Unified cardinalized probability hypothesis density filters for extended targets and unresolved targets

The unified cardinalized probability hypothesis density (CPHD) filters for extended targets and unresolved targets are proposed. The theoretically rigorous measurement-update equations for the proposed filters are derived according to the theory of random finite set (RFS) and finite-set statistics (FISST). By assuming that the predicted distributions of the extended targets and unresolved targets and the distribution of the clutter are Poisson, the exact extended-target and unresolved-target CPHD correctors reduce to the exact extended-target and unresolved-target PHD correctors, respectively. Since the exact CPHD and PHD corrector equations involve with a number of operations that grow exponentially with the number of measurements, the computationally tractable approximations for them are presented, which can be used when the extended targets and the unresolved targets are not too close together and the clutter density is not too large. Monte Carlo simulation results show that the approximate extended-target and unresolved-target CPHD filters, respectively, outperform the approximate extended-target and unresolved-target PHD filters a lot in estimating the target number and states, although the computational requirement of the CPHD filters is more expensive than that of the PHD filters.

► Unified CPHD filters for extended and unresolved targets are derived. ► The PHD filters for extended and unresolved targets are derived from the proposed CPHD filters. ► The computationally tractable approximations for the CPHD filters are presented. ► Monte Carlo simulation results about the approximated CPHD filters are shown.