This paper proposes multi-target filtering algorithms in which target dynamics are given in continuous time and measurements are obtained at discrete time instants. In particular, targets appear according to a Poisson point process (PPP) in time with a given Gaussian spatial distribution, targets move according to a general time-invariant linear stochastic differential equation, and the life span of each target is modelled with an exponential distribution. For this multi-target dynamic model, we derive the distribution of the set of new born targets and calculate closed-form expressions for the best fitting mean and covariance of each target at its time of birth by minimising the Kullback-Leibler divergence via moment matching. This yields a novel Gaussian continuous-discrete Poisson multi-Bernoulli mixture (PMBM) filter, and its approximations based on Poisson multi-Bernoulli and probability hypothesis density filtering. These continuous-discrete multi-target filters are also extended to target dynamics driven by nonlinear stochastic differential equations.

翻译：本文提出了一种多目标滤波算法，其中目标动态以连续时间描述，而量测在离散时间点获取。具体而言，目标在时间上按照泊松点过程出现，其空间分布为给定高斯分布；目标运动遵循一般时不变线性随机微分方程；每个目标的寿命则用指数分布建模。针对该多目标动态模型，我们推导了新出现目标集合的分布，并通过矩匹配最小化Kullback-Leibler散度，计算了每个目标在出生时刻最佳拟合均值与协方差的闭式表达式。由此得到了一种新型高斯连续-离散泊松多伯努利混合滤波器及其基于泊松多伯努利与概率假设密度滤波的近似形式。这些连续-离散多目标滤波器还可扩展至由非线性随机微分方程驱动的目标动态系统。