信息理论准则下的匹配场声源定位

发布时间：2018-04-09 06:26

本文选题：匹配场处理　切入点：信息理论　出处：《浙江大学》2015年博士论文

【摘要】：本论文试图从机器学习角度探讨从水听器测量数据中学习声源位置信息的问题。在优化算法指导下,机器学习通过最小化模型拷贝与实际测量数据之间在特定代价准则下的误差来进行数据结构的学习。传统的匹配场处理(Matched-field processing,简称MFP)方法(例如：Bartlett相关器,最大似然估计器和最小方差无失真响应估计器等)是通过在声源位置参数空间内网格搜索参数并选取估计器模糊度输出峰值处对应的参数来作为估计值。模糊度输出的倒数可以看做是一种广义的误差、网格搜索是一种最平白的参数搜索策略、待估计的参数反映的即是数据的结构信息,因此说机器学习囊括了传统的匹配场声源定位方法。本论文将匹配场处理建立在机器学习框架之下,选取基于信息理论原则的代价准则,来实现对拷贝模型与实际测量数据在信息意义下的距离测量。目前有很多信息理论方法来测量信息之间的距离,其中最常用的就是散度。本论文选取了在信息论和信号检测中有广泛应用的f-散度进行重点研究。f-散度包含信息论中广为人知的相对熵,其偶对称形式被称为信息散度。f-散度也包含了Hellinger积分,它可以构成信号检测理论中著名的错误概率下限Chernoff Bound。Bhattacharyya系数是Hellinger积分控制参数等于常数1/2时的结果,它可以不失一般性地表征信号检测问题的错误概率上、下限,其倒数的自然对数是可以测量信息间距离的Bhattacharyya距离。在信息理论框架之内,本论文选取Bhattacharyya距离作为代价准则,并仿照最小化相对熵得到最大似然估计器的方式获得了最小化Bhattacharyya距离估计器。虽然高斯分布不能保证对测量数据的实际分布进行精确的表征,但是它通常是最合理的选择。高斯分布具有中心极限定理、便于理论分析时的解析推导及易于生成其他分布的特性,使得它卓越不凡。特别的是,当随机过程的一、二阶矩已知时,高斯分布可以最大化Cramer-Rao限。这样,任何基于Cramer-Rao限的优化准则在高斯分布下就成为了一种Min-Max优化准则,即最小最大化的Cramer-Rao限。由于Cramer-Rao限是无偏估计可达的方差理论下限,该特性对于无偏估计方法的性能评估具有显著的指导意义。本论文中,假设信号和噪声随机过程均服从零均值高斯分布,数据的统计特性可以完全由协方差矩阵表征。实际的匹配场处理过程中,受有限信号平稳时间、相位无失真带宽等因素影响,只能获得有限的有效数据样本。此时,通过最大似然估计方法获得的采样协方差矩阵就会因数据量有限而与数据的真实协方差矩阵存在误差,导致统计特性失配、数据信息的失真。因此,发展能够在统计特性失配情况下稳定工作的匹配场处理方法具有重要的意义。本论文对匹配场声源定位问题中的信号、噪声和传播过程分别进行了建模。信号和噪声均选择了零均值圆对称的复高斯随机模型。在该模型下,以最小化Bhattacharyya距离估计器为基础推导出数学形式简洁、对称的匹配协方差估计器(Matched-Covariance Estimator,简称MCE)，该估计器通过匹配模型拷贝协方差矩阵和测量数据协方差矩阵的方式来进行参数估计,使得MCE具有对多秩信号参数估计的能力。对于噪声模型而言,本论文依据匹配场处理过程中的实际特点将噪声建模为空间白的本地噪声和空间相关的传播噪声场。其中传播噪声又可分为离散分布噪声(如：点干扰噪声)和连续分布噪声(如：海面生成噪声)o传播噪声因历经与声源信号相类似的水声信道传播,存在空间相似性,而对匹配场处理方法提出额外的挑战。在传播模型方面,本论文针对三种典型声源定位问题选取了三种各具代表性的模型：1)针对深海、自由场环境中的声源定向问题,选择了单模态平面波模型；2)针对浅海平稳波导环境下的声源定位问题,选择了多模态全波场模型；3)针对浅海起伏声场中的定位问题,选择了最近发展的多模态、多相干模态组模型。本论文通过在不同类型声源定位问题中,对不同代价准则下的机器学习系统性能比较,来从不同的角度评估机器学习架构下的匹配场声源定位性能。综合深海自由场、浅海全波场及浅海起伏声场的声源定位仿真结果,可以得出基于信息理论原则的MCE估计方法优于传统匹配场估计方法,因为：1)MCE能够同时开发信号和噪声的数据结构；2)MCE不采用对噪声抑制或抵消的操作,避免了在干扰源噪声与声源信号存在空间相似性时错误抵消信号的现象；3)MCE不限定信号空间的秩为“1”,可以完成对多秩信号的估计；及4)MCE不需要大量的持续数据来估计协方差矩阵,可以有效地缓解统计特性失配问题。
[Abstract]:This paper attempts to study the sound source location information from the sensor data measured in the problem from the perspective of learning machine. In the optimization algorithm under the guidance of machine learning in specific cost criteria by minimizing the error between the model and the actual measured data copy data structure learning. Conventional matched field processing (Matched-field processing, referred to as MFP) methods (such as: Bartlett correlator, the maximum likelihood estimator and minimum variance distortionless response estimator etc.) is through the search parameters in the parameters of the sound source location parameter space grid and selects the fuzzy estimator corresponding to the peak of the output as an estimate. The output of the fuzzy reciprocal can be regarded as a generalized error grid the search is a search strategy for most parameters, reflect the parameters to be estimated is the structural information of the data, so that machine learning include the The traditional matched field source localization methods. This paper will establish the matched field processing in machine learning framework, selecting principles of information theory to realize the cost criterion based on distance measurement model and the actual copy of the measurement data in the sense of information. At present there are many methods of information theory to measure the distance between the information, which is the most commonly used is the divergence. This thesis takes in information theory and signal detection in the widely used f- divergence of.F- divergence contains relative entropy is known in information theory, the symmetric form known as information divergence.F- divergence also contains the Hellinger integral, it can be a signal detection theory in the famous error probability limit the Chernoff Bound.Bhattacharyya Hellinger parameter is equal to the integral control coefficient is constant 1/2 results, it can be without loss of generality of signal detection problem The probability of error, the lower limit, the reciprocal of the natural logarithm of information can be measured the distance between the Bhattacharyya distance. Within the framework of information theory, this paper selects the Bhattacharyya distance as the cost criterion, and follow the minimum relative entropy obtained the maximum likelihood estimator of the way won the minimum Bhattacharyya distance estimator. While ensuring