Modeling birth for the labeled multi-Bernoulli filter using a boundary value approach

A challenging task in space situational awareness (SSA) is to track multiple space objects for the maintenance of a space object catalog (SOC). The Bayesian multitarget tracking filter addresses this issue by associating measurements to initially known or newly detected tracks and simultaneously estimating the time-varying number of targets and their orbital states. Recently, methods based on the random finite set (RFS) [1] approach have provided a general systematic treatment of multitarget systems by modeling the multitarget states as finite set valued random variables, which allow the derivation of multitarget filters based on Bayes’s theorem. The newly developed labeled RFS filters, including the labeled multi-Bernoulli (LMB) filter [2] and the δ-generalized LMB (δ-GLMB) filter [3], are able to maintain target identity using a labeled RFS. The LMB filter used in this study is an efficient approximation of the δ-GLMB filter, which has been used in several SSA applications [4–6].