提出基于随机微分方程的连续-离散多目标滤波新方法
Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation
- 用随机微分方程建模目标运动，结合泊松点过程生成目标
- 推导出生目标的均值与协方差闭式解，最小化KL散度优化匹配
- 适用于线性及非线性动态，适合雷达、跟踪等多目标场景
本文提出一种多目标滤波算法，其中目标动态在连续时间中演化，测量在离散时间点获取。目标按泊松点过程（PPP）以给定高斯空间分布出现，运动遵循一般时不变线性随机微分方程，每个目标寿命服从指数分布。针对该模型，推导了新生目标集合的分布，并通过矩匹配最小化Kullback-Leibler散度，获得各目标出生时刻最优拟合均值与协方差的闭式表达。由此提出一种新颖的高斯连续-离散泊松多伯努利混合（PMBM）滤波器，及其基于泊松多伯努利和概率假设密度的近似方法。该框架进一步扩展至非线性随机微分方程驱动的目标动态。
原文摘要 · Abstract (English)
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.
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