This paper deals with adaptive radar detection problems where several alternative hypotheses may be plausible. This kind of problems naturally extends the conventional binary tests that often occur in radar (as well as in other application fields) by including a further uncertainty degree related to the number of unknown signal parameters (model order). Such a modification consequently leads to multiple composite alternative hypotheses. In the companion paper (Addabbo et al., 2021), we have defined a new design framework which allows us to come up with decision schemes for these hypothesis testing problems by exploiting the Kullback-Leibler Information Criterion and without resorting to heuristic design criteria. The architectures devised within the proposed framework consist of the sum between the compressed log-likelihood ratio and a penalty term inherited from model order selection rules. Such a penalty term accounts for the number of unknown parameters to overcome the limitation of the generalized likelihood ratio test in the presence of nested hypotheses. In the present paper, we apply the new design framework to different detection problems related to both real aperture and (polarimetric) synthetic aperture radar. The analysis is carried out in comparison with suitable competitors (possibly based upon heuristic design criteria) and shows that the architectures devised within the proposed theoretically-founded design framework represent an effective means to deal with detection problems where the uncertainty on some parameters leads to multiple alternative hypotheses.

中文翻译：

---

使用 Kullback-Leibler 信息准则在存在多个替代假设的情况下进行自适应雷达检测 - 第二部分：应用


本文讨论自适应雷达检测问题，其中几种替代假设可能是合理的。此类问题自然地扩展了雷达（以及其他应用领域）中经常发生的传统二进制测试，包括与未知信号参数（模型阶数）数量相关的进一步不确定度。这样的修改因此导致多个复合替代假设。在配套论文（Addabbo 等人，2021）中，我们定义了一个新的设计框架，该框架使我们能够通过利用 Kullback-Leibler 信息准则而无需诉诸启发式设计标准，为这些假设检验问题提出决策方案。在所提出的框架内设计的架构由压缩对数似然比与从模型顺序选择规则继承的惩罚项之间的总和组成。这样的惩罚项考虑了未知参数的数量，以克服存在嵌套假设时广义似然比检验的限制。在本文中，我们将新的设计框架应用于与真实孔径雷达和（偏振）合成孔径雷达相关的不同检测问题。该分析是与合适的竞争对手进行比较（可能基于启发式设计标准）进行的，并表明在所提出的理论基础设计框架内设计的架构代表了处理检测问题的有效手段，其中某些参数的不确定性导致多个另类假设。