摘要翻译：
我们在汽车碰撞避免的背景下重新讨论碰撞概率的计算（潜在碰撞的估计在其他背景下也被称为冲突检测）。在回顾了现有的碰撞概率的定义和计算方法后，我们认为“在接下来的三秒钟内碰撞的概率是多少？”可以根据碰撞概率率来回答。利用向量随机过程水平交叉的结果，导出了碰撞概率率分布上界的一般表达式。该表达式适用于包括过程噪声的任意预测模型。我们在几个例子中证明了通过大规模Monte-Carlo模拟得到的分布服从该界，并且在许多情况下近似饱和该界。我们导出了一个可以在嵌入式平台上计算的碰撞概率分布的近似值。然后通过一维数值积分，得到了一个碰撞概率的上界。该方法的一个直接应用适用于扩展物体与第二个点状物体的碰撞。利用第二个物体边界的突出点来抽象第二个物体，我们提出了该方法在任意方向的两个扩展物体上的应用。最后，将碰撞概率率的分布确定为碰撞时间的分布。
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英文标题：
《A New Approach To Estimate The Collision Probability For Automotive
  Applications》
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作者：
Richard Altendorfer and Christoph Wilkmann
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最新提交年份：
2021
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Systems and Control        系统与控制
分类描述：This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类：Computer Science        计算机科学
二级分类：Systems and Control        系统与控制
分类描述：cs.SY is an alias for eess.SY. This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
cs.sy是eess.sy的别名。本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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英文摘要：
  We revisit the computation of probability of collision in the context of automotive collision avoidance (the estimation of a potential collision is also referred to as conflict detection in other contexts). After reviewing existing approaches to the definition and computation of a collision probability we argue that the question "What is the probability of collision within the next three seconds?" can be answered on the basis of a collision probability rate.   Using results on level crossings for vector stochastic processes we derive a general expression for the upper bound of the distribution of the collision probability rate. This expression is valid for arbitrary prediction models including process noise.   We demonstrate in several examples that distributions obtained by large-scale Monte-Carlo simulations obey this bound and in many cases approximately saturate the bound. We derive an approximation for the distribution of the collision probability rate that can be computed on an embedded platform. An upper bound of the probability of collision is then obtained by one-dimensional numerical integration over the time period of interest.   A straightforward application of this method applies to the collision of an extended object with a second point-like object. Using an abstraction of the second object by salient points of its boundary we propose an application of this method to two extended objects with arbitrary orientation.   Finally, the distribution of the collision probability rate is identified as the distribution of the time-to-collision.
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PDF链接：
https://arxiv.org/pdf/1711.0706