基于稀疏表征的宽带信号DOA估计

发布时间：2018-04-29 14:30

本文选题：窄带 + 宽带　；参考：《哈尔滨工业大学》2017年硕士论文

【摘要】：阵列信号处理技术是属于高级信号处理技术的一大重要研究领域,主要对到达一组传感器节点处带噪信号进行检测和定位。近年来,阵列信号处理技术得到了快速发展。许多领域,比如无线通信、石油开采、雷达、声呐以及地震探查都需要到达角估计,而这正是阵列信号处理技术的主要研究内容。到达角估计包括传感器处理和分析它的空间谱。信号的空间谱表示了从所有方向到达接收机处信号的分布情况。因此,如果科研人员一旦能够获得了信号的空间谱,则所需信号的到达角就能够得知了。从这一方面来讲,我们也可以把空间谱估计成为到达角估计。本文主要研究基于信号稀疏表示的宽带信号到达角估计问题。信号的稀疏表示或者压缩感知技术是建立于这样的事实,即我们可以在合适的基底或者字典下将信号分解,仅仅使用一些非零的基底系数就可以,在一定误差范围内,表示原始信号。总所周知,根据奈奎斯特准则,当以感兴趣信号最高频率的2倍对该信号进行均匀采样,则可以在频域通过滤波器将原始信号无损恢复出来。不幸的是,在许多重要的和新兴的应用场合,达到符合奈奎斯特定理的超高采样速率会因为成本太高,或者在物理器件上不可行而难以实现。稀疏信号额可压缩信号都可以通过在合适基底下信号的最大基底系数值和该值所在位置,而高度精确地表示原始信号。利用变换编码的概念,压缩感知作为一个新的信号获取和传感器设计的框架而出现。通过压缩感知技术,可以将能够稀疏表示或者可压缩信号的采样开销和计算复杂度进行大规模地降低。另外,根据“奈奎斯特—香农”采样定理可知,为了完全获得任意一个带宽受限信号,必须要满足特定的最小采样频率。当信号在一个一组已知基底下具有稀疏性,我们可以大规模地减小需要存储的测量数据而不损失原始信号的特征。因此,相比于经典的信号表示技术及采样方法,利用信号稀疏表示技术或者压缩感知技术,我们或许可以得到更好的结果。以下就是压缩感知技术的基本理论观点:不同于先以高速率采样之后压缩样本数据,我们寻求直接以压缩的方式感知原始数据的方法,即完成低速率采样的任务。为解决处理这类高维度数据随之而来的逻辑和计算上的困难,我们常常依赖于压缩技术,即在满足可接受误差范围内,寻找感兴趣信号最简洁的表示方式。因此,我们需要稀疏表示技术或者压缩感知技术。基于到达角估计的压缩感知技术是基于以下观察到的情况,即一帮场景下,可能的信源数量圆圆小于可能的空间频率数量,也就是接收机接收到的信号本质上是可稀疏的。近年来,很多研究人员关注于稀疏基到达角估计技术,与早期的估计技术相比,该稀疏基到达角估计技术具有更高的估计效率。考虑到现有技术通过一个“连贯—平均”协方差矩阵或者通过最大似然的方法来恢复模型阶数,估计宽带新源个数是一项非常困难的任务。本文中将介绍L1-SVD技术作为主要的到达角估计技术。本文会提出一种基于传感器测量信号稀疏表示的信源定位方法,该稀疏表示是在一个过完备基底下完成的,该过完备基底是由阵列复制得到的采样值所组成。本文通过引入基于L1—范数的惩罚项来迫使信号具有稀疏性。一系列最近关于L1惩罚项的稀疏特征的理论结果证明了该方法的有效性。另外,本文使用数据矩阵的奇异值分解来概括多时间、对频率采样。许多研究领域,比如无线通信、石油开采、雷达、声呐以及地震探查都需要宽带信号的到达角估计。宽带信号具有在中心频率两侧非常宽的频带。并且,并不需要使用傅里叶变换或者通过信号插值来明确的波长和实验特点。对于宽带信源来说,常常在频域分析到达角问题。大部分现有的宽带到达角估计算法是将宽带信号分解为若干个窄带频率带,在估计到达角之前,将各个窄带频率带集中或者变换到一个参考频率间隔。本文中,使用了不同的频率带处理。首先,信号的整个频谱被划分为若干个小频段,每个小频段支持窄带近似,之后,在每一个小频段应用L1-SVD技术来获得相干谱。上述过程完成之后,我们仅仅将每一个小窄带频谱合成一个完全的宽带频谱。这个方法看起来很复杂,实际操作起来也确实很复杂,但本文选用这种方法是因为该方法是一种检测宽带信号的有效手段。除此之外,这项技术不需要任意的强假设条件,而其他现有的类似技术往往需要关于信号源较强的假设。本文提出的基于阵列输出多重采样奇异值分解的方法使用一个二阶锥形规划算法来优化得到的目标函数。该方法的关键在于使用一个合适的非二次正则化函数,该正则化函数会引出稀疏限制和超解。因此,源定位问题就变换成一个可以通过有效算法解决的凸优化问题。综上所述,本文将会给出一个基于宽带信源压缩感知的到达角估计综述。进展如下:(1)首先,为了方便初级读者本文给出了便于初学者理解到达角估计的基础知识,稀疏表示的必要理论基础,以及稀疏表示是如何与到达角估计建立联系的。(2)其次,我建立了带有阵列传感器的DOA估计情景的通用模型。之后,本文分别推导了窄带和宽带场景下的数学模型。L1-SVD技术首先针对窄带场景进行了描述,然后扩展到宽带场景。本文给出了两张示意图来帮助读者快速理解相关概念。之后,选择调节参数的一个重要参考因素将在讨论。(3)再次,本文展示了宽带、窄带环境下,相关的到达角估计结果,其次是宽带DOA的误差估计,以显示所描述的L1-SVD方法如何跟踪入射到阵列传感器上的信号的角度。另外,考虑到所述方法的优缺点,这里本文也给出了一些关于宽带到达角估计中所用信号的基本观点,即一种在雷达和声呐探测中广泛使用的Chirp信号。(4)最后,本文也讨论了到达角估计未来的发展方向,以及如何发展以满足将来更方便、更高级的应用需求。
[Abstract]:Array signal processing technology is one of the most important research fields of advanced signal processing technology. It is mainly to detect and locate the noisy signal at a group of sensor nodes. In recent years, the array signal processing technology has been developed rapidly. Many fields, such as wireless communication, oil mining, radar, sonar and seismic exploration all need. The angle estimation, and this is the main content of the array signal processing technology. The angle of arrival includes the sensor processing and analysis of its spatial spectrum. The spatial spectrum of the signal indicates the distribution of the signal from all directions to the receiver. Therefore, if the researcher can get the spatial spectrum of the signal once enough, the signal is required. In this respect, we can also estimate the space spectrum as the estimation of the angle of arrival. This paper mainly studies the estimation of the angle of arrival of wide-band signals based on the signal sparse representation. The sparse representation of the signal or the compression sensing technique is based on the fact that we can be in the right base or in the right way. The signal is decomposed