Applying Lambert problem to association of radar-measured orbit tracks of space objects

Abstract

Thousands of orbit tracks of space objects are collected by a radar each day, and many may be from uncatalogued objects. As such, it is an urgent demand to catalogue the uncatalogued objects, which requires to determine whether two or more un-correlated tracks (UCTs) are from the same object. This paper proposes to apply the Lambert problem to associate two radar-measured orbit tracks of LEO and HEO objects. A novel method of position correction is proposed to correct the secular and short periodic effects caused by the J 2 perturbation, making the Lambert problem applicable to perturbed orbit tracks. After that, an orbit selection method based on the characteristics of residuals solves the multiple-revolution Lambert problem. Extensive experiments with simulated radar measurements of LEO and HEO objects are carried out to assess the performance of the proposed method. It is shown that the semi-major axis can be determined with an error less than 200 m from two tracks separated by 4 days. The true positive (TP) rates for associating two LEO tracks apart by less than 6 days are 94.2%. The TP rate is still at 73.1% even for two tracks apart by 8–9 days. The results demonstrate the strong applicability of the proposed method to associate radar measurements of uncatalogued objects.

Tracklet-to-object Matching for Climbing Starlink Satellites through Recursive Orbit Determination and Prediction

“…The proposed tracklet-to-object matching algorithm for the climbing Starlink satellites is validated using ground-based radar observations. The radar observing accuracy is 50 m for the range and 100 arcseconds for the angles (Liu et al 2021). The NORAD TLEs are used in the initial matching.…”

“…Such an OD/OP process is usually applicable to a space object of ballistic or natural trajectory, as its orbit dynamics characteristics can be precisely modeled. More importantly, its tracklets, short orbit arcs observed by ground-based or space-based sensors, can be easily associated (Cai et al 2018;Lei et al 2018;Liu et al 2021). However, for the maneuvering Starlink satellites, identifying the object attribution of the tracklets is more difficult, since their exact orbit maneuvering operations are unknown to the public.…”

New Space Object Cataloguing through Very-Short-Arc Data Mining

“…Following the initial orbit results outlined in the previous section, we associated two tracklets with varying durations (20-200 s) and separation times (1-9 days), and recorded the corresponding changes in the True Positive (TP) rate. The method utilized to associate two tracklets is based on correction for perturbation, which can be referred to our previous work [17].…”

“…Pastor et al described the process of establishing, maintaining, applying the space object catalogue, and compiled existing methods used in cataloguing, including IOD, data association, orbit determination, and manoeuvre detection [15]. Reihs et al and Liu et al accounted for the perturbation of Earth's oblateness in the association of radar tracklets [16,17]. Zhao et al explored the possibility of perturbation correction on GEO objects and associated optical tracklets [18].…”

“…The new object is then assigned an ID and recorded in the database of space objects with its orbital elements together. However, track association is a challenging task aimed at accurately and comprehensively associating tracklets of the same object, taking into account various factors such as observation errors, separation time between tracklets and the initial orbit accuracy of a single tracklet [16][17][18]. In order to effectively associate the tracklets of a new space object, those with a longer duration and higher accuracy are preferred.…”