轨迹集的时空约束及其在PMBM密度中的应用
Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities
摘要：
在本文中，我们介绍了时空约束的轨迹，即，轨迹必须在某个时间点（时间约束）处于状态空间的某个部分（空间约束）的限制。轨迹上的时空约束可用于回答一系列重要问题，包括，例如，"在时间t，在A区的人，之后去了哪里？".我们讨论了如何将多个约束组合成约束集，然后将约束集应用于轨迹密度集，特别是Poisson Multi-Bernoulli Mixture（PMBM）密度。对于Poisson目标出生，精确的后验密度是点目标和扩展目标的PMBM。在本文中，我们表明，如果无约束的轨迹密度集是PMBM，那么约束密度也是PMBM。约束轨迹密度的例子激励和说明的关键结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
