Linear-complexity CPHD filters

The probability hypothesis density (PHD) filter and cardinalized probability hypothesis density (CPHD) filter are principled approximations of the general multitarget Bayes recursive filter. If n is the current number of tracks and m the current number of measurements, then the former has computational complexity O(mn) and the latter O(m³ n). Although the CPHD filter has better target detection and tracking performance than the PHD filter, its cubic complexity in m will limit its practicality in many applications. The primary purpose of this paper is to derive a CPHD filter that, because of a simplified clutter model, has computational complexity O(mn). I also show how to extend this new CPHD filter to the multisensor case.