无源探测系统波达方向估计关键技术研究
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摘要
目标信号的波达方向（Direction ofArrival, DOA）估计是无源探测系统的关键环节，直接影响着无源探测系统的性能发挥，并关系着电子战后续作战决策。为了实现无源探测系统的高精度测向，使其具有分辨多个同时到达信号的能力，本文利用空间谱估计技术进行信号波达方向估计，围绕着实际工程应用中空间谱估计技术所面临的关键问题展开研究。研究内容包括实际工程应用中所亟需解决的信源数估计、提高波达方向估计的测角精度和分辨力、非均匀噪声下的波达方向估计和非圆信号的波达方向估计，论文主要研究工作如下。
信源数的精确估计是空间谱估计算法实现精确测向的前提，但是在实际系统中，由于色噪声的影响，信源数通常无法进行精确的估计。针对这个问题，提出了一种色噪声背景下的信源数估计方法，即基于特征子空间投影的信源数估计新方法，该方法根据信号子空间与噪声子空间相互正交这一原理，首先对特征向量进行划分，得到特征子空间，然后将协方差矩阵在特征子空间上进行投影，得到投影值，最后信号和噪声对投影值的贡献可由投影值的方差表示，进而实现信源数估计。计算机仿真证明了算法的有效性，并且利用实际测向系统中的接收数据验证了算法的工程实用性。
为了提高空间谱估计算法的测角精度和分辨力，提出了两种基于延时相关函数的波达方向估计方法。阵列接收数据的非零延时相关函数中蕴含了信号的角度信息，并且对噪声具有一定的抑制作用。利用这个原理，首先在均匀线阵时，经过分析发现不同阵元的延时相关函数之间具有旋转不变性，提出了基于延时相关处理的ESPRIT（Estimationof Signal Parameters via Rotational Invariance Techniques）算法；然后在任意阵列摆放形式下，提出了基于延时相关处理的MUSIC（Multiple Signal Classification）算法，并且为了提高算法的实时性，引入了变尺度的混沌优化算法，简化了二维空间谱函数的构造和谱峰搜索过程。最后利用计算机仿真实验验证了两种算法的性能。
针对实际测向系统中阵列输出噪声为非均匀噪声，经典MUSIC算法的性能下降甚至失效的问题，提出了一种非均匀噪声下的波达方向估计方法。首先利用三个变换矩阵对协方差矩阵进行处理，得到含有噪声和不含噪声的两部分数据；然后利用这两部分数据进行噪声协方差矩阵的估计；最后利用估计的噪声协方差矩阵对接收数据进行标准化处理，使得接收数据中的非均匀噪声变成了零均值的均匀白噪声，从而将非均匀噪声下的波达方向估计转变成白噪声下的波达方向估计，抑制了非均匀噪声对算法性能的影响。计算机仿真实验测试了该算法在非均匀噪声下的性能，实际测向系统中的实验验证了算法的工程实用性。
利用信号的非圆特性可以提高测向性能，针对非圆信号，提出了两种非圆信号波达方向估计方法。第一种方法是基于矩阵重构的非圆信号ESPRIT算法，该方法通过对阵列接收数据进行共轭重构，构造了与阵元个数相同的具有旋转不变关系的多个子阵，然后通过延时相关处理抑制了高斯白噪声对算法的影响，提高了非圆信号波达方向估计的测角精度和正确分辨概率。第二种方法是一种稳健的四阶累积量非圆信号波达方向估计方法，首先根据四阶累积量抑制高斯噪声的性能构造两个四阶累积量矩阵，然后根据这两个矩阵之间的旋转不变性进行波达方向估计，最后在通道幅相误差模型下分析了该算法的稳健性并得出结论：只要接收通道中任意两个通道具有一致性，不需要误差校正就能进行正确估计。仿真实验表明，算法测角精度和分辨力得到提高，并且算法对幅相误差具有稳健性。
The direction of arrival (DOA) estimation of target signal is a crucial technique inpassive detection systems, which has a significant influence on the system performance andthe consequent combat dictations in the electronic warfare. The spatial spectrum estimationtechnique is employed in this dissertation to improve the DOA estimation performance inorder to achieve the high-precision of passive detection system and distinguish multipletargets arriving simultaneously. The dissertation focuses on the important problems of spatialspectrum estimation technique in practical applications, which involve the estimation ofsource number, the improvement of the angular accuracy and resolution of DOA estimation,the DOA estimation under non-uniform noises and the DOA estimation for non-circularsignals.The detailed works are described as below:
The accurate estimation of source number is a prerequisite to the accurate directionfinding for spatial spectrum estimation algorithm. The source number is difficult to estimateaccurately in practical system, because of the effect of colored noises. Therefore, a newmethod for the estimation of source number based on the eigen subspace projection principleis proposed to solve this problem. For the signal subspace is orthogonal to the noise subspace,the value which the covariance matrix projects onto the post-processed eigen subspace isobtained, the source number can be estimated from the signal and noise’s respectivecontribution to the projection that is expressed by the projection’s variance. The effectivenessand the applicability of this method are verified by the simulation calculation andexperimental measurements.
