宽带信号波达方向估计方法研究
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摘要
波达方向(Direction of Arrival，DOA)是信号最重要的空域参数，其估计方法是阵列信号处理中两大研究热点之一。经过30多年的发展，DOA估计理论和技术已经成为阵列信号处理学科发展的主要方面，其应用涉及到雷达、声纳、勘探、生物医学等领域中。随着信号处理技术的发展，基于窄带阵列信号的高分辨算法已经比较成熟，窄带阵列探测系统已广泛应用于军事及民用领域。与窄带信号相比，利用宽带信号可以获取较大的信息量，有利于目标信号检测、参数估计和特征提取，在有源探测和无源探测系统中有更重要的应用。因此，研究宽带信号的DOA估计方法具有重要的意义。
本文以经典的空间谱估计理论（主要涉及最大似然理论、信号子空间理论、循环平稳特性、阵列误差校正等）为基础，分析了一些常规宽带测向算法的测向原理和性能。在此基础上，对宽带信号源的DOA估计算法进行了深入研究，提出了改进的新算法，并对新提出的算法进行了实验仿真和对比分析。
首先，研究了基于最大似然估计的测向方法。将窄带信号最大似然估计器推广到宽带信号最大似然估计器，针对常规算法大都是以均匀分布的高斯白噪声为背景的情况，给出了一种基于非均匀系统噪声的确定性最大似然估计方法，解决了常规算法无法求得最优闭式解的问题，且在计算上减少了搜索的维数和迭代次数，性能优于传统的确定性最大似然估计算法和随机性最大似然估计算法。
其次，研究了基于信号子空间的宽带信号DOA估计方法。通过深入分析酉聚焦矩阵的相干信号子空间类算法的原理和实质，针对相干信号子空间类算法需要角度预估计问题，利用不同频率和聚焦频率下的输出信号协方差的特征分解运算，提出一种新的聚焦方法。该方法不需要进行方位角度预估计，且去相关运算简单，可以处理相干宽带信号源的DOA估计问题。通过实验仿真和与其他常规算法的比较，验证了该算法的估计性能。
再次，研究了基于循环平稳特性的宽带信号DOA估计方法，结合信号的循环平稳特性和共轭循环平稳特性，采用子空间分解的方法，实现了宽带信号的DOA估计。该方法同时利用宽带信号循环平稳和共轭循环平稳两方面信息构造扩展循环相关矩阵，继承了Cyclic MUSIC算法的优点，并且在处理宽带信号源时不需要估计最佳延时时间。实验仿真表明，该方法具有良好的宽带信号分选识别能力，能够抑制大功率干扰信号，估计性能较好。
最后，研究了阵列误差校正及存在阵列误差时的DOA估计问题，给出了各种误差（通道幅相误差、阵元位置误差和阵元互耦效应）模型，重点分析了几种误差扰动的校正技术，并结合实例进行仿真实验，在实现阵列阵元校正的同时，还实现了信号源方位的估计。针对现有技术条件下无法准确测量和估计宽带信号阵列误差的情况，根据空间平滑技术去相关的思想，提出了一种空间平滑技术和蒙特卡罗采样预估相结合的稳健估计方法。理论分析和实验仿真均展示了该方法消除阵列误差的能力，为阵列误差模型下的宽带信号DOA估计提供了一种新的解决思路。
Direction of arrival is the most important spatial parameters of the signal. The estimationmethod of DOA is one of the two main research directions in array signal processing. Aftermore than30years’ development, DOA estimation theory and technology has become themain aspects of array signal processing discipline. Its typical applications include radar, sonar,exploration, biomedicine, etc. With the development of signal processing technology, highresolution algorithm based on the narrowband array signal is relatively mature. Thenarrowband array detection system has been widely used in military and civil fields.Compared with the narrow-band signal, wideband signals include more information. It isbetter for target signal detection, parameters estimation and signal features extraction andbecoming more important in active detection and passive detection system. Therefore, theresearch on broadband signal DOA estimation technology has important significance.
Based on the classical spatial spectrum estimation theory (mainly related to maximumlikelihood theory, signal subspace theory, cyclostationarity, array error calibration), the paperanalyses direction finding principle and performance of some conventional wideband signalestimation algorithm analysis. Based on the study above, the wideband signals DOAestimation algorithm is studied further. Some new algorithms are presented, and the newproposed algorithms are analyzed and compared with other algorithms in simulationexperiment.
