CPHD filtering with unknown probability of detection

Abstract

The conventional PHD and CPHD filters presume that the probability pD(x) that a measurement will be collected from a target with state-vector x (the state-dependent probability of detection) is known a priori. However, in many applications this presumption is false. A few methods have been devised for estimating the probability of detection, but they typically presume that pD(x) is constant in both time and the region of interest. This paper introduces CPHD/PHD filters that are capable of multitarget track-before-detect operation even when probability of detection is not known and, moreover, when it is not necessarily constant, either temporally or spatially. Furthermore, these filters are potentially computationally tractable. We begin by deriving CPHD/PHD filter equations for the case when probability of detection is unknown but the clutter model is known a priori. Then, building on the results of a companion paper, we note that CPHD/PHD filters can be derived for the case when neither probability of detection or the background clutter are known.