基于几何功率的α噪声的特征指数估计方法

doi:10.13229/j.cnki.jdxbgxb.20211329

摘要/Abstract

摘要：

$α$ 噪声背景下的信号处理问题是该领域的热点问题，但在实际工况中极难直接获得 $α$ 噪声的特征指数的相关信息，这使得分数低阶统计算法的应用变得尤为困难。针对上述问题，本文提出了一种基于 $α$ 稳定分布叠加性质以及几何功率的特征指数估计方法。首先利用叠加性质确定了多个独立同分布的 $α$ 稳定分布变量与其和分布变量的关系，然后利用其原变量以及与变量几何功率间的特点实现对特征指数的估计。实验结果表明，该算法不需要获取特征指数的范围，在0~2范围内均可对其进行准确估计，均方根误差最大约为0.1，在对海杂波数据进行估计时偏差仅为0.02，可以为 $α$ 噪声下的信号处理问题提供先验信息。

关键词: 信号处理, $α$ 噪声')"> $α$ 噪声, 特征指数, 叠加性质, 几何功率

Abstract:

Signal processing in the background of α noise is a hot issue in this field， but it is very difficult to directly obtain the relevant information of characteristic exponent of α noise in actual working conditions， which makes the application of fractional low-order statistical algorithm become particularly difficult. An estimation method based on the plus property of α-stable distribution and geometric power was proposed regarding the issue above. Firstly， the plus property is used to determine the relationship between several independent variables with the same α-stable distribution and the distribution of their sum. Then the characteristic exponent is estimated by using the characteristics the geometric power between the original variables and their sum-distribution variable. The experimental results show that this algorithm does not need to obtain the range of the characteristic exponent in advance. And it can be accurately estimated in the range of 0—2， the maximum root-mean-square error of the estimation result is only about 0.1 and the deviation is only 0.02 when it is estimated the sea clutter data， which can provide a priori information under the signal processing problem based on α noise.

Key words: signal processing, α noise, characteristic exponent, plus property, geometric power

中图分类号:

TN911.7

石屹然,齐金伟,曲思凝,潘向阳,符麟. 基于几何功率的α噪声的特征指数估计方法[J]. 吉林大学学报(工学版), 2023, 53(10): 3007-3013.

Yi-ran SHI,Jin-wei QI,Si-ning QU,Xiang-yang PAN,Lin FU. Estimation method based on geometric power for characteristic exponent of α noise[J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(10): 3007-3013.

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估计方法	α=0.2	α=0.9	α=1.2	α=1.9
几何功率法	0.000 34	0.000 32	0.000 39	0.000 35
组合分布法（p=0.1）	0.000 89	0.000 87	0.000 95	0.000 82
负阶矩法	0.123 1	0.124 3	0.125 5	0.123 7

估计方法	估计值	偏差
几何功率法	1.54	0.02
组合分布法（p=0.8）	1.61	0.05
组合分布法（p=1.5）	1.81	0.25
负阶矩法	1.64	0.08