Alpha稳定分布噪声环境下基于相关熵的时延估计算法研究
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摘要
本文主要以相关熵理论研究为基础,通过改进传统算法或者提出新算法来解决在alpha稳定分布噪声环境下的时间延迟估计问题。时延估计是现代信号处理中信号参数提取问题的一个重要组成部分,在众多领域里面发挥着重要作用,因此具有重要的理论意义和现实意义。作为时延估计领域发展的一个重要方向,非高斯噪声环境下的时延估计问题一直备受人们的关注。由于人们通常用alpha稳定分布来表述非高斯噪声,并且稳定分布的最小分散系数与分数低阶矩成正比,因此,分数低阶统计量理论逐渐成为解决非高斯噪声环境时延估计问题的理论基础,但是分数低阶统计量理论并不是解决问题的唯一理论根据。
相关熵作为随机变量间局部相似性的度量,是一种能够反映其分散系数信息的统计量,近些年来受到广泛关注。本文通过深入研究相关熵理论的特性,探讨用相关熵理论解决非高斯噪声环境时延估计问题的可能性并且通过理论证明和实验得出了肯定的结论。具体内容介绍如下：
(1)本文在理论上证明了可以利用相关熵作为自适应时延估计算法的代价函数来进行时延估计。通过数学推导,得出最大相关熵准则与最小分散系数具有等价性的结论,从而验证了以相关熵作为代价函数来构造自适应算法的可能性,为最大相关熵时延估计算法(MCC)的产生提供了理论依据。
(2)本文针对MCC算法抗噪声能力的不足,提出多种MCC改进算法。深入研究非高斯环境能够下自适应时延估计算法抗噪声能力较差的原因,构造出两种有效的MCC改进算法以提高自适应时延算法在处理复杂非高斯脉冲噪声环境下的精度和准确性。
(3)提出了广义相关熵函数法。深入研究经典的相关算法的特点,构造出了基本相关熵函数,通过搜索相关熵函数的极大值来估计时延值。此算法在非高斯噪声环境下不仅估计精度和抗造性能优异,并且算法简单程度与经典相关算法相同,同时,也弥补了相关熵理论在时延估计领域算法思路单一的不足,具有较大的推广价值。
(4)提出了以广义相关熵函数为基础的石油管道盗油预警技术。由分布式光纤传感器获得多组带有时延信息的真实石油输送管道数据,通过检测和提取等多种信号处理手段对数据进行筛选和处理,最后测试多种时延估计算法的性能。
This thesis is mainly concerned with the time delay estimation (TDE) issue under the alpha-stable distribution noise environment by studying the conrrentropy theory. The research object is to find new TDE algorithms and improve traditional algorithms based on the conrrentropy theory. The TDE weighs very much in terms of the extraction of model parameters in the signal processing fields and it is of great meaning to the topic of TDE both in theory and application. As one of the promising ways of development in the TDE fields, the TDE under impulsive noise environment has been given great attention by people. Usually, the impulsive noise model is described by alpha-stable distribution and because of the direct ratio between minimum dispersion and fractional lower order moment, the theory of fractional lower order statistics has become the theoretical principle to solve the TDE problem under impulsive noise background. However, it is not the only way.
Correntropy, as a measure of two random variables, is a kind of statistics moment which could also reflect the information of dispersion coefficient. In this thesis, the possibility to solve the TDE issue with correntropy has been discussed and several TDE methods have been proposed with details as follows:
Firstly, the equivalency of the maximum correntropy criterion and the minimum dispersion criterion is derived from the parametric representation for zero location SaS distributions. This result is used to propose the adaptive time delay estimation under SaS noise background.
Secondly, considering the fact that the self-adaptive algorithm based on conrrentropy could not give satisfying TDE results under impulsive noise background, two improved MCC methods has been proposed. Theoretical analysis and simulation experiments show that these two estimation methods can give satisfactory results.
Thirdly, the traditional algorithms time delay estimation (TDE) underα-stable distribution noise conditions are usually based on the fractional lower order statistics (FLOS), This paper proposes a generalized correntropy function (GCF) algorithm for non-Gaussianα-stable distribution noise environments based on the correntropy. It is demonstrated by computer simulations that the new proposed algorithm is robust under various noise conditions and presents a very good performance.
Finally, an oil pipe leakage alarming system based on generalized correntropy function (GCF) algorithm has been put forward. The Real datas are obtained from the sensors around pipes. After being processed by detection and extraction, the datas are used to testify the abilities of various TDE methods.
