Evaluation and improvement of tracklet correlation methods

Abstract

Nowadays, space-based systems for navigation, communication, Earth observation, meteorology and many other applications are indispensable for services critical for society. In order to preserve these vital applications among the increased risks in space, the Space Surveillance and Tracking segment of the Space Situational Awareness program has been set up in the last decade by the European Space Agency. This segment is occupied with one core activity: maintaining and building up a space object catalog. The object states within it can be used for conjunction assessment, collision avoidance and fragmentation event detection, allowing active satellites to be protected.

For objects in Low Earth Orbit, the Space Surveillance and Tracking segment primarily employs radar, which uses active signals, whose signal strength degrades with the fourth power of the distance. Beyond this orbit regime, passive optical sensors are primarily used, because they do not require an active signal and are therefore able to observe beyond Low Earth Orbit without large power requirements. As a consequence of the sparse optical sensors which have to track the large population of space objects, the optical observing arcs are typically very short: minutes at most. These short optical arcs are called tracklets.

Determining an orbit from a short arc is a challenging problem and is commonly referred to as the too short arc problem. Specifically, this problem entails that a single short arc tracklet is insufficient to construct an orbit with realistic state estimates. In order to obtain accurate state estimates, the object corresponding to the tracklet must be re-observed during a later pass to obtain six independent parameters of high quality. The initial problem to solve, however, is to identify which tracklets are correlated and thus associated with the same object. Thus, tracklet correlation is a critical step in the cataloging of objects. Evaluating and improving the performance of tracklet correlation methods is the key subject of this thesis. The performance is assessed on three key metrics: the association accuracy, the computational efficiency and the robustness.

In the first part of this thesis, tracklet correlation methods are evaluated. The most promising ones have been identified to be the Adapted Gooding method, the BVP optimization and IVP optimization. The performance of these methods is evaluated for different data distribution characteristics and orbit regimes, first without incorporating perturbations in the tracklet correlation methods.

In the second part, the tracklet correlation methods are modified to improve the performance. A major gap in the state of the art has been successfully addressed, namely to incorporate perturbations in the tracklet correlation methods. Results have shown a significant increase in association accuracy. Specifically, tracklet pairs with arbitrary time gap can be associated with the same true positive rate. Moreover, tracklet pairs from different orbit regimes can be associated with a similar true positive rate if the most important perturbations are incorporated.

Finally, the BVP and IVP optimization are found to be robust to noise, while the Adapted Gooding method severely suffers from the perfect measurement assumption. The performance of the latter has been improved by improving the accuracy of the angles through a Least Squares fit. Although the BVP and IVP optimization are robust to noise, the performance is limited by the accuracy of the angle rates, according to the Chi-squared distribution. A novel tracklet correlation method called the BVP-DC2-DC3 is developed to overcome this limitation, achieving an excellent TPR of 100% and a TNR of 99% for the analyzed objects in GEO for tracklets with a measurement noise of one arcsecond. This accuracy is superior to literature. Moreover, the computational efficiency is superior or comparable to literature. Additionally, the BVP-DC2-DC3 has a high robustness, because for the analyzed GEO tracklets with a measurement noise of five arcseconds, a TPR of 100% and a TNR of 95% can still be achieved.