Multiple-Object Space Surveillance Tracking Using Finite-Set Statistics

The dynamic tracking of objects is, in general, concerned with state estimation using imperfect data. Multiple object tracking adds the difficulty of encountering unknown associations between the collected data and the objects. State estimation of objects necessitates the prediction of uncertainty through nonlinear (in the general case) dynamical systems and the processing of nonlinear (in the general case) measurement data in order to provide corrections that refine the system uncertainty, where the uncertainty may be non-Gaussian in nature. The sensors, which provide the measurement data, are imperfect with possible misdetections, false alarms, and noise-affected data. The resulting measurements are inherently unassociated upon reception. In this paper, a Bayesian method for tracking an arbitrary, but known, number of objects is developed. The method is based on finite-set statistics coupled with finite mixture model representations of the multiobject probability density function. Instead of relying on first-moment approximations, such as the probability hypothesis density filter, to the full multiobject Bayesian posterior, as is often done for multiobject filtering, the proposed method operates directly on the exact Bayesian posterior. Results are presented for application of the method to the problem of tracking multiple space objects using synthetic line-of-sight data