Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in totally different performances in many practical applications. In this paper, we propose a total Bregman divergence-based matrix information geometry (TBD-MIG) detector and apply it to detect targets emerged into nonhomogeneous clutter. In particular, each sample data is assumed to be modeled as a Hermitian positive-definite (HPD) matrix and the clutter covariance matrix is estimated by the TBD mean of a set of secondary HPD matrices. We then reformulate the problem of signal detection as discriminating two points on the HPD matrix manifold. Three TBD-MIG detectors, referred to as the total square loss, the total log-determinant and the total von Neumann MIG detectors, are proposed, and they can achieve great performances due to their power of discrimination and robustness to interferences. Simulations show the advantage of the proposed TBD-MIG detectors in comparison with the geometric detector using an affine invariant Riemannian metric as well as the adaptive matched filter in nonhomogeneous clutter.

中文翻译：

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通过基于总 Bregman 散度的矩阵信息几何检测器在非均匀杂波内进行目标检测

信息发散通常用于衡量统计流形上两个元素的不同。具有不同散度的可微流形可能具有不同的几何特性，这在许多实际应用中会导致完全不同的性能。在本文中，我们提出了一种基于总 Bregman 散度的矩阵信息几何 (TBD-MIG) 检测器，并将其应用于检测出现在非均匀杂波中的目标。特别是，假设每个样本数据都被建模为 Hermitian 正定 (HPD) 矩阵，并且杂波协方差矩阵由一组二级 HPD 矩阵的 TBD 均值估计。然后，我们将信号检测问题重新表述为区分 HPD 矩阵流形上的两个点。三个TBD-MIG检测器，简称总平方损失，提出了总对数行列式和总冯诺依曼 MIG 检测器，由于它们的鉴别能力和对干扰的鲁棒性，它们可以获得很好的性能。仿真显示了所提出的 TBD-MIG 检测器与使用仿射不变黎曼度量以及非齐次杂波中的自适应匹配滤波器的几何检测器相比的优势。