Firstly, direction finding technique of maximum likelihood estimation is researched. Themaximum likelihood estimator for wideband signal is obtained from narrowband signalsestimator. Conventional algorithms are mostly based on uniform distribution of Gauss whitenoise background. The paper gives a maximum likelihood estimation method with thenon-uniform noise. It solves the problem in the optimal calculation of closed form, andreduces the search dimensions and the number of iterations. The performance is better thanthe traditional deterministic maximum likelihood estimation algorithm and stochasticmaximum likelihood estimation algorithm.
Secondly, the signal subspace DOA estimation technology is researched. By deeplyanalyzing the principle and essence of unitary focusing matrix for coherent signal subspacealgorithm, and under that coherent signal subspace algorithms need preliminary DOAestimation, the paper proposed a new algorithm which obtains the eigenvector througheigen-decomposition of the covariance matrix of array output signals corresponding to different frequencies and focusing frequency. The method does not need preliminary anglesestimation and can process the coherent wideband signals. Computer simulations areconducted to show the better performances of new algorithm. Through the simulationexperiment and comparison with the properties of other conventional algorithm, the algorithmshows better performances.
Thirdly, wideband signal DOA estimation technique based on f cyclostationarity isresearched. The paper combines with the cyclostationarity and conjugate cyclostationaritysignal properties and use subspace decomposition method to realize the DOA estimation ofwideband signals. The method utilizes both wide-band cyclostationarity and conjugatecyclostationarity signal information to obtain extended cyclic correlation matrix, inherits theadvantages of Cyclic MUSIC algorithm, and does not need to estimate the time delay inprocessing of wideband signal source. Experimental results show that, this method has a goodselection ability of wideband signal and the ability to identify and can inhibit high powerinterference signal. It has better estimation performance.
Finally, the array calibration and DOA estimation in array modeling error is researched.The paper gives various error models (amplitude and phase errors, array element positionerror and mutual coupling effect), analyses the calibration technology of several perturbation,and carries on the simulation experiment with examples. Using some methods, we could notonly realize the array calibration, but also can estimate signal DOA at the same time. Inaccordance with the situation that existing technical conditions can not accurately measureand estimate array error of wideband DOA estimation, using the de-correlation idea of spatialsmoothing technology, the paper proposes a robust method which combines the spatialsmoothing technique and Monte Carlo sampling estimation technique. Theoretical analysisand experimental simulation results demonstrated the ability of the method to eliminate thearray error. The paper puts forward a new way to solve the problem of estimation forwideband DOA array error model.
本文以经典的空间谱估计理论（主要涉及最大似然理论、信号子空间理论、循环平稳特性、阵列误差校正等）为基础，分析了一些常规宽带测向算法的测向原理和性能。在此基础上，对宽带信号源的DOA估计算法进行了深入研究，提出了改进的新算法，并对新提出的算法进行了实验仿真和对比分析。
首先，研究了基于最大似然估计的测向方法。将窄带信号最大似然估计器推广到宽带信号最大似然估计器，针对常规算法大都是以均匀分布的高斯白噪声为背景的情况，给出了一种基于非均匀系统噪声的确定性最大似然估计方法，解决了常规算法无法求得最优闭式解的问题，且在计算上减少了搜索的维数和迭代次数，性能优于传统的确定性最大似然估计算法和随机性最大似然估计算法。
其次，研究了基于信号子空间的宽带信号DOA估计方法。通过深入分析酉聚焦矩阵的相干信号子空间类算法的原理和实质，针对相干信号子空间类算法需要角度预估计问题，利用不同频率和聚焦频率下的输出信号协方差的特征分解运算，提出一种新的聚焦方法。该方法不需要进行方位角度预估计，且去相关运算简单，可以处理相干宽带信号源的DOA估计问题。通过实验仿真和与其他常规算法的比较，验证了该算法的估计性能。
再次，研究了基于循环平稳特性的宽带信号DOA估计方法，结合信号的循环平稳特性和共轭循环平稳特性，采用子空间分解的方法，实现了宽带信号的DOA估计。该方法同时利用宽带信号循环平稳和共轭循环平稳两方面信息构造扩展循环相关矩阵，继承了Cyclic MUSIC算法的优点，并且在处理宽带信号源时不需要估计最佳延时时间。实验仿真表明，该方法具有良好的宽带信号分选识别能力，能够抑制大功率干扰信号，估计性能较好。
最后，研究了阵列误差校正及存在阵列误差时的DOA估计问题，给出了各种误差（通道幅相误差、阵元位置误差和阵元互耦效应）模型，重点分析了几种误差扰动的校正技术，并结合实例进行仿真实验，在实现阵列阵元校正的同时，还实现了信号源方位的估计。针对现有技术条件下无法准确测量和估计宽带信号阵列误差的情况，根据空间平滑技术去相关的思想，提出了一种空间平滑技术和蒙特卡罗采样预估相结合的稳健估计方法。理论分析和实验仿真均展示了该方法消除阵列误差的能力，为阵列误差模型下的宽带信号DOA估计提供了一种新的解决思路。