accurate characterization of the actual distribution of measurement the data of Gauss distribution can not, but it is usually the most reasonable choice. Gauss distribution is the central limit theorem for analytic theory analysis and easy to generate other distribution characteristics, making it extraordinary. Especially, when the stochastic process, two moments are known, the Gauss distribution can maximize Cramer-Rao any limit. So the optimization criterion of Cramer-Rao limit based on Gauss distribution has become a Min-Max optimization criterion, which is the minimum The maximum limit of Cramer-Rao. Because the Cramer-Rao limit is the unbiased estimation of variance theory limit was, the characteristics for the unbiased estimation of evaluation is of guiding significance for the performance. In this paper, the assumption that the signal and noise are subject to random process with zero mean Gauss distribution, the statistical properties of the data can be completely characterized by the covariance matrix. The matched field processing, limited signal stationary time, phase distortion free bandwidth and other factors, can only obtain valid data of limited samples. At the same time, through the maximum likelihood estimation method to obtain the sample covariance matrix will be due to limited data and real data and the error covariance matrix, leading to the statistical characteristics of mismatch, distortion data information. Therefore, the development can mismatch stability matched field processing method in statistical characteristics is of great significance. In this paper. The signal source localization problem, noise and propagation process were established. The signal and noise are chosen with zero mean circularly symmetric complex Gauss stochastic model. In this model, to minimize the distance based Bhattacharyya estimator is derived form simple, symmetric covariance estimator (Matched-Covariance Estimator, referred to as MCE), the estimator by matching the model copy covariance matrix and the covariance matrix of measurement data to estimate the parameters, the MCE has ability to estimate multi rank signal parameters. For the noise model, this paper on the basis of the actual characteristics, field in the process of modeling the spatial white noise of the local noise and spatial noise field related. The propagation of noise can be divided into discrete distribution of noise (such as: noise) and continuous noise (such as: sea surface generation Noise) of underwater acoustic channel o transmission noise and sound source signal after similar, spatial similarity, and the matched field method presents additional challenges. In the propagation model in this paper, three kinds of typical sound source localization problem has selected three representative models: 1) in the deep sea, sound source orientation free field environment, the choice of single mode plane wave model; 2) to solve the problem of sound source localization in shallow water waveguide stable environment, selection of multi modal full wave field model; 3) for localization in shallow sea undulating in the field, choose the multi modality of the recent development of multiple coherent mode group model. In the thesis, the problems of different types of sound source localization, comparison of different cost criteria of machine learning system performance, machine learning under the framework of matched field source localization performance from different angles. The comprehensive evaluation from the deep sea From the field, the simulation results of sound source localization in shallow water and shallow acoustic full wave field fluctuation, it can be based on the principles of information theory MCE estimation method is better than the traditional matched field estimation method, because: 1) the MCE data structure can also develop the signal and noise; 2) MCE is not used to the noise suppression or offset operation. To avoid the existence of Space Similarity error signal offset of the interference source in noise and sound source signal; 3) MCE does not limit the signal space rank as "1", can complete the estimation of multi rank signal; and 4) MCE does not need to continue a large amount of data to estimate the covariance matrix, can effectively alleviate the statistics the characteristics of mismatch problem.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB56;TP181

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