基于貝葉斯壓縮感知的波達(dá)方向估計(jì)算法研究
發(fā)布時(shí)間：2018-12-18 09:15
【摘要】：波達(dá)方向(Direction of Arrival,DOA)估計(jì)是陣列信號(hào)處理的重要分支之一,自從第二次世界大戰(zhàn)以來,其發(fā)展迅速,并且被廣泛應(yīng)用在軍事和民用的各個(gè)方面。經(jīng)典的DOA估計(jì)算法主要分為子空間分解和子空間擬合兩類,這兩類算法都需要在多快拍條件下進(jìn)行,并且都有著各自本身難以克服的缺陷。壓縮感知(Compressive Sensing,CS)理論克服了 Nyquist采樣定理的限制,為信號(hào)處理提供了新的思路。其中,貝葉斯壓縮感知理論是壓縮感知理論的新成果,其從統(tǒng)計(jì)學(xué)的角度,利用假定的先驗(yàn)知識(shí)計(jì)算后驗(yàn)概率,從而得到估計(jì)值。本文正是研究如何利用貝葉斯壓縮感知理論更有效地估計(jì)DOA。首先,論文介紹了課題的研究背景,介紹了 DOA估計(jì)和壓縮感知理論的研究現(xiàn)狀,然后分別研究了窄帶信號(hào)與寬帶信號(hào)下的DOA估計(jì)模型,并重點(diǎn)研究了三種經(jīng)典的子空間類DOA估計(jì)方法和DOA估計(jì)中的克拉美-勞界的問題,這為之后的研究奠定了基礎(chǔ)。其次,研究了壓縮感知兩類重要的重構(gòu)算法,貪婪算法和凸優(yōu)化算法。在貪婪算法中,研究了單快拍(SMV)和多快拍(MMV)下的OMP算法,并將其分別應(yīng)用到DOA估計(jì)中。研究了凸優(yōu)化算法在DOA估計(jì)中的應(yīng)用,L1-SVD算法,L1-SVD通過構(gòu)造懲罰項(xiàng)轉(zhuǎn)化L1范數(shù)的求解問題,并通過奇異值分解對(duì)數(shù)據(jù)降維,最后利用凸優(yōu)化求解。然后引入將寬帶在頻域分組變成一系列窄帶,進(jìn)而對(duì)窄帶進(jìn)行處理的方法,給出了 L1-SVD在寬帶下的實(shí)現(xiàn)方案,即L1-SVD-WDOA算法。仿真結(jié)果表明,L1-SVD-WDOA有較好的估計(jì)性能,并且天線數(shù)增加的越多,其性能的改善越明顯。最后,研究了基于RVM的貝葉斯壓縮感知(RVM-BCS)、基于Laplace先驗(yàn)的貝葉斯壓縮感知(LP-BCS),以及多快拍下的壓縮感知(MBCS)算法。RVM-BCS與LP-BCS的最大差別在于先驗(yàn)信息的不同,LP-BCS比RVM-BCS增加了一個(gè)先驗(yàn)信息,因此LP-BCS的重構(gòu)性能優(yōu)于RVM-BCS,公式推導(dǎo)將RVM-BCS和LP-BCS的更新參數(shù)公式統(tǒng)一化,更易于二者的比較。然后將LP-BCS和MBCS應(yīng)用在DOA估計(jì)中。仿真中可以看出,將BCS應(yīng)用到DOA中,在算法性能上有一定的優(yōu)勢(shì)。
[Abstract]:Direction of arrival (Direction of Arrival,DOA) estimation is one of the important branches of array signal processing. Since the second World War, it has developed rapidly and has been widely used in military and civilian fields. The classical DOA estimation algorithms are mainly divided into subspace decomposition and subspace fitting. Both of these algorithms need to be carried out under the condition of multiple beats, and both have their own defects which are difficult to overcome. Compression perception (Compressive Sensing,CS) theory overcomes the limitation of Nyquist sampling theorem and provides a new idea for signal processing. Among them, Bayesian compressed perception theory is a new achievement of compressed perception theory. From the point of view of statistics, the posteriori probability is calculated by using the assumed prior knowledge, and the estimated value is obtained. This paper is to study how to estimate DOA. more effectively by using Bayesian compressed perception theory. Firstly, this paper introduces the research background of the subject, introduces the research status of DOA estimation and compression sensing theory, and then studies the DOA estimation model of narrowband signal and wideband signal, respectively. Three classical subspace-like DOA estimators and the Clame-Laurian bound in the DOA estimator are studied, which lays a foundation for further research. Secondly, two important reconstruction algorithms, greedy algorithm and convex optimization algorithm, are studied. In the greedy algorithm, the OMP algorithm based on single-shot (SMV) and multi-shot (MMV) is studied and applied to DOA estimation. In this paper, the application of convex optimization algorithm in DOA estimation is studied. L1-SVD algorithm and L1-SVD transform L1 norm by constructing penalty term. The dimension of data is reduced by singular value decomposition. Finally, convex optimization is used to solve the problem. Then, the method of converting broadband packet into a series of narrow bands in frequency domain is introduced, and then the method of processing narrow band is introduced. The implementation scheme of L1-SVD under broadband is given, that is, L1-SVD-WDOA algorithm. The simulation results show that L1-SVD-WDOA has better estimation performance, and the more the number of antennas increases, the better the performance is. Finally, Bayesian compression perception (RVM-BCS) based on RVM and Bayesian compression perception (LP-BCS) based on Laplace priori are studied. The biggest difference between RVM-BCS and LP-BCS lies in the difference of prior information. LP-BCS adds a priori information to RVM-BCS, so the reconstruction performance of LP-BCS is superior to that of RVM-BCS,. The formula derivation unifies the updating parameter formula of RVM-BCS and LP-BCS, which is easier to compare. Then LP-BCS and MBCS are applied to DOA estimation. Simulation results show that BCS has some advantages in algorithm performance when it is applied to DOA.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TN911.7
