Abstract We exploit persymmetry to study the adaptive detection problem with multiple observations in partially homogeneous environments where noise shares the same covariance matrix up to different power levels between the test and training data. A persymmetric subspace model is designed for taking into account steering vector mismatches. Based on the persymmetric subspace model, we propose adaptive detectors in partially homogeneous environments, according to the criteria of two-step generalized likelihood ratio test (GLRT), Wald test, and Rao test. It is found that the proposed GLRT and Wald test coincide, while the Rao test does not exist. The proposed detector is proved to exhibit a constant false alarm rate property against both the covariance matrix structure and the scaling factor. Numerical examples show that the proposed detector, compared to its counterparts, is more robust to steering vector mismatches.

中文翻译：

---

对转向矢量失配具有改进鲁棒性的过对称自适应检测

摘要 我们利用对称性来研究在部分同质环境中具有多个观察的自适应检测问题，其中噪声在测试和训练数据之间的不同功率水平上共享相同的协方差矩阵。设计过对称子空间模型以考虑转向矢量失配。基于过对称子空间模型，我们根据两步广义似然比检验 (GLRT)、Wald 检验和 Rao 检验的标准，在部分均匀环境中提出了自适应检测器。发现提出的 GLRT 和 Wald 检验一致，而 Rao 检验不存在。所提出的检测器被证明对协方差矩阵结构和缩放因子都表现出恒定的误报率特性。数值例子表明，所提出的检测器，