Direction of arrival is the most important spatial parameters of the signal. The estimationmethod of DOA is one of the two main research directions in array signal processing. Aftermore than30years’ development, DOA estimation theory and technology has become themain aspects of array signal processing discipline. Its typical applications include radar, sonar,exploration, biomedicine, etc. With the development of signal processing technology, highresolution algorithm based on the narrowband array signal is relatively mature. Thenarrowband array detection system has been widely used in military and civil fields.Compared with the narrow-band signal, wideband signals include more information. It isbetter for target signal detection, parameters estimation and signal features extraction andbecoming more important in active detection and passive detection system. Therefore, theresearch on broadband signal DOA estimation technology has important significance.
Based on the classical spatial spectrum estimation theory (mainly related to maximumlikelihood theory, signal subspace theory, cyclostationarity, array error calibration), the paperanalyses direction finding principle and performance of some conventional wideband signalestimation algorithm analysis. Based on the study above, the wideband signals DOAestimation algorithm is studied further. Some new algorithms are presented, and the newproposed algorithms are analyzed and compared with other algorithms in simulationexperiment.
Firstly, direction finding technique of maximum likelihood estimation is researched. Themaximum likelihood estimator for wideband signal is obtained from narrowband signalsestimator. Conventional algorithms are mostly based on uniform distribution of Gauss whitenoise background. The paper gives a maximum likelihood estimation method with thenon-uniform noise. It solves the problem in the optimal calculation of closed form, andreduces the search dimensions and the number of iterations. The performance is better thanthe traditional deterministic maximum likelihood estimation algorithm and stochasticmaximum likelihood estimation algorithm.
Secondly, the signal subspace DOA estimation technology is researched. By deeplyanalyzing the principle and essence of unitary focusing matrix for coherent signal subspacealgorithm, and under that coherent signal subspace algorithms need preliminary DOAestimation, the paper proposed a new algorithm which obtains the eigenvector througheigen-decomposition of the covariance matrix of array output signals corresponding to different frequencies and focusing frequency. The method does not need preliminary anglesestimation and can process the coherent wideband signals. Computer simulations areconducted to show the better performances of new algorithm. Through the simulationexperiment and comparison with the properties of other conventional algorithm, the algorithmshows better performances.
Thirdly, wideband signal DOA estimation technique based on f cyclostationarity isresearched. The paper combines with the cyclostationarity and conjugate cyclostationaritysignal properties and use subspace decomposition method to realize the DOA estimation ofwideband signals. The method utilizes both wide-band cyclostationarity and conjugatecyclostationarity signal information to obtain extended cyclic correlation matrix, inherits theadvantages of Cyclic MUSIC algorithm, and does not need to estimate the time delay inprocessing of wideband signal source. Experimental results show that, this method has a goodselection ability of wideband signal and the ability to identify and can inhibit high powerinterference signal. It has better estimation performance.
Finally, the array calibration and DOA estimation in array modeling error is researched.The paper gives various error models (amplitude and phase errors, array element positionerror and mutual coupling effect), analyses the calibration technology of several perturbation,and carries on the simulation experiment with examples. Using some methods, we could notonly realize the array calibration, but also can estimate signal DOA at the same time. Inaccordance with the situation that existing technical conditions can not accurately measureand estimate array error of wideband DOA estimation, using the de-correlation idea of spatialsmoothing technology, the paper proposes a robust method which combines the spatialsmoothing technique and Monte Carlo sampling estimation technique. Theoretical analysisand experimental simulation results demonstrated the ability of the method to eliminate thearray error. The paper puts forward a new way to solve the problem of estimation forwideband DOA array error model.
引文
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