A PHD filter with negative binomial clutter

The Probability Hypothesis Density (PHD) filter has brought significant advances in multi-object estimation since it not only estimates the spatial distribution of a population of objects but also provides estimates about the actual object number which is unknown in many scenarios. However, strict assumptions have to be made for the framework to be practical, in particular through the choice of the distribution for target and false alarm numbers. The exponential form of the Poisson distribution, for example, offers great simplicity in the derivation of the filter, but in many applications, this assumption is very restrictive, e.g. when there is a lot of variability in the number of measurements. This paper introduces a variation of the original PHD filter which assumes a negative binomial distribution for the false alarm number. It will be demonstrated that the altered formulation of the filter simply leads to an additional factor in the update equation and that the original PHD filter is a special case of the proposed method. A Gaussian Mixture (GM) implementation of both filters is used to test and compare their performance on simulated data.