model. If these two challenges are not well addressed, it may lead to catalog maintenance failure or even loss of objects. This paper proposes a method to correctly match tracklets to the climbing Starlink satellites. It is based on the recursive OD and OP, in which the orbit maneuver is modeled and the thrust is estimated, such that the subsequent OP accuracy guarantees the correct match of tracklets shortly after the OD time. Experiments with climbing Starlink satellites demonstrate that the tracklets within three days of the last TLE (two-line element) are all correctly matched to the right satellites. With the matched tracklets, the thrust accelerations of climbing Starlink satellites can be precisely estimated through an orbit control approach, and the position prediction accuracy over 48 hours is at the level of a few kilometers, providing accurate orbit knowledge for reliable collision warning involving Starlink satellites.

Covariance of the orbital state of a resident space object (RSO) is a necessary requirement for various space situational awareness tasks, like the space collision warning. It describes an accuracy envelope of the RSO’s location. However, in current space surveillance, the tracking data of an individual RSO is often found insufficiently accurate and sparsely distributed, making the predicted covariance (PC) derived from the tracking data and classical orbit dynamic system usually unrealistic in describing the error characterization of orbit predictions. Given the fact that the tracking data of a RSO from a single station or a fixed network shares a similar temporal and spatial distribution, the evolution of PC could share a hidden relationship with that data distribution. This study proposes a novel method to generate accurate PC by combining the classical covariance propagation method and the data-driven approach. Two popular machine learning algorithms are applied to model the inconsistency between the orbit prediction error and the PC from historical observations, and then this inconsistency model is used to the future PC. Experimental results with the Swarm constellation satellites demonstrate that the trained Random Forest models can capture more than 95% of the underlying inconsistency in a tracking scenario of sparse observations. More importantly, the trained models show great generalization capability in correcting the PC of future epochs and other RSOs with similar orbit characteristics and observation conditions. Besides, a deep analysis of generalization performance is carried out to describe the temporal and spatial similarities of two data sets, in which the Jaccard similarity is used. It demonstrates that the higher the Jaccard similarity is, the better the generalization performance will be, which may be used as a guide to whether to apply the trained models of a satellite to other satellites. Further, the generalization performance is also evaluated by the classical Cramer von Misses test, which also shows that trained models have encouraging generalization performance.