﻿ 具有校正项的K分布形状参数的V-估计器
 文章快速检索 高级检索

V-estimator with corrective term for K-distribution shape parameter
LI Dapeng
Abstract:The V-estimator (VE) for K-distribution shape parameter proposed by Oliver in 1993, bears the characteristics of without solving non-linear equations so it has a high estimating efficiency, but the estimating accuracy of it is lower than that of many other moment estimators, sometimes the VE even results in odd value. In order to make the best use of the advantages and bypass the disadvantages, on the basis of derivation and analysis of the VE bias, by means of a set of Monte-Carlo experiments, the V-estimator with corrective term (VCE) was discussed, which overcomes the shortcomings above of the VE. Simulation results show that not only the estimating accuracy of the VCE is significantly superior to the VE, but also, on both of estimating accuracy and efficiency, to the U-estimator considered as the moment estimator with the highest accuracy usually. Especially, experiment results demonstrate that the VCE is better suited to performing in the case of small samples, this feature makes it possible that the VCE is more applicable to the practice.
Key words: K-distribution     shape parameter     V-estimator     corrective term     corrective coefficient

1 对V-估计器的改进 1.1 V-估计器及其偏差分析

1993年,Oliver[11]提出了3种著名的K分布形状参数的矩估计器.其中的V-估计器(VE)形式如下:

1.2 校正项和校正系数

1.3 校正系数的确定

 图 1 在估计器VCE中,校正系数j取不同值 所得估计均值比较Fig. 1 Comparison of estimating mean value obtained by the VCE for different corrective coefficient j

 图 2 在估计器VCE中,校正系数j取不同值 所得估计偏差比较Fig. 2 Comparison of estimating bias obtained by the VCE for different corrective coefficient j

 图 3 在估计器VCE中,校正系数j取不同值 所得估计标准差比较Fig. 3 Comparison of estimating standard error obtained by the VCE for different corrective coefficient j

2 仿真实验

 图 4 U,VE和VCE估计器所得对v的估计的均值比较Fig. 4 Comparison of mean value for estimating v obtained by U,VE and VCE
 图 5 U,VE和VCE估计器所得对v的估计的偏差比较Fig. 5 Comparison of bias for estimating v obtained by U,VE and VCE
 图 6 U,VE和VCE估计器所得对v的估计的 标准差比较Fig. 6 Comparison of standard error for estimating v obtained by U,VE and VCE

3 结 论

1) 本文提出的具有校正项的V估计器VCE,在保留与VE同样高的估计效率的同时,显著提高了估计的精度,在估计均值、估计偏差和估计标准差3个方面全面明显超过VE估计器.

2) 仿真实验表明,本文提出的具有校正项的V-估计器VCE,在小样本情况下,对K分布形状参数v估计的精度与效率都优于U-估计器.VCE对样本长度有着较为广泛的适应性,更便于在实践中应用.

 [1] Blacknell D,Tough R J A. Parameter estimation for the K-distribution based on [z log(z)][J].IEE Proceedings:Radar,Sonar and Navigation,2001,148(6):309-312. Click to display the text [2] 李永晨,刘浏.SAR图像统计模型综述[J].计算机工程与应用,2013,49(13):184-190.Li Y C,Liu L.Review of statistical method of SAR image[J].Computer Engineering and Applications,2013,49(13):184-190(in Chinese). Cited By in Cnki (1) [3] 孙增国.基于第二类统计量的K分布参数估计[J].计算机应用研究,2013,30(1):1-4.Sun Z G.Parameter estimation of K distribution based on second-kind statistics[J].Application Research of Computers,2013,30(1):1-4(in Chinese). Cited By in Cnki (2) [4] 李亚超,周瑞雨,全英汇,等.自适应背景窗的舰船目标检测算法[J].西安交通大学学报,2013,36(3):1-6.Li Y C,Zhou R Y,Quan Y H,et al.An algorithm of ship target detection based on the adaptive background window function[J].Journal of Xi'an Jiaotong University,2013,36(3):1-6(in Chinese). Cited By in Cnki (3) [5] 杨永生,张宗杰.基于分数阶矩和NM单纯形算法的海杂波参数估计[J].遥感技术与应用,2011,25(6):70-73.Yang Y S,Zhang Z J.Parameters estimation of sea clutter based on fractional order moments and NM algorithm[J].Remote Sensing Technology,2011,25(6):70-73(in Chinese). Cited By in Cnki (1) [6] 徐伟,陈永森.一种K分布杂波参数估计方法[J].舰船电子对抗,2013,36(3):89-91.Xu W,Chen Y S.An estimation method for K-distribution clutter parameters[J].Shipboard Electronic Countermeasure,2013,36(3):89-91(in Chinese). Cited By in Cnki (1) [7] 胡文琳,王永良,王首勇.基于zrlog(z)期望的K分布参数估计[J].电子与信息学报,2008,30(1):203-205.Hu W L,Wang Y L,Wang S Y.Estimation of the parameters K-distribution based on zrlog(z)[J].Journal of Electronics & Information Technology,2008,30(1):203-205(in Chinese). Cited By in Cnki (8) [8] 李大朋,姚迪.对Jahangir组合式矩估计器的改进[J].北京航空航天大学学报,2012,38(6):788-792.Li D P,Yao D.Improvement of Jahangir's multiple moments estimator[J].Journal of Beijing University of Aeronautics and Astronautics,2012,38(6):788-792(in Chinese). Cited By in Cnki (1) [9] 李大朋,姚迪.对K分布形状参数M估计器的再改进[J].电子与信息学报,2011,33(7):1752-1755.Li D P,Yao D.A further enhanced M-estimator for the K-distribution shape parameter[J].Journal of Electronics & Information Technology,2011,33(7):1752-1755(in Chinese). Cited By in Cnki (2) | Click to display the text [10] Joughin I R.Maximum likelihood estimation of K-distribution parameters for SAR data[J].IEEE Trans on Geosciences and Remote Sensing,1993,31(5):989-999. Click to display the text [11] Oliver C J.Optimum texture estimators for SAR clutter[J].Journal of Physics D:Applied Physics,1993,26(11):1824-1835. Click to display the text [12] Blacknell D.Comparison of parameter for K-distribution[J].IEE Proceedings:Radar,Sonar and Navigation,1994,141(1):45-52. Click to display the text [13] Jahangir M,Blacknell D,White R G.Accurate approximation to the optimum parameter estimate for K-distributed clutter[J].IEE Proceedings:Radar,Sonar and Navigation,1996,143(6):383-390. Click to display the text [14] 郝程鹏,侯朝焕.一种K-分布杂波背景下的双参数恒虚警检测器[J].电子与信息学报,2007,29(3):756-759.Hao C P,Hou C H.A two parameter CFAR detector in K-distribution clutter[J].Journal of Electronics & Information Technology,2007,29(3):756-759(in Chinese). Cited By in Cnki (9) [15] 郝程鹏,侯朝焕,鄢锦.一种新的K分布形状参数估计器[J].电子与信息学报,2005,27(9):1404-1407.Hao C P,Hou C H,Yan J.A new estimator for estimating the parameters of K-distribution[J].Journal of Electronics & Information Technology,2005,27(9):1404-1407(in Chinese) Cited By in Cnki (15)

文章信息

LI Dapeng

V-estimator with corrective term for K-distribution shape parameter

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 45-49.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0054