【作者】 宋雪松；

【导师】 姚桂锦；

【作者基本信息】 吉林大学 ， 信号与信息处理， 2014， 硕士

【摘要】 波达方向估计是阵列信号处理的重要研究内容和持续研究热点之一，主要目的是利用和处理传感器阵列接收的测量数据，估计和提取待测空间信号来波方向、信号数目、功率以及信号互相关信息等参数，在通信、雷达、军事、地震等众多实际工程领域中得到广泛应用。首先，本文针对常规MUSIC算法和ESPRIT算法不能有效估计相干信号源波达方向的问题。基于修正MUSIC算法（Modified MUSIC，简称MMUSIC），通过引入变换矩阵，并且在顾及到阵列接收数据及其相应变换矩阵的自相关和互相关信息后，结合总体最小二乘ESPRIT算法提出了能够同时适应相干和非相干信号源情况的波达方向估计改进ESPRIT算法（Improved ESPRIT，简称IM-ESPRIT算法），数值仿真实验表明IM-ESPRIT算法在相干信号源来波角度间隔较小和低信噪比条件下，具有较好的估计精度、分辨率和稳定性。其次，通过对DOA估计算法研究发现，信号源数目是很多DOA估计算法需要预先已知的一个关键参数。本文利用ULA传感器阵列时延定值特征和特定参考阵元信号（如阵列中第一个阵元）与其他阵元信号的互相关函数，通过时延差分操作，推导出一个用于DOA估计的矩阵方程组，理论表明，方程组系数矩阵为Hankel矩阵，对Hankel矩阵进行奇异值或特征值分解，其奇异值或特征值数目只与信号源数目有关；同时，在信号源数目未知条件下，依据预设信号源数目，可相应构建维数可变的Hankel矩阵。根据Hankel矩阵的这一性质，我们提出一种基于阵元时延结构信息的估计信号源数目的奇异值分解算法（ATDS-SVD算法）。我们针对独立信号源、相干信号源和混合信号源（相干与非相干信号源共存）三种情况，利用ATDS-SVD算法进行信号源数目估计编程仿真实验和分析，结果表明，同常规信号源数目估计方法（AIC、MDL等）比较，ATDS-SVD算法能够同时估计相干和非相干信号源数目，并且具有渐近一致性，稳定性和估计精度较好。最后，本文利用Hankel矩阵，结合IM-ESPRIT算法角度估计原理，对ULA进行了DOA估计的仿真编程和分析。仿真实验表明，利用Hankel矩阵的IM-ESPRIT算法能够对不同信号源情况的波达方向进行估计，特别适用于低信噪比情况，表现出较好的稳定性、估计精度和分辨率，同时初步论证了该DOA估计算法的有效性和可行性。更多还原

【Abstract】 Direction of arrival (DOA) estimation is one of the important research contentand successive hot point in array signal processing, the main purpose of DOAestimation is to use and process the measurement data which received by sensor array,estimate and extract parameters such as the direction of arrival of the spatial signal tobe measured, the number of signals, the power and cross correlation information.DOA has been widely applied in many practical engineerings includingcommunication, radar, military, earthquake, etc.Firstly, for the conventional MUSIC algorithm and ESPRIT algorithm can noteffectively achieve DOA estimation of the coherent source. Based on modifiedMUSIC (MMUSIC), introducing the transformation matrix and considering the auto-correlation and cross-autocorrelation of the array output and the correspondingtransformed matrix, and combined with total least-squares ESPRIT algorithm, animproved ESPRIT algorithm (IM-ESPRIT) that is suitable for the cases of thenon-coherent and coherent sources has been proposed. it is shown by the numericalsimulation that IM-ESPRIT algorithm has the better estimation accuracy under thecondition of the small angle interval of the coherent sources and lower SNR.Secondly, this study of the DOA estimation algorithms found that the number ofsignals is a need to pre-known key parameter of many DOA algorithms. This paperused ULA sensor array delay value array element characteristics and specificreference array element signal (such as the first array element of array) and thecross-correlation function of other array element signals, through the delay differentialoperation, derived a matrix equations for DOA estimation, the theory shown that thecoefficient matrix equation is Hankel matrix, we resolved Hankel matrix with singularvalues or characteristic values decomposition, the number of singular values orcharacteristic values only related to the number of signal sources; meanwhile.Moreover, under the condition of the number of signal sources is unknown, accordingto the preset number of the signal source, we can construct variable dimension Hankelmatrix correspondently. By the nature of Hankel matrix, we proposed a singular valuedecomposition algorithm to estimate the number of signal sources which based onarray element time delay structure information (Array element Time delay Structuralinformation Singular Value Decomposition, ATDS-SVD). To the following threecases such as independent signal source, coherent signal source and mixed-signalsource (coherent and non-coherent sources coexist), we used the ATDS-SVDalgorithm to simulate and analysis the experiment around estimating the number ofsignal sources. Compared with the conventional number of signal source estimation method (AIC, MDL, etc.), it is shown by the simulation results that ATDS-SVDalgorithm can estimate the number of coherent and non-coherent signal sourcesynchronously and has asymptotic consistency, better stability and estimationaccuracy.Finally, we used the Hankel matrix to simulate programming and analysis theDOA estimation for ULA with IM-ESPRIT algorithm angle estimation principle. It isshown by the simulation experiment that the IM-ESPRIT algorithm is suitable forestimating DOA direction under the condition of different signal sources with Hankelmatrix; Especially, this algorithm showed better stability, estimation accuracy andresolution under the cases of lower SNR, furthermore, we demonstrated theeffectiveness and feasibility of the DOA estimation algorithm preliminarily.更多还原