本文選題：窄帶 + 寬帶��； 參考：《哈爾濱工業(yè)大學(xué)》2017年碩士論文

【摘要】：陣列信號處理技術(shù)是屬于高級信號處理技術(shù)的一大重要研究領(lǐng)域,主要對到達(dá)一組傳感器節(jié)點處帶噪信號進(jìn)行檢測和定位。近年來,陣列信號處理技術(shù)得到了快速發(fā)展。許多領(lǐng)域,比如無線通信、石油開采、雷達(dá)、聲吶以及地震探查都需要到達(dá)角估計,而這正是陣列信號處理技術(shù)的主要研究內(nèi)容。到達(dá)角估計包括傳感器處理和分析它的空間譜。信號的空間譜表示了從所有方向到達(dá)接收機(jī)處信號的分布情況。因此,如果科研人員一旦能夠獲得了信號的空間譜,則所需信號的到達(dá)角就能夠得知了。從這一方面來講,我們也可以把空間譜估計成為到達(dá)角估計。本文主要研究基于信號稀疏表示的寬帶信號到達(dá)角估計問題。信號的稀疏表示或者壓縮感知技術(shù)是建立于這樣的事實,即我們可以在合適的基底或者字典下將信號分解,僅僅使用一些非零的基底系數(shù)就可以,在一定誤差范圍內(nèi),表示原始信號�？偹苤�,根據(jù)奈奎斯特準(zhǔn)則,當(dāng)以感興趣信號最高頻率的2倍對該信號進(jìn)行均勻采樣,則可以在頻域通過濾波器將原始信號無損恢復(fù)出來。不幸的是,在許多重要的和新興的應(yīng)用場合,達(dá)到符合奈奎斯特定理的超高采樣速率會因為成本太高,或者在物理器件上不可行而難以實現(xiàn)。稀疏信號額可壓縮信號都可以通過在合適基底下信號的最大基底系數(shù)值和該值所在位置,而高度精確地表示原始信號。利用變換編碼的概念,壓縮感知作為一個新的信號獲取和傳感器設(shè)計的框架而出現(xiàn)。通過壓縮感知技術(shù),可以將能夠稀疏表示或者可壓縮信號的采樣開銷和計算復(fù)雜度進(jìn)行大規(guī)模地降低。另外,根據(jù)“奈奎斯特—香農(nóng)”采樣定理可知,為了完全獲得任意一個帶寬受限信號,必須要滿足特定的最小采樣頻率。當(dāng)信號在一個一組已知基底下具有稀疏性,我們可以大規(guī)模地減小需要存儲的測量數(shù)據(jù)而不損失原始信號的特征。因此,相比于經(jīng)典的信號表示技術(shù)及采樣方法,利用信號稀疏表示技術(shù)或者壓縮感知技術(shù),我們或許可以得到更好的結(jié)果。以下就是壓縮感知技術(shù)的基本理論觀點:不同于先以高速率采樣之后壓縮樣本數(shù)據(jù),我們尋求直接以壓縮的方式感知原始數(shù)據(jù)的方法,即完成低速率采樣的任務(wù)。為解決處理這類高維度數(shù)據(jù)隨之而來的邏輯和計算上的困難,我們常常依賴于壓縮技術(shù),即在滿足可接受誤差范圍內(nèi),尋找感興趣信號最簡潔的表示方式。因此,我們需要稀疏表示技術(shù)或者壓縮感知技術(shù)�；诘竭_(dá)角估計的壓縮感知技術(shù)是基于以下觀察到的情況,即一幫場景下,可能的信源數(shù)量圓圓小于可能的空間頻率數(shù)量,也就是接收機(jī)接收到的信號本質(zhì)上是可稀疏的。近年來,很多研究人員關(guān)注于稀疏基到達(dá)角估計技術(shù),與早期的估計技術(shù)相比,該稀疏基到達(dá)角估計技術(shù)具有更高的估計效率�？紤]到現(xiàn)有技術(shù)通過一個“連貫—平均”協(xié)方差矩陣或者通過最大似然的方法來恢復(fù)模型階數(shù),估計寬帶新源個數(shù)是一項非常困難的任務(wù)。本文中將介紹L1-SVD技術(shù)作為主要的到達(dá)角估計技術(shù)。