In this paper, we propose a class of median-based matrix information geometry (MIG) detectors with a manifold filter and apply them to signal detection in nonhomogeneous environments. As customary, the sample data is assumed to be modeled as Hermitian positive-definite (HPD) matrices, and the geometric median of a set of HPD matrices is interpreted as an estimate of the clutter covariance matrix (CCM). Then, the problem of signal detection can be reformulated as discriminating two points on the manifold of HPD matrices, one of which is the HPD matrix in the cell under test while the other represents the CCM. By manifold filter, we map a set of HPD matrices to another set of HPD matrices by weighting them, that consequently improves the discriminative power by reducing the intra-class distances while increasing the inter-class distances. Three MIG median detectors are designed by resorting to three geometric measures on the matrix manifold, and the corresponding geometric medians are shown to be robust to outliers. Numerical simulations show the advantage of the proposed MIG median detectors in comparison with their state-of-the-art counterparts as well as the conventional detectors in nonhomogeneous environments.

在本文中，我们提出了一类具有流形滤波器的基于中值的矩阵信息几何 (MIG) 检测器，并将它们应用于非均匀环境中的信号检测。按照惯例，假设样本数据被建模为 Hermitian 正定 (HPD) 矩阵，并且一组 HPD 矩阵的几何中值被解释为杂波协方差矩阵 (CCM) 的估计值。然后，信号检测的问题可以重新表述为区分 HPD 矩阵流形上的两个点，其中一个是被测单元中的 HPD 矩阵，而另一个代表 CCM。通过流形过滤器，我们通过加权将一组 HPD 矩阵映射到另一组 HPD 矩阵，从而通过减少类内距离同时增加类间距离来提高判别能力。三个 MIG 中值检测器是通过在矩阵流形上采用三种几何度量来设计的，并且相应的几何中值被证明对异常值具有鲁棒性。数值模拟显示了所提出的 MIG 中值探测器与其最先进的同类探测器以及非均匀环境中的传统探测器相比的优势。