基于连续小波变换的水下信号处理技术研究
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摘要
在水下信号处理中，参数估计和目标识别是两类非常重要的问题。准确地进行目标参量估计及目标识别，可以保证水下对抗和反对抗地有效实施，从而确保新形势下海洋战略中的主动地位。近年来小波分析在水下信号处理方面的应用得到了长足的发展，鉴于其良好的时频局部化特点，本文将基于连续小波变换的时频分析作为工具，就参数估计和目标识别两方面的问题做了系统研究和深入探讨。
首先是瞬时频率的估计问题。文中将基于连续小波变换的‘Simple’方法引入到水下信号的瞬时频率估计中来，也即通过寻求连续小波变换幅值的最大值来得到小波脊，再根据小波脊与信号频率之间的对应关系，最终完成信号的瞬时频率估计。基于上述方法，文中分别对单频矩形脉冲信号、线性调频脉冲信号以及多分量信号进行了瞬时频率估计，并与其他几种常用瞬时频率估计方法的性能以及CRB进行了系统比较。对于线性调频脉冲信号瞬时频率估计中出现的边缘效应，文中提出采用线性拟合方法对其进行了一定修正。通过仿真发现，在单频回波的瞬时频率估计中，基于CWT的方法最为有效，随着信噪比的提高，其均方误差曲线越来越接近克拉美—罗界；在线性调频回波的瞬时频率估计中，WVD法得到的效果最好，而CWT与STFT法的估计效果比较接近；在多分量信号的瞬时频率估计中，相对于STFT和WVD法，CWT法是一个更好的选择。
其次研究了目标方位的估计问题。首先在传统的频域波束形成算法的基础上，提出对宽带信号的频率补偿，也即对宽带回波信号的各空间频率根据时间频率的差异进行相应补偿，然后对各阵元输出求和来得到方位估计；其次将连续小波变换引入到空间—频率处理中，从而完成对目标方位的估计，并进行了相应地补偿。文中对于窄带回波与宽带回波均进行了一定信噪比下方位估计的计算机仿真，并与基于FFT、STFT以及WVD的时频分析方法以及CRB曲线进行了有关比较。从估计结果发现，对于窄带回波信号，基于FFT的方法估计性能大大优于其他方法；对于宽带回波信号，在信噪比达到一定程度(高于约-7dB)时，补偿后的几种估计法的性能改善均比较明显，误差曲线越来越接近CRB曲线；对于回波中存在多频率多方位的情况，空间—频率分布图能提供较为直观的频率及方位信息，因此应用空间—频率估计法来进行方位估计，更有利于进一步对回波的具体方位进行准确判断和估计。
最后研究了水下目标的分类识别问题。针对莱蒙湖底的岩石、沙、卵石、砂砾、淤泥等五类目标，文中所提取的特征主要有时频矩阵的奇异值、直方图的有关参数以及不变矩等三类特征。分类结果发现，对于以上五类目标，利用直方
图有关参数作为分类特征比奇异值特征有效，前者效果可达 90％以上，而后者
低于 80％；对于沙、砂砾、淤泥三类目标而言，奇异值特征比不变矩特征更为
有效，前者效果可达 92％以上，而后者为 84％；从本文中抽取的特征如直方图
的参数以及奇异值来看，岩石与淤泥的特征比较接近，而卵石与砂砾的特征比较
接近，沙的特征则与其他四类有明显区别。
对于瞬时频率及方位估计问题，文中均给出了有关水池实验结果。
During underwater signal processing, parameter estimation and target identification are two kinds of important problems. To precisely estimate the target parameters and identify the right target will guarantee the effective operation of underwater counterwork and anti-counterwork, so as to keep an active position for a country in new situation of ocean strategy. These years wavelet theory has been widely applied in underwater signal processing. Whereas its excellent time-frequency localization, this dissertation takes Continuous Wavelet Transform(CWT) as research tool and devoted to systematic research and deep exploration of two aspects in underwater signal processing field-estimation of parameters and target classification and identification.