To improve the resolution and angular accuracy of spatial spectrum estimationalgorithms, two DOA estimation methods based on delay correlation function are proposed.Non-zero delay correlation function of received data contains the DOA information of signals,and has a restraining influence on the noise. Considering this principle, the rotationalinvariance of delay correlation functions among different antennas of the uniform linear array(ULA) has been found. An ESPRIT (Estimation of Signal Parameters via RotationalInvariance Techniques) algorithm based on delay correlation processing is proposed. For anarbitrary array, a MUSIC (Multiple Signal Classification) algorithm based on delaycorrelation processing is developed. To improve the real-time performance of the algorithm,the mutative scale chaos optimization algorithm is used to simplify the construction oftwo-dimensional spectral function and the spectral peak searching. The performances of these two algorithms are tested with the computer simulation.
In actual direction finding system, the performance of classical MUSIC algorithm maybe deteriorated due to the effect of non-uniform noise received by the array. To solve thisproblem, a new method for DOA estimation is proposed under the condition of non-uniformnoise. Firstly, by processing the covariance matrix with three transformation matrixes, twoparts of data without and with noise are obtained respectively. Then, the noise covariancematrix is estimated with the two parts of data. Finally, the non-uniform noise is changed towhite noise with equivalent value by standardizing the received data with the estimated noisecovariance matrix. Tthe non-uniform noise background for DOA estimation turns into thewhite noise background, which could minimize the effect of non-uniform noise on theperformance of algorithm. Simulation results testify to the performance of proposed algorithmunder non-uniform noise background and experimental results in actual direction findingsystem prove the engineering practicability of the proposed algorithm.
The non-circular characteristics of signals can be used to improve the performance ofdirection finding. According to the characteristics of non-circular signals, two DOAestimation algorithms are designed. The first method is the ESPRIT algorithm of non-circularsignals based on the matrix regrouping. Sub-matrixes that have the same amount of elementsin array with rotational invariance relationship are constructed through theconjugatereconstruction of received data. Then the influence of Gaussian white noise on thealgorithm is restrained by delaying correlation processing, the simulation results show that theperformance of the proposed algorithm are better than the ESPRIT algorithm. The second oneis a robust non-circular signal DOA estimation method on the basis of fourth-order cumulant.Fourth-order cumulant could extend array aperture and suppress Gaussian noise. In view ofthese characteristics, two fourth-order cumulant matrixes are constructed, and the DOAestimation is completed on the basis of the rotational invariance of the two matrixes. Then, therobustness of this algorithm with the channel amplitude and phase error model is analyzedand the conclusions are as follows: if only any two of the reception channels arefairlyconsistent, the accurate DOA estimation could be acquired without error correction. Theangular accuracy and the resolution are improved obviously from predictions, and theproposed algorithm is robust to amplitude-phase error.