相关熵作为随机变量间局部相似性的度量,是一种能够反映其分散系数信息的统计量,近些年来受到广泛关注。本文通过深入研究相关熵理论的特性,探讨用相关熵理论解决非高斯噪声环境时延估计问题的可能性并且通过理论证明和实验得出了肯定的结论。具体内容介绍如下：
(1)本文在理论上证明了可以利用相关熵作为自适应时延估计算法的代价函数来进行时延估计。通过数学推导,得出最大相关熵准则与最小分散系数具有等价性的结论,从而验证了以相关熵作为代价函数来构造自适应算法的可能性,为最大相关熵时延估计算法(MCC)的产生提供了理论依据。
(2)本文针对MCC算法抗噪声能力的不足,提出多种MCC改进算法。深入研究非高斯环境能够下自适应时延估计算法抗噪声能力较差的原因,构造出两种有效的MCC改进算法以提高自适应时延算法在处理复杂非高斯脉冲噪声环境下的精度和准确性。
(3)提出了广义相关熵函数法。深入研究经典的相关算法的特点,构造出了基本相关熵函数,通过搜索相关熵函数的极大值来估计时延值。此算法在非高斯噪声环境下不仅估计精度和抗造性能优异,并且算法简单程度与经典相关算法相同,同时,也弥补了相关熵理论在时延估计领域算法思路单一的不足,具有较大的推广价值。
(4)提出了以广义相关熵函数为基础的石油管道盗油预警技术。由分布式光纤传感器获得多组带有时延信息的真实石油输送管道数据,通过检测和提取等多种信号处理手段对数据进行筛选和处理,最后测试多种时延估计算法的性能。
This thesis is mainly concerned with the time delay estimation (TDE) issue under the alpha-stable distribution noise environment by studying the conrrentropy theory. The research object is to find new TDE algorithms and improve traditional algorithms based on the conrrentropy theory. The TDE weighs very much in terms of the extraction of model parameters in the signal processing fields and it is of great meaning to the topic of TDE both in theory and application. As one of the promising ways of development in the TDE fields, the TDE under impulsive noise environment has been given great attention by people. Usually, the impulsive noise model is described by alpha-stable distribution and because of the direct ratio between minimum dispersion and fractional lower order moment, the theory of fractional lower order statistics has become the theoretical principle to solve the TDE problem under impulsive noise background. However, it is not the only way.
Correntropy, as a measure of two random variables, is a kind of statistics moment which could also reflect the information of dispersion coefficient. In this thesis, the possibility to solve the TDE issue with correntropy has been discussed and several TDE methods have been proposed with details as follows:
Firstly, the equivalency of the maximum correntropy criterion and the minimum dispersion criterion is derived from the parametric representation for zero location SaS distributions. This result is used to propose the adaptive time delay estimation under SaS noise background.
Secondly, considering the fact that the self-adaptive algorithm based on conrrentropy could not give satisfying TDE results under impulsive noise background, two improved MCC methods has been proposed. Theoretical analysis and simulation experiments show that these two estimation methods can give satisfactory results.
Thirdly, the traditional algorithms time delay estimation (TDE) underα-stable distribution noise conditions are usually based on the fractional lower order statistics (FLOS), This paper proposes a generalized correntropy function (GCF) algorithm for non-Gaussianα-stable distribution noise environments based on the correntropy. It is demonstrated by computer simulations that the new proposed algorithm is robust under various noise conditions and presents a very good performance.
Finally, an oil pipe leakage alarming system based on generalized correntropy function (GCF) algorithm has been put forward. The Real datas are obtained from the sensors around pipes. After being processed by detection and extraction, the datas are used to testify the abilities of various TDE methods.
引文
[1]王宏禹,邱天爽.自适应噪声抵消与时间延迟估计[M].大连：大连理工大学出版社,1999。
[2]马雯,水下目标被动定位方法研究,西北工业大学硕士学位论文,1999.
[3]邱天爽,魏东兴,唐洪,张安清.通信中的自适应信号处理[M].北京：电子工业出版社,2005.
[4]解家宝,李坤,胡博.时差定位系统中时延估计的研究[J].电子工程,2008,3：40-44.
[5]Zheng C, Tjeng T T. A New Time Delay Estimator Based on ETDE[J]. IEEE Transactions on Signal Processing,2003,51(7):1859-1869.
[6]So H C, Ching P C, Chan Y T. A New Algorithm for Explicit Adaptation of Time Delay[J]. IEEE Transactions on Signal Processing,1994,42(7):1816-1820.
