Due to their shorter operating range and large bandwidth, automotive radars can resolve many reflections from their targets of interest, mainly vehicles. This calls for the use of extended-target models in place of simpler and more widely-adopted point-like target models. However, despite some preliminary work, the fundamental connection between the radar’s accuracy as a function of the target vehicle state (range, orientation, shape) and radar properties remains largely unknown for extended targets. In this work, we first devise a mathematically tractable analytical model for a vehicle with arbitrary shape, modeled as an extended target parameterized by the center position, the orientation (heading) and the perimeter contour. We show that the derived expressions of the backscatter signal are tractable and correctly capture the effects of the extended-vehicle shape. Analytical derivations of the exact and approximate hybrid Cramér-Rao bounds for the position, orientation and contour are provided, which reveal connections with the case of point-like target and uncover the main dependencies with the received energy, bandwidth, and array size. The theoretical investigation is performed on the two different cases of known and unknown vehicle shape. Insightful simulation results are finally presented to validate the theoretical findings, including an analysis of the diversity effect of multiple radars sensing the extended target.

中文翻译：

---

具有已知和未知形状的扩展车辆目标的雷达的 Cramér-Rao 边界分析

由于其更短的工作范围和大带宽，汽车雷达可以解决来自其感兴趣目标（主要是车辆）的许多反射。这需要使用扩展目标模型来代替更简单和更广泛采用的点状目标模型。然而，尽管进行了一些初步工作，但作为目标车辆状态（范围、方向、形状）的函数的雷达精度与雷达特性之间的基本联系对于扩展目标仍然很大程度上未知。在这项工作中，我们首先为具有任意形状的车辆设计了一个数学上易于处理的分析模型，该模型被建模为由中心位置、方向（航向）和周边轮廓参数化的扩展目标。我们表明，反向散射信号的派生表达式是易于处理的，并且正确地捕捉了扩展车辆形状的影响。提供了位置、方向和轮廓的精确和近似混合 Cramér-Rao 边界的分析推导，揭示了与点状目标情况的联系，并揭示了与接收能量、带宽和阵列大小的主要依赖关系。对已知和未知车辆形状的两种不同情况进行了理论研究。最后给出了富有洞察力的仿真结果来验证理论发现，包括分析多个雷达感知扩展目标的分集效应。提供了方向和轮廓，揭示了与点状目标情况的联系，并揭示了与接收能量、带宽和阵列大小的主要依赖关系。对已知和未知车辆形状的两种不同情况进行了理论研究。最后给出了富有洞察力的仿真结果来验证理论发现，包括分析多个雷达感知扩展目标的分集效应。提供了方向和轮廓，揭示了与点状目标情况的联系，并揭示了与接收能量、带宽和阵列大小的主要依赖关系。对已知和未知车辆形状的两种不同情况进行了理论研究。最后给出了富有洞察力的仿真结果来验证理论发现，包括分析多个雷达感知扩展目标的分集效应。