Adaptive Matrix Information Geometry Detector With Local Metric Tensor

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.