  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 with weakly repulsive pair interactions. 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, 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.
