本文選題：陣列信號(hào)處理 + 信源參數(shù)估計(jì)�。� 參考：《吉林大學(xué)》2014年博士論文

【摘要】：信源參數(shù)估計(jì)是陣列信號(hào)處理領(lǐng)域的主要研究?jī)?nèi)容之一，在雷達(dá)、聲吶、無(wú)線通信、醫(yī)學(xué)成像、電子對(duì)抗及地震勘探等領(lǐng)域有著重要的應(yīng)用價(jià)值。傳統(tǒng)的信源參數(shù)估計(jì)方法中以子空間類(lèi)方法最具代表性，然而正是由于子空間理論框架的限制，其存在的共有以及特有的一些缺點(diǎn)目前還無(wú)法被完全突破。近年來(lái)，隨著壓縮感知理論體系的出現(xiàn)和不斷完善，，作為其核心理論的稀疏信號(hào)重構(gòu)引起了國(guó)內(nèi)外學(xué)者的廣泛關(guān)注。從稀疏信號(hào)重構(gòu)角度進(jìn)行陣列信號(hào)參數(shù)估計(jì)可以獲得諸如高分辨率、強(qiáng)噪聲魯棒性和無(wú)需信源數(shù)的先驗(yàn)信息等諸多潛在優(yōu)勢(shì)，稀疏重構(gòu)理論和方法為解決或者規(guī)避傳統(tǒng)信源參數(shù)估計(jì)方法中存在的問(wèn)題提供了一條可能的途徑。 現(xiàn)有基于稀疏重構(gòu)的信源參數(shù)估計(jì)方法主要集中于遠(yuǎn)場(chǎng)源的一維DOA參數(shù)估計(jì)，且大多存在估計(jì)偏或者全局最優(yōu)性不能保證等問(wèn)題。本文以魯棒的陣列信號(hào)多參數(shù)估計(jì)的理論需求為牽引，以稀疏信號(hào)重構(gòu)為數(shù)學(xué)處理手段，在系統(tǒng)分析與評(píng)價(jià)現(xiàn)有代表性稀疏重構(gòu)算法在信源參數(shù)估計(jì)中的適用性的基礎(chǔ)上，由淺入深、循序漸進(jìn)的對(duì)陣列遠(yuǎn)場(chǎng)源DOA和功率參數(shù)估計(jì)、陣列遠(yuǎn)近場(chǎng)混合源DOA和距離參數(shù)估計(jì)，以及極化敏感陣列下的遠(yuǎn)場(chǎng)源DOA、功率和極化參數(shù)估計(jì)問(wèn)題進(jìn)行深入的研究。旨在稀疏信號(hào)重構(gòu)框架下為不同場(chǎng)景下的陣列信號(hào)多參數(shù)估計(jì)問(wèn)題研究提供新而有效的解決思路。 本文的主要貢獻(xiàn)與創(chuàng)新性工作包括： 1.在高斯白噪聲、未知非均勻噪聲背景下，應(yīng)用TLP、DC分解理論以及求和平均運(yùn)算，提出了基于二階統(tǒng)計(jì)量向量稀疏表示和l0范數(shù)逼近的DOA和功率參數(shù)聯(lián)合估計(jì)新算法。從理論上證明了所提的l0范數(shù)逼近稀疏重構(gòu)算法不僅是收斂的，而且是穩(wěn)定的、漸進(jìn)無(wú)偏的。分別采用差異原則和交叉驗(yàn)證選擇合理的正則化參數(shù)和調(diào)整參數(shù)。該算法不僅可以有效地抑制高斯白噪聲和未知非均勻噪聲，而且克服了現(xiàn)有l(wèi)1范數(shù)約束方法（如LASSO、BPDN或Group LASSO）中普遍存在的估計(jì)偏的問(wèn)題，獲得了更高的分辨率、估計(jì)精度和噪聲魯棒性，而且無(wú)需精確的初始條件。 2.在未知色噪聲背景下，利用協(xié)方差差分可以有效抑制具有對(duì)稱(chēng)Topelitz結(jié)構(gòu)的色噪聲的特性，提出了基于Adaptive LASSO和協(xié)方差差分的DOA和功率估計(jì)新算法。借助過(guò)完備基矩陣的特殊結(jié)構(gòu)，利用留一交叉驗(yàn)證的一種特殊形式來(lái)選擇合理的正則化參數(shù)。該算法不僅有效地抑制了色噪聲的影響，獲得了更高的DOA和功率參數(shù)估計(jì)精度，而且避免了噪聲協(xié)方差矩陣的估計(jì)以及無(wú)需信源數(shù)的先驗(yàn)信息。同時(shí)還可以通過(guò)對(duì)譜峰值正負(fù)號(hào)的判斷，簡(jiǎn)單而有效地解決應(yīng)用協(xié)方差差分技術(shù)帶來(lái)的偽峰區(qū)分問(wèn)題。 