Firstly the estimation of instantaneous frequency is discussed. The 'Simple' method based on CWT is inducted to underwater signal processing to estimate the instantaneous frequency of echo. In essential, this method is to extract the wavelet ridge from the maximum of continuous wavelet transform, according to the corresponding relationship between wavelet ridge and signal frequency, finally to obtain the estimated instantaneous frequency. Based on the method, this dissertation deals with several kinds of signals including Cosine Wave(CW), Linear Frequency Modulated(LFM) and multi-component signal, Furthermore the systematic comparison of estimation effect among CWT and several other usual methods as well Cramer-Rao Bound(CRB) is given. During the instantaneous frequency estimation of LFM, there exists some error in the edge, so in the dissertation, a fitting method is proposed to modify it. From the computer simulation, the following result is obtained: For CW , the method based on CWT is most effective, and with the SNR rising, the error curve of it is more and more closer to CRB. For LFM, the method based on WVD gives the best result, and the effects of CWT and STFT are similar For multi-component signal, Compared to STFT and WVD, CWT is a better choice.
Secondly the estimation of DOA is studied. At first some modification is made in conventional beam forming of frequency domain, namely to estimate DOA by arrays outputs on compensated spacial frequency points of echoes. Then the CWT is utilized to signal processing in space-frequency domain for estimation of DOA, and the corresponding modification is also made. In the dissertation, the computer simulations of DOA estimation for both narrow-band and wide-band echoes are given, so do the necessary comparison among several methods and CRB. From the result we
get the following conclusion: For narrow-band signal, the effect of the method based on FFT is best. For wide-band signal, when SNR is up to certain degree(higher than -7dB or so), the curves of square error of modified methods are more obvious and closer to CRB. For an echo composed of more than one frequency or direction, space-frequency distribution could show more direct information of frequency and direction, which is more advantaged to make precise judge and estimation for DOA of echo.
Finally the target classification and identification are studied. Aiming at five kinds of targets from Geneva Lake which are rock, sand, pebble, grit and sullage, the
features we extracted based on the CWT time-frequency matrix are singular values,
some parameters of histogram and invariant moment. From the result we conclude:
For these five kinds of targets, the parameters of histogram are more effective than singular values. The identification rate of the former could be above 90% , whereas the later is below 80%. For three kinds of targets involving sand, grit and sullage, the feature of singular values excels that of invariant moment, the identification of the former could be to 92%, whereas the later is 84%. Analyzing the features this dissertation extracts, we can find that the features of rock and sullage are more similar, so do pebble and grit, and the features of sand are obviously distinguished.
As to the estimation of instantaneous frequency and DOA, s
首先是瞬时频率的估计问题。文中将基于连续小波变换的‘Simple’方法引入到水下信号的瞬时频率估计中来，也即通过寻求连续小波变换幅值的最大值来得到小波脊，再根据小波脊与信号频率之间的对应关系，最终完成信号的瞬时频率估计。基于上述方法，文中分别对单频矩形脉冲信号、线性调频脉冲信号以及多分量信号进行了瞬时频率估计，并与其他几种常用瞬时频率估计方法的性能以及CRB进行了系统比较。对于线性调频脉冲信号瞬时频率估计中出现的边缘效应，文中提出采用线性拟合方法对其进行了一定修正。通过仿真发现，在单频回波的瞬时频率估计中，基于CWT的方法最为有效，随着信噪比的提高，其均方误差曲线越来越接近克拉美—罗界；在线性调频回波的瞬时频率估计中，WVD法得到的效果最好，而CWT与STFT法的估计效果比较接近；在多分量信号的瞬时频率估计中，相对于STFT和WVD法，CWT法是一个更好的选择。
其次研究了目标方位的估计问题。首先在传统的频域波束形成算法的基础上，提出对宽带信号的频率补偿，也即对宽带回波信号的各空间频率根据时间频率的差异进行相应补偿，然后对各阵元输出求和来得到方位估计；其次将连续小波变换引入到空间—频率处理中，从而完成对目标方位的估计，并进行了相应地补偿。文中对于窄带回波与宽带回波均进行了一定信噪比下方位估计的计算机仿真，并与基于FFT、STFT以及WVD的时频分析方法以及CRB曲线进行了有关比较。从估计结果发现，对于窄带回波信号，基于FFT的方法估计性能大大优于其他方法；对于宽带回波信号，在信噪比达到一定程度(高于约-7dB)时，补偿后的几种估计法的性能改善均比较明显，误差曲线越来越接近CRB曲线；对于回波中存在多频率多方位的情况，空间—频率分布图能提供较为直观的频率及方位信息，因此应用空间—频率估计法来进行方位估计，更有利于进一步对回波的具体方位进行准确判断和估计。
最后研究了水下目标的分类识别问题。针对莱蒙湖底的岩石、沙、卵石、砂砾、淤泥等五类目标，文中所提取的特征主要有时频矩阵的奇异值、直方图的有关参数以及不变矩等三类特征。分类结果发现，对于以上五类目标，利用直方
图有关参数作为分类特征比奇异值特征有效，前者效果可达 90％以上，而后者
低于 80％；对于沙、砂砾、淤泥三类目标而言，奇异值特征比不变矩特征更为
