Gaussian mixture implementation of the cardinalized probability hypothesis density filter for superpositional sensors

In the past few years, probability hypothesis density (PHD) and cardinalized probability hypothesis density (CPHD) filters have been successfully applied to multi object localization. However, one mayor limitation of these filters originates from the fact that a measurement vector may only contain information about a single object. Thus, when localizing multiple objects, a finite set of measurement vectors must be provided, which in the best case contains one measurement vector for each object in the surveillance area. Nevertheless, most sensors do not provide multiple measurements. Instead, preprocessing techniques are often used to subdivide the raw measurement signal into multiple signals. Unfortunately, this is often not easy and results in an information loss. Realizing, that there is a need for a CPHD filter variant that does not possess the aforementioned limitation, Mahler provided the theoretical foundation for a CPHD filter variant for superpositional sensors. However, in its current form the CPHD filter for superpositional sensors (SPS-CPHD) is computationally intractable. In this paper, a closed form solution of the SPS-CPHD filter equations using Gaussian mixture models is presented.