A Data-Driven Probability Hypothesis Density Filter with Parameter Flow Implementation for Space Situational Awareness

Abstract The Finite Sets Statistics-based Probability Hypothesis Density filter offers a description of a group of known or unknown targets as a single random entity with a Bayesian filtering framework. The Probability Hypothesis Density filter has often been employed in the Space Situational Awareness detection and tracking of space objects. One of its challenges is the determination of key probabilistic parameters, such as birth rates and birth intensities, for the detection of new space objects. Additionally, the challenge of incorporating nonlinear measurements requires the choice of simplifying assumptions on the prior, therefore introducing errors to the posterior. In this paper, a data-driven parameter flow version of the Probability Hypothesis Density filter is introduced, which performs the measurement update step using both birth and persistent likelihood densities while alleviating errors introduced to the posterior intensity. Therefore, preventing a shift of the birth intensity from the prediction step. A birth intensity is instantiated by performing a measurement correlation optimization, where the solution and likelihood are used to parametrize the intensity. In a data-driven discrete parameter flow Gaussian Mixture Probability Hypothesis Density filter implementation, the performance of the new birth is shown in a simulated ground-based optical tracking scenario. In optical tracking scenarios, tracklets composed of angles and angle rates are often assumed to be available. A multi-layer Probability Hypothesis Density filter is introduced, which forms tracklets before employing the full orbital data-driven Probability Hypothesis filter and the birth process. A Gaussian Mixture implementation of the multi-layer Probability Hypothesis filter is tested with a dataset for a GPS satellite collected from the Purdue Optical Ground Station.