论文标题
适用于PMBM密度的轨迹集的时空约束
Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities
论文作者
论文摘要
在本文中，我们介绍了轨迹的时空约束，即限制轨迹必须在某个时间点（时间约束）处于状态空间的某些部分（空间约束）。关于轨迹的时空矛盾可用于回答一系列重要问题，例如，“在时间t区域t地区的人在哪里？”。我们讨论如何将多个约束组合到约束集合中，然后我们将约束集应用于轨迹密度集，特别是泊松多伯努利混合物（PMBM）密度。对于泊松目标出生，确切的后部密度为两个点目标和扩展目标的PMBM。在本文中，我们表明，如果不受约束的轨迹密度为PMBM，则约束密度也为PMBM。受限轨迹密度的示例激励并说明了关键结果。
In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., "where did the person that were in area A at time t, go afterwards?". We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results.
