不同信噪比下四种黎曼度量的数学机理和分析
Mathematical Mechanism and Analysis of Four Riemannian Distances with Different Signal-to-Noise Ratios
DOI: 10.12677/PM.2023.134113, PDF,   
作者: 余 婷：长沙理工大学数学与统计学院，湖南 长沙
关键词: 矩阵流形；黎曼度量；散度；Matrix Manifold； Riemann Distance； Divergence
摘要: 针对对称正定矩阵流形，通过理论分析给出了四种不同的黎曼度量与典型性质，并通过仿真实验，分析了正弦信号在叠加不同信噪比的高斯噪声情况下，信号与噪声之间不同度量下的距离变化趋势。实验结果表明，不同的黎曼度量将呈现特有的变化趋势。
Abstract: For symmetric positive definite matrix manifolds, four kinds of Riemannian measurements and typical properties are given by theoretical analysis, and the variation trend of distance between sinusoidal signal and noise under different measurements is analyzed by simulation experiment under the condition of superimposing Gaussian noise with different signal-to-noise ratio. The ex-perimental results show that different Riemannian measures will show unique trends.
文章引用：余婷. 不同信噪比下四种黎曼度量的数学机理和分析[J]. 理论数学, 2023, 13(4): 1073-1078. https://doi.org/10.12677/PM.2023.134113

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