3.針對(duì)對(duì)稱(chēng)均勻線性陣列，分別在二階統(tǒng)計(jì)量域和四階累積量域構(gòu)建稀疏觀測(cè)模型，基于多維參數(shù)求解轉(zhuǎn)化為多個(gè)一維參數(shù)分別求解的思想，提出了基于四階累積量向量稀疏表示和重加權(quán)l(xiāng)1范數(shù)約束的遠(yuǎn)近場(chǎng)混合源參數(shù)估計(jì)方法、基于加權(quán)l(xiāng)1范數(shù)約束和MUSIC的遠(yuǎn)近場(chǎng)混合源參數(shù)估計(jì)方法。分別采用交叉驗(yàn)證和L曲線法選擇合理的正則化參數(shù)。所提的兩種新算法在保證參數(shù)估計(jì)精度的同時(shí)，不僅有效地降低了計(jì)算復(fù)雜度、避免了不必要的網(wǎng)格劃分和參數(shù)配對(duì)過(guò)程，而且還適用于遠(yuǎn)場(chǎng)源和近場(chǎng)源情況下的參數(shù)估計(jì)，是一類(lèi)通用的算法。 4.率先將稀疏重構(gòu)思想拓展至極化敏感陣列，提出了交叉電偶極子陣下基于稀疏重構(gòu)的DOA、功率和極化參數(shù)估計(jì)新算法。討論了如何在極化敏感陣列下基于稀疏重構(gòu)獲得精確的多參數(shù)估計(jì)以及如何借助極化信息來(lái)進(jìn)一步改善算法的適用性和參數(shù)估計(jì)性能。仿真結(jié)果顯示所提算法不僅可以同時(shí)估計(jì)信源的DOA、功率和極化參數(shù)，而且可以獲得改進(jìn)的分辨率和噪聲魯棒性，同時(shí)還可借助極化信息有效地區(qū)分兩個(gè)入射角度一樣的信源信號(hào)。 本文在稀疏信號(hào)重構(gòu)理論框架下，對(duì)標(biāo)量陣列和矢量陣列下的信號(hào)多參數(shù)估計(jì)問(wèn)題進(jìn)行了深入的研究。提出的上述新算法，在估計(jì)精度、噪聲魯棒性、分辨率和對(duì)信源數(shù)的敏感性等方面較現(xiàn)有方法均有一定的改善，為進(jìn)一步研究基于稀疏重構(gòu)理論的陣列信號(hào)處理相關(guān)問(wèn)題提供參考。
[Abstract]:The source parameter estimation is one of the main research fields in the field of array signal processing. It has important application value in radar, sonar, wireless communication, medical imaging, electronic countermeasures and seismic exploration. The subspace class method is the most representative of the traditional source parameter estimation methods, but it is due to the limit of the subspace theory frame. In recent years, with the emergence and continuous improvement of the theory of compressed sensing theory, sparse signal reconstruction, as its core theory, has aroused wide attention of scholars both at home and abroad. Such as high resolution, strong noise robustness and prior information without the need for the number of sources, sparse reconstruction theory and methods provide a possible way to solve or avoid the existing problems in the traditional source parameter estimation method.
