时频分析在雷达信号多参数估计中的应用研究
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摘要
时频分布形式为非平稳信号的研究提供了有效的手段，而对于这类频谱时变的信号，传统的时域和频率域的分析方法都不能够全面的反映信号的特征。本文主要讨论了时频分析方法与阵列信号处理的结合在雷达信号参数估计中的应用。传统的时频分析方法都着眼于单通道信号的分析，而在雷达信号侦察中由于采用了阵列接收的方式，因此存在利用多通道数据对时频分布进行改善的可能性。本文主要讨论了利用时频分布的到达角估计、高效的时频分布计算方法和信号的时频特征提取等问题。主要工作和贡献有：
1．虽然Cohen类分布能够提供较高的时频聚集度，但是会产生具有干扰作用的交叉项，并且叠加的噪声也会影响对信号的分析。目前多数处理方法都针对单通道的数据，而本文提出的利用对称阵元的互Wigner分布平均算法，这种方法能够有效的补偿信号在不同阵元上面产生的时差，并且获得较好的表示效果。与传统的Wigner分布阵列平均方法相比，由于到达不同阵元的噪声之间彼此不相干，因此采用互Wigner分布平均的方法能够有效去除噪声的干扰，获得改善的时频分布形式。
2．计算信号的时频分布并不是最终的目的，而只是为信号的进一步分析进行准备。因此我们考虑时频分布的后处理方法。与通常的计算核函数设计方法有所区别，如果把时频分布当作一幅图像，则每一个时频点都对应着图像中的一个像素，时频分布的幅度对应图像的灰度。从图像处理的角度来看，时频分布中的自项对应图像中有用的对象成分，而交叉项和噪声则构成了图像的干扰背景。因此对时频分布的改善可以等效为对图像中有效成分的提取以及背景抑制的问题。本文提出了利用数字图像处理技术的时频分布改善算法。
3．指数遗忘分布作为一类高效的时频分布迭代算法被提出，在这种方法中，信号的旧样本不是简单的丢弃，而是通过特殊类型的计算窗口来逐渐的消除其影响。同时在某一个时间点上面的时频分布可以通过有效的利用在前面的数据段上的计算结果来获得，这样将大大提高运算的效率。本文提出了指数遗忘分布的改进算法，分析表明其具有最高效率的计算结构。同时还分析了指数遗忘分布的瞬时频率表示性能，分析表明采用单边计算窗口的时频分布类型不能够准确及时的跟踪信号的频率变化。在分析频率快速变化的信号的时候，该类分布会产生频率表示的漂移现象。
4．提出了采用对称计算窗口的双边指数遗忘分布形式，与其他类型的时频分布相比，这种方法具有很高的计算效率，同时能够获得比指数遗忘分布更为准确的瞬时频率表示效果，瞬时频率表示的偏差和方差都大大的减小了。文章中还提
出了利用余弦窗口的信号时频分布迭代算法。由于余弦窗口对称并且具有有限的
宽度，因此这种分布形式能够兼顾计算的效率与实时性要求。
5.提出了基于对称阵元互Wigner分布平均的瞬时频率估计算法，这种方法利
用多通道数据对时频分布的瞬时频率估计方法的性能进行了有效的改善，并且能
够在低信噪比的条件下获得良好的估计效果，
6.对于具有恒定幅度的调频信号而言，瞬时频率代表了其全部的信息，可以
据此对信号进行识别和分类。然而如果信号中出现频率或者相位的不连续点的时
候，会相应的引起时频分布的幅度变化，为有效的提取信号的时频特征，本文对
由于信号相位和频率的不连续点引起的时频分布幅度变化规律进行了讨论。分析
表明这种方法能够准确的定位这些不连续点，同时对跳变值进行估计。
7.提出了基于瞬时频率的信号到达角估计算法。与信号子空间拟合方法不同，
这种方法有效利用频率的估计结果，对不同阵元上面的时差进行计算，从而估算
出信号的到达角。这种方法可以应用于宽带信号场合。
关键词:时频分布，阵列信号处理，空间平滑，迭代算法，瞬时频率，相位不连
续点，到达角估计
Time-frequency distributions were introduced as a means of representing signals whose frequency content is varying with time, and for which both time domain representation and frequency representation are inadequate to describe the signal appropriately. This dissertation is intended to incorporate time-frequency analysis into array signal processing for the estimation of radar signal parameters. Compared with traditional solutions that try to analyze signals received by single sensor, in the situation of radar signal estimation the source array manifolds make it possible to improve time-frequency representation through time sequences obtained through multi-channel. The estimation of direction of arrival, extraction of time-frequency characters, algorithms for efficient time-frequency computation and the methods to estimate instantaneous frequency are discussed.1. However the Cohen class time-frequency distributions can provide better concentration, they are suffered from the cross-terms and the noise in the time-frequency plane. Different from traditional practice that tries to deal with this problem through samples obtained from single channel, the approach to improve time-frequency distribution using averaged cross Wigner-Ville distributions between the sensors at symmetrical places is investigated, which tries to make full use of the advantage of sensor array. Compared with the array averaged Wigner distribution, it can provide better performance and compensate the time delays among the signals impinging on different antennas. Since the noise arrives at each sensor is uncorrelated. The average of cross Wigner distributions can effectively improve the time-frequency representation.2. To compute time-frequency distribution is not the aim but just a preparation for further estimation. So we consider the post process of TFD. Unlike the methods such as computational kernel design, the time-frequency representation can be considered as an image where the pixels correspond to the time-frequency points and their intensity to the magnitude of the transform. From the viewpoint of image processing, the auto-terms of the signal can be defined as objects in the image while all the interfering cross terms and the noise form the background in the image. Therefore it is natural for the introduction of image processing technique to time-frequency representation area, and the attempt to promote the time-frequency representation is equal to extract these
