Modeling birth in a space-object CPHD filter using the probabilistic admissible region

This paper presents a measurement-based birth model with the Cardinalized Probabilistic Hypothesis Density (CPHD) filter using the probabilistic admissible region (PAR) for tracking space objects. Insufficient information content in a short-duration time series of observations makes track instantiation for space objects difficult. Models based on the admissible region define the initial probability density function for a target's kinematic state using a single tracklet. The measurement-based, partially-uniform birth model in the CPHD assumes independence between the measurement density and the probabilistic representation of the single-target state in unobserved directions. Previous applications of the admissible region for modeling new-target birth define the probability density in the unobserved directions as a function of the realized observation, thereby violating the birth model's assumption. Combining a uniform distribution over the sensor field of view with a PAR-based model ensures independence with realized measurements and enables its use in a partially-uniform birth model. This paper presents the proposed birth model and demonstrates filter performance in a simulation for tracking space objects via optical observations.