in the dictionary, and only some non zero base coefficients can be used to represent the original signal in a certain error range. It is well known that, according to Nyquist criterion, the original signal can be recovered in the frequency domain by a filter, when the signal is uniformly sampled at 2 times the highest frequency of the signal of interest. Fortunately, in many important and emerging applications, the high sampling rate that meets the Nyquist theorem will be difficult to achieve because of the high cost or infeasible on the physical device. The sparse signal volume compressible signal can all pass through the maximum base system value of the signal under the appropriate base and the position of the value, and the height of the signal. Using the concept of transform coding, compression perception appears as a new framework for signal acquisition and sensor design. By compressed sensing technology, the sampling overhead and computational complexity of sparse representation or compressible signals can be greatly reduced. In addition, according to "Nyquist -" Shannon's sampling theorem shows that in order to fully obtain any bandwidth limited signal, it is necessary to satisfy a specific minimum sampling frequency. When the signal is sparsely under a set of known bases, we can reduce the measured data that needs to be stored on a large scale without losing the characteristics of the original signal. Therefore, compared to the classic signal. We may be able to get better results by means of technology and sampling methods, using signal sparse representation or compressed sensing technology. The following is the basic theory of compressed sensing technology: different from compression sample data after high rate sampling, we seek a method of sensing raw data in a compressed way. That is, To accomplish the task of low rate sampling. In order to solve the logical and computational difficulties associated with this kind of high dimensional data, we often rely on the compression technique, that is, to find the most concise expression of the interest signal within the acceptable range of error. Therefore, we need sparse representation or compression sensing technology. The compressed sensing technology of the angular estimation is based on the following observations, that is, in a group of scenes, the number of possible sources is less than the possible number of spatial frequencies, or the signal received by the receiver is in essence sparse. In recent years, many researchers have paid attention to the estimation of the sparse base of arrival angle and the early estimation techniques. In comparison, the sparse base arrival angle estimation technique has a higher estimation efficiency. Considering the existing technology to restore the model order through a "coherent - average" covariance matrix or the maximum likelihood method, it is a very difficult task to estimate the number of new sources of broadband. This paper will introduce the L1-SVD technology as the main one. In this paper, a source localization method based on sparse representation of sensor measurement signals is proposed. This sparse representation is completed under an overcomplete base. The overcomplete substrate is composed of the sampled values obtained by the array replication. This paper introduces a L1 - norm based penalty term to force the signal to be sparsely. A series of recent theoretical results about the sparse characteristics of L1 penalty terms prove the effectiveness of the method. In addition, this paper