objects from the resultant image with background suppression.3. Exponentially forgetting transform (EFT) is discussed in detail in this paper, as an efficient recursive algorithm .to compute time-frequency distribution. In this approach, instead of excluding the old samples, their importance is diminished by using a special computational window, thus recursive operations can be introduced which incorporate knowledge of the time-frequency distribution from previous data blocks into the current estimate and greatly increase the computation efficiency. Under its analysis, we propose the modified version, which has the simplest recursive computation structure. The performance of EFT is investigated, which indicates that time-frequency distributions using single-sided window could not accurately trace the variation of the instantaneous frequency, since their performance depend only on the history of the signal, so they are biased frequency estimator. The excursion of instantaneous frequency representation will be resulted when EFT is applied to signals with rapidly varying frequency contents.4. The double-sided exponentially forgetting transform (DSEFT) is also presented which offers better time-frequency resolution. Compared with other forms of time-frequency representation, DSEFT is highly computational efficient. Analysis shows that DSEFT is superior to traditional exponential forgetting transform as an instantaneous frequency estimator. The bias and the mean square deviation of the estimator are much less than that of the previous one. An
1．虽然Cohen类分布能够提供较高的时频聚集度，但是会产生具有干扰作用的交叉项，并且叠加的噪声也会影响对信号的分析。目前多数处理方法都针对单通道的数据，而本文提出的利用对称阵元的互Wigner分布平均算法，这种方法能够有效的补偿信号在不同阵元上面产生的时差，并且获得较好的表示效果。与传统的Wigner分布阵列平均方法相比，由于到达不同阵元的噪声之间彼此不相干，因此采用互Wigner分布平均的方法能够有效去除噪声的干扰，获得改善的时频分布形式。
2．计算信号的时频分布并不是最终的目的，而只是为信号的进一步分析进行准备。因此我们考虑时频分布的后处理方法。与通常的计算核函数设计方法有所区别，如果把时频分布当作一幅图像，则每一个时频点都对应着图像中的一个像素，时频分布的幅度对应图像的灰度。从图像处理的角度来看，时频分布中的自项对应图像中有用的对象成分，而交叉项和噪声则构成了图像的干扰背景。因此对时频分布的改善可以等效为对图像中有效成分的提取以及背景抑制的问题。本文提出了利用数字图像处理技术的时频分布改善算法。
3．指数遗忘分布作为一类高效的时频分布迭代算法被提出，在这种方法中，信号的旧样本不是简单的丢弃，而是通过特殊类型的计算窗口来逐渐的消除其影响。同时在某一个时间点上面的时频分布可以通过有效的利用在前面的数据段上的计算结果来获得，这样将大大提高运算的效率。本文提出了指数遗忘分布的改进算法，分析表明其具有最高效率的计算结构。同时还分析了指数遗忘分布的瞬时频率表示性能，分析表明采用单边计算窗口的时频分布类型不能够准确及时的跟踪信号的频率变化。在分析频率快速变化的信号的时候，该类分布会产生频率表示的漂移现象。
4．提出了采用对称计算窗口的双边指数遗忘分布形式，与其他类型的时频分布相比，这种方法具有很高的计算效率，同时能够获得比指数遗忘分布更为准确的瞬时频率表示效果，瞬时频率表示的偏差和方差都大大的减小了。文章中还提
出了利用余弦窗口的信号时频分布迭代算法。由于余弦窗口对称并且具有有限的
宽度，因此这种分布形式能够兼顾计算的效率与实时性要求。
5.提出了基于对称阵元互Wigner分布平均的瞬时频率估计算法，这种方法利
用多通道数据对时频分布的瞬时频率估计方法的性能进行了有效的改善，并且能
够在低信噪比的条件下获得良好的估计效果，
6.对于具有恒定幅度的调频信号而言，瞬时频率代表了其全部的信息，可以
据此对信号进行识别和分类。然而如果信号中出现频率或者相位的不连续点的时
候，会相应的引起时频分布的幅度变化，为有效的提取信号的时频特征，本文对
由于信号相位和频率的不连续点引起的时频分布幅度变化规律进行了讨论。分析
表明这种方法能够准确的定位这些不连续点，同时对跳变值进行估计。
7.提出了基于瞬时频率的信号到达角估计算法。与信号子空间拟合方法不同，
这种方法有效利用频率的估计结果，对不同阵元上面的时差进行计算，从而估算
出信号的到达角。这种方法可以应用于宽带信号场合。
关键词:时频分布，阵列信号处理，空间平滑，迭代算法，瞬时频率，相位不连
续点，到达角估计
