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Compared to the probability hypothesis density (PHD) and cardinalized PHD(CPHD) filters, the trajectory PHD (TPHD) and trajectory CPHD (TCPHD) filtersare for sets of trajectories, and thus are able to produce trajectory estimateswith better estimation performance. In this paper, we develop the TPHD andTCPHD filters which can adaptively learn the history of the unknown targetdetection probability, and therefore they can perform more robustly inscenarios where targets are with unknown and time-varying detectionprobabilities. These filters are referred to as the unknown TPHD (U-TPHD) andunknown TCPHD (U-TCPHD) filters.By minimizing the Kullback-Leibler divergence(KLD), the U-TPHD and U-TCPHD filters can obtain, respectively, the bestPoisson and independent identically distributed (IID) density approximationsover the augmented sets of trajectories. For computational efficiency, we alsopropose the U-TPHD and U-TCPHD filters that only consider the unknown detectionprofile at the current time. Specifically, the Beta-Gaussian mixture method isadopted for the implementation of proposed filters, which are referred to asthe BG-U-TPHD and BG-U-TCPHD filters. The L-scan approximations of thesefilters with much lower computational burden are also presented. Finally,various simulation results demonstrate that the BG-U-TPHD and BG-U-TCPHDfilters can achieve robust tracking performance to adapt to unknown detectionprofile. Besides, it also shows that usually a small value of the L-scanapproximation can achieve almost full efficiency of both filters but with amuch lower computational costs.

Trajectory PHD and CPHD Filters with Unknown Detection Profile