本文會提出一種基于傳感器測量信號稀疏表示的信源定位方法,該稀疏表示是在一個過完備基底下完成的,該過完備基底是由陣列復(fù)制得到的采樣值所組成。本文通過引入基于L1—范數(shù)的懲罰項來迫使信號具有稀疏性。一系列最近關(guān)于L1懲罰項的稀疏特征的理論結(jié)果證明了該方法的有效性。另外,本文使用數(shù)據(jù)矩陣的奇異值分解來概括多時間、對頻率采樣。許多研究領(lǐng)域,比如無線通信、石油開采、雷達(dá)、聲吶以及地震探查都需要寬帶信號的到達(dá)角估計。寬帶信號具有在中心頻率兩側(cè)非常寬的頻帶。并且,并不需要使用傅里葉變換或者通過信號插值來明確的波長和實驗特點。對于寬帶信源來說,常常在頻域分析到達(dá)角問題。大部分現(xiàn)有的寬帶到達(dá)角估計算法是將寬帶信號分解為若干個窄帶頻率帶,在估計到達(dá)角之前,將各個窄帶頻率帶集中或者變換到一個參考頻率間隔。本文中,使用了不同的頻率帶處理。首先,信號的整個頻譜被劃分為若干個小頻段,每個小頻段支持窄帶近似,之后,在每一個小頻段應(yīng)用L1-SVD技術(shù)來獲得相干譜。上述過程完成之后,我們僅僅將每一個小窄帶頻譜合成一個完全的寬帶頻譜。這個方法看起來很復(fù)雜,實際操作起來也確實很復(fù)雜,但本文選用這種方法是因為該方法是一種檢測寬帶信號的有效手段。除此之外,這項技術(shù)不需要任意的強(qiáng)假設(shè)條件,而其他現(xiàn)有的類似技術(shù)往往需要關(guān)于信號源較強(qiáng)的假設(shè)。本文提出的基于陣列輸出多重采樣奇異值分解的方法使用一個二階錐形規(guī)劃算法來優(yōu)化得到的目標(biāo)函數(shù)。該方法的關(guān)鍵在于使用一個合適的非二次正則化函數(shù),該正則化函數(shù)會引出稀疏限制和超解。因此,源定位問題就變換成一個可以通過有效算法解決的凸優(yōu)化問題。綜上所述,本文將會給出一個基于寬帶信源壓縮感知的到達(dá)角估計綜述。進(jìn)展如下:(1)首先,為了方便初級讀者本文給出了便于初學(xué)者理解到達(dá)角估計的基礎(chǔ)知識,稀疏表示的必要理論基礎(chǔ),以及稀疏表示是如何與到達(dá)角估計建立聯(lián)系的。(2)其次,我建立了帶有陣列傳感器的DOA估計情景的通用模型。之后,本文分別推導(dǎo)了窄帶和寬帶場景下的數(shù)學(xué)模型。L1-SVD技術(shù)首先針對窄帶場景進(jìn)行了描述,然后擴(kuò)展到寬帶場景。本文給出了兩張示意圖來幫助讀者快速理解相關(guān)概念。之后,選擇調(diào)節(jié)參數(shù)的一個重要參考因素將在討論。(3)再次,本文展示了寬帶、窄帶環(huán)境下,相關(guān)的到達(dá)角估計結(jié)果,其次是寬帶DOA的誤差估計,以顯示所描述的L1-SVD方法如何跟蹤入射到陣列傳感器上的信號的角度。另外,考慮到所述方法的優(yōu)缺點,這里本文也給出了一些關(guān)于寬帶到達(dá)角估計中所用信號的基本觀點,即一種在雷達(dá)和聲吶探測中廣泛使用的Chirp信號。(4)最后,本文也討論了到達(dá)角估計未來的發(fā)展方向,以及如何發(fā)展以滿足將來更方便、更高級的應(yīng)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.

【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN911.7

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