基于贝叶斯压缩感知的波达方向估计算法研究
发布时间：2018-12-18 09:15
【摘要】：波达方向(Direction of Arrival,DOA)估计是阵列信号处理的重要分支之一,自从第二次世界大战以来,其发展迅速,并且被广泛应用在军事和民用的各个方面。经典的DOA估计算法主要分为子空间分解和子空间拟合两类,这两类算法都需要在多快拍条件下进行,并且都有着各自本身难以克服的缺陷。压缩感知(Compressive Sensing,CS)理论克服了 Nyquist采样定理的限制,为信号处理提供了新的思路。其中,贝叶斯压缩感知理论是压缩感知理论的新成果,其从统计学的角度,利用假定的先验知识计算后验概率,从而得到估计值。本文正是研究如何利用贝叶斯压缩感知理论更有效地估计DOA。首先,论文介绍了课题的研究背景,介绍了 DOA估计和压缩感知理论的研究现状,然后分别研究了窄带信号与宽带信号下的DOA估计模型,并重点研究了三种经典的子空间类DOA估计方法和DOA估计中的克拉美-劳界的问题,这为之后的研究奠定了基础。其次,研究了压缩感知两类重要的重构算法,贪婪算法和凸优化算法。在贪婪算法中,研究了单快拍(SMV)和多快拍(MMV)下的OMP算法,并将其分别应用到DOA估计中。研究了凸优化算法在DOA估计中的应用,L1-SVD算法,L1-SVD通过构造惩罚项转化L1范数的求解问题,并通过奇异值分解对数据降维,最后利用凸优化求解。然后引入将宽带在频域分组变成一系列窄带,进而对窄带进行处理的方法,给出了 L1-SVD在宽带下的实现方案,即L1-SVD-WDOA算法。仿真结果表明,L1-SVD-WDOA有较好的估计性能,并且天线数增加的越多,其性能的改善越明显。最后,研究了基于RVM的贝叶斯压缩感知(RVM-BCS)、基于Laplace先验的贝叶斯压缩感知(LP-BCS),以及多快拍下的压缩感知(MBCS)算法。RVM-BCS与LP-BCS的最大差别在于先验信息的不同,LP-BCS比RVM-BCS增加了一个先验信息,因此LP-BCS的重构性能优于RVM-BCS,公式推导将RVM-BCS和LP-BCS的更新参数公式统一化,更易于二者的比较。然后将LP-BCS和MBCS应用在DOA估计中。仿真中可以看出,将BCS应用到DOA中,在算法性能上有一定的优势。
[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.
【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
本文编号：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.
【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
【参考文献】
相关期刊论文 前2条
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2 刘云;李志舜;;宽带波达方向估计的克拉美-罗界研究[J];声学学报;2006年02期
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