uses the singular value decomposition of the data matrix to generalize the multi time and frequency sampling. Many research fields, such as wireless communication, oil mining, radar, sonar, and seismic exploration, all need the estimation of the wideband signal. Wideband signals have a very wide band on both sides of the center frequency. Moreover, it is not necessary to use Fourier transform or signal interpolation to determine the wavelength and experimental characteristics. For broadband sources, the angle of arrival is often analyzed in the frequency domain. Most existing wideband angle estimation algorithms are the decomposition of a wide band signal into several Narrow band frequency band, before estimating arrival angle, each band frequency band is concentrated or converted to a reference frequency interval. In this paper, different frequency band processing is used. First, the whole spectrum of the signal is divided into several small bands, each small band supports narrowband similar. After that, the L1-SVD technology is applied to each small frequency band. The coherent spectrum is obtained. After the process is completed, we only synthesize a complete broadband spectrum of each small narrow band spectrum. This method looks very complex and really complicated, but this method is chosen because the method is an effective means to detect broadband signals. In this paper, a two order conical programming algorithm is used to optimize the obtained objective function. The key of this method is to use a suitable non two time positive. Thus, the regularization function will lead to sparse and super solutions. Therefore, the source localization problem is transformed into a convex optimization problem that can be solved by an effective algorithm. In this paper, a summary of the estimation of the angle of arrival based on the wideband source compression perception is given. (1) first, for the convenience of the primary reader The basic knowledge that is convenient for beginners to understand the estimation of the angle of arrival, the necessary theoretical basis of sparse representation, and how the sparse representation is associated with the estimation of the angle of arrival. (2) Secondly, I have established a general model of the DOA estimation scenario with an array sensor. After that, the mathematical model.L in the narrow band and the broadband scene is derived. The 1-SVD technology first describes the narrow band scene and then extends to the wideband scene. In this paper, two schematic diagrams are given to help the reader to quickly understand the related concepts. After that, an important reference factor for selecting the parameters of the adjustment will be discussed. (3) again, this paper shows the estimated results of the related angle of arrival in the broadband and narrow band environment, secondly, It is an error estimate of the wideband DOA to show how the L1-SVD method described to track the angle of the signal incident on the array sensor. In addition, taking into account the advantages and disadvantages of the proposed method, this paper also gives some basic views on the signals used in the wideband angle of arrival estimation, that is, widely used in radar and sonar detection. Chirp signal. (4) finally, the future development direction of DOA estimation is also discussed, and how to develop it to meet future more convenient and more advanced application needs.

【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

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