α噪声,特征指数,叠加性质,几何功率," /> α噪声,特征指数,叠加性质,几何功率,"/> Estimation method based on geometric power for characteristic exponent of <i>α</i> noise

Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (10): 3007-3013.doi: 10.13229/j.cnki.jdxbgxb.20211329

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Estimation method based on geometric power for characteristic exponent of α noise

Yi-ran SHI(),Jin-wei QI,Si-ning QU,Xiang-yang PAN,Lin FU   

  1. College of Communication Engineering，Jilin University，Changchun 130022，China
  • Received:2021-12-06 Online:2023-10-01 Published:2023-12-13

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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

CLC Number: 

  • TN911.7

Fig.1

Estimation result of α"

Fig.2

Estimation RMSE curve of α"

Fig.3

Estimation result of αunder different γ"

Fig.4

Estimation RMSE curve of α under different γ"

Fig.5

Estimation result of α under different samplingtimes"

Fig.6

Estimation RMSE curve of α under differentsampling times"

Fig.7

Estimation result of αunder different total datalength"

Fig.8

Estimation RMSE curve of α under differenttotal data length"

Fig.9

Estimation result of αunder different algorithm"

Fig.10

Estimation RMSE curve of α under different algorithm"

Table 1

Calculation time of different algorithms"

估计方法α=0.2α=0.9α=1.2α=1.9
几何功率法0.000 340.000 320.000 390.000 35
组合分布法（p=0.1）0.000 890.000 870.000 950.000 82
负阶矩法0.123 10.124 30.125 50.123 7

Table 2

Validation of measured data"

估计方法估计值偏差
几何功率法1.540.02
组合分布法（p=0.8）1.610.05
组合分布法（p=1.5）1.810.25
负阶矩法1.640.08
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