This paper presents a novel approach to multitarget multisensor tracking, based on the combination of a probability hypothesis density (PHD) smoother and hard multisensor multiscan data association (MMDA) used in a feedback connection. The PHD smoother allows to initiate target tracks without resorting to complicated measurement-to-measurement association procedures while the feedback from the hard MMDA, besides providing track labeling, makes the PHD smoother, and hence the overall tracker, more robust to missed detections and false alarms. An application of the proposed tracker to passive multistatic radar tracking is worked out in order to demonstrate its effectiveness in critical situations where the lack of single-sensor observability prevents the use of traditional track initiation methods. As a further contribution, an extension to the multisensor case of the multicommodity approach to multiscan data association, originally presented for the single-sensor case, is provided.