[7]. Weiss A J, Weinstein E. Fundamental Limitations in Passive Time Delay Estimation-Part I:Narrow-Band Systems[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1983,31(2):472-486.
[8]Sharma K K, Joshi S D. Time Delay Estimation Using Fractional Fourier Transform[J]. Signal Processing,2007,87(5):853-865.
[9]四阶统计量在时差定位中的应用[J].雷达与对抗,2002(2)：27-31.
[10]Burrus C S, Gopinath R A, Haitao G. Introduction to Wavelets and Wavelet Transforms[M],第一版.北京：机械工业出版社,2008.
[11]郭莹,邱天爽,张艳丽等.脉冲噪声环境下基于分数低阶循环相关的自适应时延估计方法[J]通信学报,2007,28(3)：8-14.
[12]Chen J D, Benesty J, Huang Y et al. New Insights Into the Noise Reduction Wiener Filter[J]. IEEE Transactions on Audio, Speech, and Language Processing,2006, 14(4):1218-1234.
[13]Chen J D, Benesty J, Huang Y et al. New Insights Into the Noise Reduction Wiener Filter[J]. IEEE Transactions on Audio, Speech, and Language Processing,2006, 14(4):1218-1234.
[14]G. Clifford Carter. Time Delay Estimation for passive sonar signal processing[J]. IEEE transactions on acoustics, speech, and signal processing,1981,29(3):463-469.
[15]杨德森,时洁,刘伯胜.基于倒谱分析的水声信号被动定位时延估计算法研究[J].系统仿真学报,2009,21(2)：610-616.
[16]贾颖.移动位置服务的技术原理及市场前景[J].邮电规划,2003(1)：14-18.
[17]毛汉领,陈仲仪,庄红宇.能量比时间延迟估计法及在定位仲的应用[J].广西工学院学报,1994,5(2)：12-17.
[18]X. Ma and C. L. Nikias,“Joint estimation of time delay and frequency delay in impulsive noise using fractional lower-order statistics,”IEEE Trans. Signal Processing, vol.44, pp.2669-2687, Nov.1996.
[19]Etter DM, Stearns SD. Adaptive estimation of time delays in sampled data systems[J]. IEEE trans on acoustics, speech, signal processing,1981,29(3):582-587.
[20]Santamaria I, Pokharel P P, Principe J C. Generalized correlation function:definition, properties, and application to blind equalization. IEEE Transactions on Signal Processing,2006,54(6):2187-2197.
[21]Liu W F, Pokharel P P, Principe J C. Correntropy:properties and applications in non-Gaussian signal processing. IEEE Transactions on Signal Processing,2007,55 (11): 5286-5298.
[22]Bessa R J, Miranda V, Gama J. Entropy and correntropy against minimum square error in offline and online three-day ahead wind power forecasting. IEEE Transactions on Power Systems,2009,24(4):1657-1666.
[23]Jeong K H, Liu W F, Han S, etal..The correntropy MACE filter. Pattern Recognit,2009, 42(5):871-885.
[24]Singh A, Principe J C. Using correntropy as a cost function in linear adaptive filters. Proceedings of the 2009 international joint conference on Neural Networks, Atlanta, USA, Jun.14-19,2009,2950-2955.
[25]Gunduz A, Principe J C. Correntropy as a novel measure for nonlinearity tests. Signal Processing,2009,89(1):14-23.
[26]So H C. Fractional lower-order moment based adaptive algorithms for time delay estimation in impulsive noise.42 Midwest Symposium on Circuits and Systems, Las Cruces, NM,8-11 Aug.,1999, vol.2:985-988.
[27]宋爱民,邱天爽,佟祉谏.对称稳定分布的相关熵及其在时间延迟估计上的应用.投稿于电子与信息学报,已录用,2010.
[28]吴光弼,祝琳瑜.一种变步长LMS自适应算法[J].电子学报.1994,22(1)：55-60.
[29]高鹰,谢胜利.一种变步长LMS自适应滤波算法及分析[J].电子学报.2001,29(8)：1094-1097.
[30]Gitlin R D, Weinstein S D, The effects of large interference on the tracking capability of digitally implemented echo cancellers [J]. IEEE Trans on COM,1978 (6):833-83.
[2]马雯,水下目标被动定位方法研究,西北工业大学硕士学位论文,1999.
[3]邱天爽,魏东兴,唐洪,张安清.通信中的自适应信号处理[M].北京：电子工业出版社,2005.
[4]解家宝,李坤,胡博.时差定位系统中时延估计的研究[J].电子工程,2008,3：40-44.
