Reduced Palm Intensity for Track Extraction

The pair correlation function is introduced to target tracking filters that use a finite point process target model as a means to investigate interactions in the Bayes posterior target process. It is shown that the Bayes posterior target point process of the probability hypothesis density (PHD) filter-before using the Poisson point process approximation to close the recursion-is a spatially correlated process that shows repulsive behavior. The reduced Palm target point process is introduced to define the conditional target point process given the state of one or more known targets. Using the intensity function of the reduced Palm process, or the Papangelou conditional intensity function, an approximate two-stage pseudo maximum a posteriori track extractor is developed. The proposed track extractor is formulated for the PHD filter and implemented in a numerical study that involves tracking two close-by targets. Numerical results demonstrate improvement in the mean optimal subpattern assignment statistic for the proposed track extractor in comparison to the Gaussian mixture PHD filter's state extractor.