Evaluating the time-delay, Doppler effect and carrier phase of a received signal is a challenging estimation problem that was addressed in a large variety of remote sensing applications. This problem becomes more difficult and less understood when the signal is reflected off one or multiple surfaces and interferes with itself at the receiver stage. This phenomenon might deteriorate the overall system performance, as for the multipath effect in Global Navigation Satellite Systems (GNSS), and mitigation strategies must be accounted for. In other applications such as GNSS reflectometry (GNSS-R) it may be interesting to estimate the parameters of the reflected signal to deduce the geometry and the surface characteristics. In either case, a better understanding of this estimation problem is directly brought by the corresponding lower performance bounds. In the high signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér-Rao bound (CRB) provides an accurate lower bound in the mean square error sense. In this article, we derive a new compact CRB expression for the joint time-delay and Doppler estimation in a dual source context, considering a band-limited signal and its specular reflection. These compact CRBs are expressed in terms of the baseband signal samples, making them especially easy to use whatever the baseband signal considered, therefore being valid for a variety of remote sensors. This extends existing results in the single source context and opens the door to a plethora of usages to be discussed in the article. The proposed CRB expressions are validated in two representative navigation and radar examples.

中文翻译：

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双源上下文中的联合时延-多普勒估计性能

评估接收信号的时延，多普勒效应和载波相位是一个具有挑战性的评估问题，已在多种遥感应用中得到解决。当信号从一个或多个表面反射并在接收器阶段干扰其自身时，此问题将变得更加困难且难以理解。对于全球导航卫星系统（GNSS）中的多径效应，此现象可能会降低整个系统的性能，因此必须考虑缓解策略。在诸如GNSS反射法（GNSS-R）之类的其他应用中，估计反射信号的参数以推导几何形状和表面特性可能会很有趣。无论哪种情况，都可以通过相应的较低性能范围直接更好地理解此估计问题。在高斯条件信号模型的高信噪比条件下，克拉姆-劳边界（CRB）提供了均方误差意义上的准确下边界。在本文中，我们考虑了带限信号及其镜面反射，为双源上下文中的联合时延和多普勒估计推导了新的紧凑型CRB表达式。这些紧凑的CRB用基带信号样本表示，因此无论考虑什么基带信号，它们都特别易于使用，因此对于各种远程传感器都是有效的。这将在单个源上下文中扩展现有结果，并为本文中将要讨论的大量用法打开了大门。在两个代表性的导航和雷达示例中验证了所提出的CRB表达式。