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 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, 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.

概率假设密度（PHD）过滤器用于基于传感器测量的多目标跟踪，它依赖于点过程的一阶矩或强度函数的传播。该算法假定目标独立运行，由于潜在的目标交互作用，该假设在实践中可能不成立。在本文中，我们基于确定点过程构造了二阶PHD滤波器，该模型能够对目标之间的排斥进行建模。这样的过程的特征在于它们的一阶和二阶矩，除了一阶目标计数估计值之外，它还允许算法传播方差和协方差信息。我们的方法依赖于后矩公式来估计细化操作和与Poisson点过程的叠加之后的一般隐蔽点过程，以及确定点过程设置中的合适近似公式。行列式点过程的排斥特性适用于不同测量域之间负相关的建模。提供了具有相关估计的蒙特卡洛模拟。