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 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.