Time-frequency distributions were introduced as a means of representing signals whose frequency content is varying with time, and for which both time domain representation and frequency representation are inadequate to describe the signal appropriately. This dissertation is intended to incorporate time-frequency analysis into array signal processing for the estimation of radar signal parameters. Compared with traditional solutions that try to analyze signals received by single sensor, in the situation of radar signal estimation the source array manifolds make it possible to improve time-frequency representation through time sequences obtained through multi-channel. The estimation of direction of arrival, extraction of time-frequency characters, algorithms for efficient time-frequency computation and the methods to estimate instantaneous frequency are discussed.1. However the Cohen class time-frequency distributions can provide better concentration, they are suffered from the cross-terms and the noise in the time-frequency plane. Different from traditional practice that tries to deal with this problem through samples obtained from single channel, the approach to improve time-frequency distribution using averaged cross Wigner-Ville distributions between the sensors at symmetrical places is investigated, which tries to make full use of the advantage of sensor array. Compared with the array averaged Wigner distribution, it can provide better performance and compensate the time delays among the signals impinging on different antennas. Since the noise arrives at each sensor is uncorrelated. The average of cross Wigner distributions can effectively improve the time-frequency representation.2. To compute time-frequency distribution is not the aim but just a preparation for further estimation. So we consider the post process of TFD. Unlike the methods such as computational kernel design, the time-frequency representation can be considered as an image where the pixels correspond to the time-frequency points and their intensity to the magnitude of the transform. From the viewpoint of image processing, the auto-terms of the signal can be defined as objects in the image while all the interfering cross terms and the noise form the background in the image. Therefore it is natural for the introduction of image processing technique to time-frequency representation area, and the attempt to promote the time-frequency representation is equal to extract these
objects from the resultant image with background suppression.3. Exponentially forgetting transform (EFT) is discussed in detail in this paper, as an efficient recursive algorithm .to compute time-frequency distribution. In this approach, instead of excluding the old samples, their importance is diminished by using a special computational window, thus recursive operations can be introduced which incorporate knowledge of the time-frequency distribution from previous data blocks into the current estimate and greatly increase the computation efficiency. Under its analysis, we propose the modified version, which has the simplest recursive computation structure. The performance of EFT is investigated, which indicates that time-frequency distributions using single-sided window could not accurately trace the variation of the instantaneous frequency, since their performance depend only on the history of the signal, so they are biased frequency estimator. The excursion of instantaneous frequency representation will be resulted when EFT is applied to signals with rapidly varying frequency contents.4. The double-sided exponentially forgetting transform (DSEFT) is also presented which offers better time-frequency resolution. Compared with other forms of time-frequency representation, DSEFT is highly computational efficient. Analysis shows that DSEFT is superior to traditional exponential forgetting transform as an instantaneous frequency estimator. The bias and the mean square deviation of the estimator are much less than that of the previous one. An
引文
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