This article develops models and algorithms for continuous-discrete multiple target filtering, in which the multi-target system is modelled in continuous time and measurements are available at discrete time steps. In order to do so, this paper first proposes a statistical model for multi-target appearance, dynamics and disappearance in continuous time, based on continuous time birth/death processes and stochastic differential equations. The multitarget state is observed at known time instants based on the standard measurement model, and the objective is to compute the distribution of the multi-target state at these time steps. For the Wiener velocity model, we derive a closed-form formula to obtain the best Gaussian Poisson point process fit to the birth density based on Kullback-Leibler minimisation. The resulting discretised model gives rise to the continuous-discrete Gaussian Poisson multi-Bernoulli mixture (PMBM) filter, the continuous-discrete Gaussian mixture probability hypothesis density (PHD) filter and the continuous-discrete Gaussian mixture cardinality PHD (CPHD) filter. The proposed filters are specially useful for multi-target estimation when the time interval between measurements is non-uniform.

中文翻译：

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连续离散多目标滤波：PMBM、PHD 和 CPHD 滤波器实现

本文开发了用于连续离散多目标滤波的模型和算法，其中多目标系统在连续时间建模，测量值在离散时间步长可用。为此，本文首先基于连续时间生/死过程和随机微分方程，提出了一个连续时间多目标出现、动态和消失的统计模型。基于标准测量模型在已知时刻观察多目标状态，目的是计算这些时间步长的多目标状态分布。对于 Wiener 速度模型，我们推导出一个封闭式公式，以基于 Kullback-Leibler 最小化获得适合出生密度的最佳高斯泊松点过程。由此产生的离散模型产生了连续离散高斯泊松多伯努利混合 (PMBM) 滤波器、连续离散高斯混合概率假设密度 (PHD) 滤波器和连续离散高斯混合基数 PHD (CPHD) 滤波器。当测量之间的时间间隔不均匀时，所提出的滤波器对于多目标估计特别有用。