Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Abstract

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. This paper demonstrates the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.