  Compared to the probability hypothesis density (PHD) and cardinalized PHD
(CPHD) filters, the trajectory PHD (TPHD) and trajectory CPHD (TCPHD) filters
are for sets of trajectories, and thus are able to produce trajectory estimates
with better estimation performance. In this paper, we develop the TPHD and
TCPHD filters which can adaptively learn the history of the unknown target
detection probability, and therefore they can perform more robustly in
scenarios where targets are with unknown and time-varying detection
probabilities. These filters are referred to as the unknown TPHD (U-TPHD) and
unknown TCPHD (U-TCPHD) filters.By minimizing the Kullback-Leibler divergence
(KLD), the U-TPHD and U-TCPHD filters can obtain, respectively, the best
Poisson and independent identically distributed (IID) density approximations
over the augmented sets of trajectories. For computational efficiency, we also
propose the U-TPHD and U-TCPHD filters that only consider the unknown detection
profile at the current time. Specifically, the Beta-Gaussian mixture method is
adopted for the implementation of proposed filters, which are referred to as
the BG-U-TPHD and BG-U-TCPHD filters. The L-scan approximations of these
filters with much lower computational burden are also presented. Finally,
various simulation results demonstrate that the BG-U-TPHD and BG-U-TCPHD
filters can achieve robust tracking performance to adapt to unknown detection
profile. Besides, it also shows that usually a small value of the L-scan
approximation can achieve almost full efficiency of both filters but with a
much lower computational costs.