[5]Zheng C, Tjeng T T. A New Time Delay Estimator Based on ETDE[J]. IEEE Transactions on Signal Processing,2003,51(7):1859-1869.
[6]So H C, Ching P C, Chan Y T. A New Algorithm for Explicit Adaptation of Time Delay[J]. IEEE Transactions on Signal Processing,1994,42(7):1816-1820.
[7]. Weiss A J, Weinstein E. Fundamental Limitations in Passive Time Delay Estimation-Part I:Narrow-Band Systems[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1983,31(2):472-486.
[8]Sharma K K, Joshi S D. Time Delay Estimation Using Fractional Fourier Transform[J]. Signal Processing,2007,87(5):853-865.
[9]四阶统计量在时差定位中的应用[J].雷达与对抗,2002(2)：27-31.
[10]Burrus C S, Gopinath R A, Haitao G. Introduction to Wavelets and Wavelet Transforms[M],第一版.北京：机械工业出版社,2008.
[11]郭莹,邱天爽,张艳丽等.脉冲噪声环境下基于分数低阶循环相关的自适应时延估计方法[J]通信学报,2007,28(3)：8-14.
[12]Chen J D, Benesty J, Huang Y et al. New Insights Into the Noise Reduction Wiener Filter[J]. IEEE Transactions on Audio, Speech, and Language Processing,2006, 14(4):1218-1234.
[13]Chen J D, Benesty J, Huang Y et al. New Insights Into the Noise Reduction Wiener Filter[J]. IEEE Transactions on Audio, Speech, and Language Processing,2006, 14(4):1218-1234.
[14]G. Clifford Carter. Time Delay Estimation for passive sonar signal processing[J]. IEEE transactions on acoustics, speech, and signal processing,1981,29(3):463-469.
[15]杨德森,时洁,刘伯胜.基于倒谱分析的水声信号被动定位时延估计算法研究[J].系统仿真学报,2009,21(2)：610-616.
[16]贾颖.移动位置服务的技术原理及市场前景[J].邮电规划,2003(1)：14-18.
[17]毛汉领,陈仲仪,庄红宇.能量比时间延迟估计法及在定位仲的应用[J].广西工学院学报,1994,5(2)：12-17.
[18]X. Ma and C. L. Nikias,“Joint estimation of time delay and frequency delay in impulsive noise using fractional lower-order statistics,”IEEE Trans. Signal Processing, vol.44, pp.2669-2687, Nov.1996.
[19]Etter DM, Stearns SD. Adaptive estimation of time delays in sampled data systems[J]. IEEE trans on acoustics, speech, signal processing,1981,29(3):582-587.
[20]Santamaria I, Pokharel P P, Principe J C. Generalized correlation function:definition, properties, and application to blind equalization. IEEE Transactions on Signal Processing,2006,54(6):2187-2197.
[21]Liu W F, Pokharel P P, Principe J C. Correntropy:properties and applications in non-Gaussian signal processing. IEEE Transactions on Signal Processing,2007,55 (11): 5286-5298.
[22]Bessa R J, Miranda V, Gama J. Entropy and correntropy against minimum square error in offline and online three-day ahead wind power forecasting. IEEE Transactions on Power Systems,2009,24(4):1657-1666.
[23]Jeong K H, Liu W F, Han S, etal..The correntropy MACE filter. Pattern Recognit,2009, 42(5):871-885.
[24]Singh A, Principe J C. Using correntropy as a cost function in linear adaptive filters. Proceedings of the 2009 international joint conference on Neural Networks, Atlanta, USA, Jun.14-19,2009,2950-2955.
[25]Gunduz A, Principe J C. Correntropy as a novel measure for nonlinearity tests. Signal Processing,2009,89(1):14-23.
[26]So H C. Fractional lower-order moment based adaptive algorithms for time delay estimation in impulsive noise.42 Midwest Symposium on Circuits and Systems, Las Cruces, NM,8-11 Aug.,1999, vol.2:985-988.
[27]宋爱民,邱天爽,佟祉谏.对称稳定分布的相关熵及其在时间延迟估计上的应用.投稿于电子与信息学报,已录用,2010.
[28]吴光弼,祝琳瑜.一种变步长LMS自适应算法[J].电子学报.1994,22(1)：55-60.
[29]高鹰,谢胜利.一种变步长LMS自适应滤波算法及分析[J].电子学报.2001,29(8)：1094-1097.
[30]Gitlin R D, Weinstein S D, The effects of large interference on the tracking capability of digitally implemented echo cancellers [J]. IEEE Trans on COM,1978 (6):833-83.