矩阵信息几何中值检测器

doi:10.12263/DZXB.20200684

摘要/Abstract

摘要：

本文以矩阵信息几何理论为基础，提出一种新的信号检测器框架，该检测器将样本数据建模为正定矩阵，利用参考单元对应正定矩阵的几何中值来估计杂波协方差矩阵，从而将信号检测问题转化为度量矩阵流形上两点间的差异性大小，通过比较流形上两点间的差异值与阈值大小来实现信号检测.此外，深入分析了流形上不同几何度量所反映出的几何结构差异，并依据各向异性定义了几何度量的区分能力描述子.由于几何度量的区分性较好，并且几何中值对干扰具有较好的鲁棒性，因此，矩阵信息几何中值检测器在小样本、非均匀环境下具有较好的性能.实验结果表明，与自适应匹配滤波相比，所提出的信号检测器在小样本、非均匀环境下具有明显的性能优势.

关键词: 矩阵信息几何, 信号检测, 矩阵流形, 几何中值, 小样本, 非均匀环境

Abstract:

This paper systematically summarizes the previous work, and proposes a new signal detector in the framework of matrix information geometry theory. The sample data is modeled as a hermitian positive definite(HPD) matrix, and a set of secondary HPD matrices is used for estimating the clutter covariance matrix by the geometric median. Then, the problem of signal detection is treated as discriminating two points on the HPD manifold, and signal detection is realized by comparing the difference between the two points with a given threshold. In addition, we analyze the differences in geometric structure that is reflected by different geometric measures on manifolds. The discrimination ability descriptor of a geometric measure is defined based on the anisotropy. Since the geometric measures are more discriminative and their corresponding medians are robust to the interference, matrix information geometric median detectors can exhibit well performances. Experimental results confirm the advantages of the proposed geometric median detectors in comparison with the adaptive matched filtering in nonhomogeneous environments with limited sample data.

Key words: matrix information geometry, signal detection, matrix manifold, geometric median, small sample, nonhomogeneous environment

中图分类号:

TN911.23

华小强, 程永强, 王宏强, 等. 矩阵信息几何中值检测器[J]. 电子学报, 2022, 50(2): 284-294.

Xiao-qiang HUA, Yong-qiang CHENG, Hong-qiang WANG, et al. Matrix Information Geometric Median Detectors[J]. Acta Electronica Sinica, 2022, 50(2): 284-294.

图/表 7

图1 矩阵信息几何检测器的基本原理

图2 不同几何度量的等位球

图3 不同干扰数对几何中值的影响

图4 不同样本数对几何中值的影响

图5 不同几何度量的区分能力

图6 高斯与非高斯杂波下不同信杂比下的检测性能

图7 不同特征和矩阵结构下KLD的检测性能

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