This paper is the fourth in a series aimed at weakening the independence assumptions that are typically presumed in multitarget tracking. Specifically, we assume that, in a multisensory scenario, the sensors are not necessarily independent but, rather, have known correlations (i.e., their joint single-target joint likelihood function is known). From this, we construct a multitarget measurement model for sensors with known correlations. From this model we derive, as an illustrative example, the filtering equations for a probability hypothesis density (PHD) filter for sensors with known correlations. We emphasize the two-sensor case of this filter, for which the measurement-update equations involve a summation over all measurement-to-measurement associations between the two sensors.