本文編號(hào)：2385631
[Abstract]:Direction of arrival (Direction of Arrival,DOA) estimation is one of the important branches of array signal processing. Since the second World War, it has developed rapidly and has been widely used in military and civilian fields. The classical DOA estimation algorithms are mainly divided into subspace decomposition and subspace fitting. Both of these algorithms need to be carried out under the condition of multiple beats, and both have their own defects which are difficult to overcome. Compression perception (Compressive Sensing,CS) theory overcomes the limitation of Nyquist sampling theorem and provides a new idea for signal processing. Among them, Bayesian compressed perception theory is a new achievement of compressed perception theory. From the point of view of statistics, the posteriori probability is calculated by using the assumed prior knowledge, and the estimated value is obtained. This paper is to study how to estimate DOA. more effectively by using Bayesian compressed perception theory. Firstly, this paper introduces the research background of the subject, introduces the research status of DOA estimation and compression sensing theory, and then studies the DOA estimation model of narrowband signal and wideband signal, respectively. Three classical subspace-like DOA estimators and the Clame-Laurian bound in the DOA estimator are studied, which lays a foundation for further research. Secondly, two important reconstruction algorithms, greedy algorithm and convex optimization algorithm, are studied. In the greedy algorithm, the OMP algorithm based on single-shot (SMV) and multi-shot (MMV) is studied and applied to DOA estimation. In this paper, the application of convex optimization algorithm in DOA estimation is studied. L1-SVD algorithm and L1-SVD transform L1 norm by constructing penalty term. The dimension of data is reduced by singular value decomposition. Finally, convex optimization is used to solve the problem. Then, the method of converting broadband packet into a series of narrow bands in frequency domain is introduced, and then the method of processing narrow band is introduced. The implementation scheme of L1-SVD under broadband is given, that is, L1-SVD-WDOA algorithm. The simulation results show that L1-SVD-WDOA has better estimation performance, and the more the number of antennas increases, the better the performance is. Finally, Bayesian compression perception (RVM-BCS) based on RVM and Bayesian compression perception (LP-BCS) based on Laplace priori are studied. The biggest difference between RVM-BCS and LP-BCS lies in the difference of prior information. LP-BCS adds a priori information to RVM-BCS, so the reconstruction performance of LP-BCS is superior to that of RVM-BCS,. The formula derivation unifies the updating parameter formula of RVM-BCS and LP-BCS, which is easier to compare. Then LP-BCS and MBCS are applied to DOA estimation. Simulation results show that BCS has some advantages in algorithm performance when it is applied to DOA.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TN911.7
【參考文獻(xiàn)】
相關(guān)期刊論文 前2條
1 李磊;任麗香;包云霞;何佩琨;;寬帶頻率步進(jìn)信號(hào)參數(shù)估計(jì)的克拉美羅界研究[J];電子與信息學(xué)報(bào);2011年04期
2 劉云;李志舜;;寬帶波達(dá)方向估計(jì)的克拉美-羅界研究[J];聲學(xué)學(xué)報(bào);2006年02期
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