Recently, the matrix information geometry (MIG) detectors have been speedily developed and demonstrated satisfactory performance in numerous applications. However, the MIG detector with a specific geometric measure is not always satisfactory under changing environments. This paper proposes the adaptive MIG detector with local metric tensor to match the detection environment for improving the adaptability of MIG detectors. The determination of the adaptive local metric tensor is formulated as an optimization problem based on the Neyman-Pearson criterion. Although this optimization is non-convex and constrained, this paper shows the equivalence between it and its Lagrange dual, and then a two-stage gradient descent method is designed to solve it. Moreover, the performance guarantee of the proposed method is provided, which reveals that it achieves asymptotically optimal detection performance among all MIG detectors. Experimentally, the adaptability and the effectiveness of the adaptive MIG detector are validated in three detection scenarios.

中文翻译：

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具有局部度量张量的自适应矩阵信息几何检测器

最近，矩阵信息几何（MIG）探测器得到了迅速发展，并在众多应用中表现出令人满意的性能。然而，具有特定几何测量的 MIG 探测器在不断变化的环境下并不总是令人满意。本文提出了具有局部度量张量的自适应MIG检测器来匹配检测环境，以提高MIG检测器的适应性。自适应局部度量张量的确定被表述为基于 Neyman-Pearson 准则的优化问题。虽然这种优化是非凸的和有约束的，但本文展示了它与其拉格朗日对偶的等价性，然后设计了一种两阶段梯度下降法来解决它。此外，提供了所提出方法的性能保证，这表明它在所有 MIG 检测器中实现了渐近最优的检测性能。实验上，在三种检测场景下验证了自适应 MIG 检测器的适应性和有效性。