  The Probability Hypothesis Density (PHD) filter, which is used for
multi-target tracking based on sensor measurements, relies on the propagation
of the first-order moment, or intensity function, of a point process. This
algorithm assumes that targets behave independently, an hypothesis which may
not hold in practice due to potential target interactions. In this paper, we
construct a second-order PHD filter based on Determinantal Point Processes
(DPPs) which are able to model repulsion between targets. Such processes are
characterized by their first and second-order moments, which allows the
algorithm to propagate variance and covariance information in addition to
first-order target count estimates. Our approach relies on posterior moment
formulas for the estimation of a general hidden point process after a thinning
operation and a superposition with a Poisson Point Process (PPP), and on
suitable approximation formulas in the determinantal point process setting. The
repulsive properties of determinantal point processes apply to the modeling of
negative correlation between distinct measurement domains. Monte Carlo
simulations with correlation estimates are provided.
