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

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 200m 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.