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For Geosynchronous Earth Orbit (GEO) objects, space-based optical surveillance has advantages over regional ground surveillance in terms of both the timeliness and space coverage. However, space-based optical surveillance may only collect sparse and short orbit arcs, and thus make the autonomous arc association and orbit determination a challenge for new GEO objects without a priori orbit information. In this paper, a three-step approach tackling these two critical problems is proposed. First, under the near-circular orbit assumption, a multi-point optimal initial orbit determination (IOD) method is developed to improve the IOD convergence rate and the accuracy of the IOD solution with angles-only observations over a short arc. Second, the Lambert equation is applied to associate two independent short arcs in an attempt to improve accuracy of the single-arc IOD semi-major axis (SMA) with the use of virtual ranges between the optical sensor and GEO object. The key idea in the second step is to generate accurate ranges at observation epochs, which, along with the real angle data, are then used to achieve much improved SMA accuracy. The third step is basically the repeated application of the second step to three or more arcs. The high success rate of arc associations and accurate orbit determination using the proposed approach are demonstrated with simulated space-based angle data over short arcs, each being only 3 min. The results show that the proposed approach is able to determine the orbit of a new GEO at a three-dimensional accuracy of about 15 km from about 10 arcs, each having a length of about 3 min, thus achieving reliable cataloguing of uncatalogued GEO objects. The IOD and two-arc association methods are also tested with the real ground-based observations for both GEO and LEO objects of near-circular orbits, further validating the effectiveness of the proposed methods.

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.