The existing estimation methods of source parameters based on sparse reconstruction mainly focus on the one dimension DOA parameter estimation of far field sources, and most of them have the problem of estimation bias or global optimality. In this paper, the theoretical requirement of Robust Array Signal multi parameter estimation is tractive and sparse signal signal reconstruction is used as a mathematical processing method. Based on the applicability of the existing representative sparse reconstruction algorithm in the source parameter estimation, the problem of the estimation of the power and polarization parameters of the array far field source DOA and power parameter estimation, the array far and near field hybrid source DOA and the distance parameter estimation, the far field source DOA under the polarization sensitive array, and the estimation of the power and polarization parameters are carried out in the light of the existing representative sparse reconstruction algorithm. The aim of this study is to provide a new and effective solution for multi parameter estimation of array signals in different scenarios under the framework of sparse signal reconstruction.
The main contributions and innovative work of this article include:
1. under the background of Gauss white noise and unknown nonuniform noise, a new algorithm for joint estimation of DOA and power parameters based on the sparse representation of the two order statistics vector and the approximation of the l0 norm is proposed by using the TLP, DC decomposition theory and the summation mean operation. It is theoretically proved that the proposed l0 norm approximation sparse reconstruction algorithm is not only convergent, but also a new algorithm. It is stable, asymptotically unbiased. Using the principle of difference and cross validation, we choose reasonable regularization parameters and adjustment parameters. This algorithm can not only effectively suppress Gauss white noise and unknown nonuniform noise, but also overcome the existing L1 norm constraint methods (such as LASSO, BPDN or Group LASSO). It achieves higher resolution, estimation accuracy and noise robustness, and does not require precise initial conditions.
2. under the background of unknown color noise, the characteristic of color noise with symmetric Topelitz structure can be effectively suppressed by covariance difference. A new algorithm for DOA and power estimation based on Adaptive LASSO and covariance difference is proposed. The algorithm not only effectively inhibits the influence of color noise, but also obtains higher accuracy of DOA and power parameter estimation, and avoids the estimation of the noise covariance matrix and the prior information of the number of sources without the need of the number of sources. The problem of pseudo peak distinction is brought about by the operation.
3. for symmetric and uniform linear array, the sparse observation model is constructed in the two order statistics domain and the four order cumulant domain respectively. Based on the multi-dimensional parameter solution to the idea of multiple one-dimensional parameters, a method based on the four order cumulant vector sparse representation and the heavy weighted L1 norm constraint is proposed. The weighted L1 norm constraint and the far and near field hybrid source parameter estimation method of MUSIC are used to select the reasonable regularization parameters with the cross validation and the L curve method respectively. The two new algorithms not only effectively reduce the computational complexity, but also avoid unnecessary mesh division and parameter matching process. It is also applicable to parameter estimation in far-field sources and near field sources. It is a general algorithm.
4. first, the sparse reconstruction idea is extended to the polarization sensitive array, and a new algorithm for estimating the power and polarization parameters based on the sparse reconfiguration is proposed in the cross electric dipole array based on the sparse reconfiguration. How to obtain accurate multi parameter estimation and how to improve the algorithm by polarization information is discussed under the sparse reconfiguration of the polarization sensitive array. The simulation results show that the proposed algorithm can not only estimate the DOA, power and polarization parameters of the source at the same time, but also obtain improved resolution and noise robustness. At the same time, the proposed algorithm can also be effectively divided into two signal source signals with the aid of polarization information.
Under the framework of sparse signal reconstruction, this paper studies the multi parameter estimation of signal under scalar array and vector array. The new algorithm proposed in this paper has a certain improvement in estimation accuracy, noise robustness, resolution and sensitivity to the number of sources. Sparse reconstruction theory provides reference for array signal processing.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TN911.23

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