有效，前者效果可达 92％以上，而后者为 84％；从本文中抽取的特征如直方图
的参数以及奇异值来看，岩石与淤泥的特征比较接近，而卵石与砂砾的特征比较
接近，沙的特征则与其他四类有明显区别。
对于瞬时频率及方位估计问题，文中均给出了有关水池实验结果。
During underwater signal processing, parameter estimation and target identification are two kinds of important problems. To precisely estimate the target parameters and identify the right target will guarantee the effective operation of underwater counterwork and anti-counterwork, so as to keep an active position for a country in new situation of ocean strategy. These years wavelet theory has been widely applied in underwater signal processing. Whereas its excellent time-frequency localization, this dissertation takes Continuous Wavelet Transform(CWT) as research tool and devoted to systematic research and deep exploration of two aspects in underwater signal processing field-estimation of parameters and target classification and identification.
Firstly the estimation of instantaneous frequency is discussed. The 'Simple' method based on CWT is inducted to underwater signal processing to estimate the instantaneous frequency of echo. In essential, this method is to extract the wavelet ridge from the maximum of continuous wavelet transform, according to the corresponding relationship between wavelet ridge and signal frequency, finally to obtain the estimated instantaneous frequency. Based on the method, this dissertation deals with several kinds of signals including Cosine Wave(CW), Linear Frequency Modulated(LFM) and multi-component signal, Furthermore the systematic comparison of estimation effect among CWT and several other usual methods as well Cramer-Rao Bound(CRB) is given. During the instantaneous frequency estimation of LFM, there exists some error in the edge, so in the dissertation, a fitting method is proposed to modify it. From the computer simulation, the following result is obtained: For CW , the method based on CWT is most effective, and with the SNR rising, the error curve of it is more and more closer to CRB. For LFM, the method based on WVD gives the best result, and the effects of CWT and STFT are similar For multi-component signal, Compared to STFT and WVD, CWT is a better choice.
Secondly the estimation of DOA is studied. At first some modification is made in conventional beam forming of frequency domain, namely to estimate DOA by arrays outputs on compensated spacial frequency points of echoes. Then the CWT is utilized to signal processing in space-frequency domain for estimation of DOA, and the corresponding modification is also made. In the dissertation, the computer simulations of DOA estimation for both narrow-band and wide-band echoes are given, so do the necessary comparison among several methods and CRB. From the result we
get the following conclusion: For narrow-band signal, the effect of the method based on FFT is best. For wide-band signal, when SNR is up to certain degree(higher than -7dB or so), the curves of square error of modified methods are more obvious and closer to CRB. For an echo composed of more than one frequency or direction, space-frequency distribution could show more direct information of frequency and direction, which is more advantaged to make precise judge and estimation for DOA of echo.
Finally the target classification and identification are studied. Aiming at five kinds of targets from Geneva Lake which are rock, sand, pebble, grit and sullage, the
features we extracted based on the CWT time-frequency matrix are singular values,
some parameters of histogram and invariant moment. From the result we conclude:
For these five kinds of targets, the parameters of histogram are more effective than singular values. The identification rate of the former could be above 90% , whereas the later is below 80%. For three kinds of targets involving sand, grit and sullage, the feature of singular values excels that of invariant moment, the identification of the former could be to 92%, whereas the later is 84%. Analyzing the features this dissertation extracts, we can find that the features of rock and sullage are more similar, so do pebble and grit, and the features of sand are obviously distinguished.
As to the estimation of instantaneous frequency and DOA, s
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