信源数的精确估计是空间谱估计算法实现精确测向的前提，但是在实际系统中，由于色噪声的影响，信源数通常无法进行精确的估计。针对这个问题，提出了一种色噪声背景下的信源数估计方法，即基于特征子空间投影的信源数估计新方法，该方法根据信号子空间与噪声子空间相互正交这一原理，首先对特征向量进行划分，得到特征子空间，然后将协方差矩阵在特征子空间上进行投影，得到投影值，最后信号和噪声对投影值的贡献可由投影值的方差表示，进而实现信源数估计。计算机仿真证明了算法的有效性，并且利用实际测向系统中的接收数据验证了算法的工程实用性。
为了提高空间谱估计算法的测角精度和分辨力，提出了两种基于延时相关函数的波达方向估计方法。阵列接收数据的非零延时相关函数中蕴含了信号的角度信息，并且对噪声具有一定的抑制作用。利用这个原理，首先在均匀线阵时，经过分析发现不同阵元的延时相关函数之间具有旋转不变性，提出了基于延时相关处理的ESPRIT（Estimationof Signal Parameters via Rotational Invariance Techniques）算法；然后在任意阵列摆放形式下，提出了基于延时相关处理的MUSIC（Multiple Signal Classification）算法，并且为了提高算法的实时性，引入了变尺度的混沌优化算法，简化了二维空间谱函数的构造和谱峰搜索过程。最后利用计算机仿真实验验证了两种算法的性能。
针对实际测向系统中阵列输出噪声为非均匀噪声，经典MUSIC算法的性能下降甚至失效的问题，提出了一种非均匀噪声下的波达方向估计方法。首先利用三个变换矩阵对协方差矩阵进行处理，得到含有噪声和不含噪声的两部分数据；然后利用这两部分数据进行噪声协方差矩阵的估计；最后利用估计的噪声协方差矩阵对接收数据进行标准化处理，使得接收数据中的非均匀噪声变成了零均值的均匀白噪声，从而将非均匀噪声下的波达方向估计转变成白噪声下的波达方向估计，抑制了非均匀噪声对算法性能的影响。计算机仿真实验测试了该算法在非均匀噪声下的性能，实际测向系统中的实验验证了算法的工程实用性。
利用信号的非圆特性可以提高测向性能，针对非圆信号，提出了两种非圆信号波达方向估计方法。第一种方法是基于矩阵重构的非圆信号ESPRIT算法，该方法通过对阵列接收数据进行共轭重构，构造了与阵元个数相同的具有旋转不变关系的多个子阵，然后通过延时相关处理抑制了高斯白噪声对算法的影响，提高了非圆信号波达方向估计的测角精度和正确分辨概率。第二种方法是一种稳健的四阶累积量非圆信号波达方向估计方法，首先根据四阶累积量抑制高斯噪声的性能构造两个四阶累积量矩阵，然后根据这两个矩阵之间的旋转不变性进行波达方向估计，最后在通道幅相误差模型下分析了该算法的稳健性并得出结论：只要接收通道中任意两个通道具有一致性，不需要误差校正就能进行正确估计。仿真实验表明，算法测角精度和分辨力得到提高，并且算法对幅相误差具有稳健性。
The direction of arrival (DOA) estimation of target signal is a crucial technique inpassive detection systems, which has a significant influence on the system performance andthe consequent combat dictations in the electronic warfare. The spatial spectrum estimationtechnique is employed in this dissertation to improve the DOA estimation performance inorder to achieve the high-precision of passive detection system and distinguish multipletargets arriving simultaneously. The dissertation focuses on the important problems of spatialspectrum estimation technique in practical applications, which involve the estimation ofsource number, the improvement of the angular accuracy and resolution of DOA estimation,the DOA estimation under non-uniform noises and the DOA estimation for non-circularsignals.The detailed works are described as below:
The accurate estimation of source number is a prerequisite to the accurate directionfinding for spatial spectrum estimation algorithm. The source number is difficult to estimateaccurately in practical system, because of the effect of colored noises. Therefore, a newmethod for the estimation of source number based on the eigen subspace projection principleis proposed to solve this problem. For the signal subspace is orthogonal to the noise subspace,the value which the covariance matrix projects onto the post-processed eigen subspace isobtained, the source number can be estimated from the signal and noise’s respectivecontribution to the projection that is expressed by the projection’s variance. The effectivenessand the applicability of this method are verified by the simulation calculation andexperimental measurements.
To improve the resolution and angular accuracy of spatial spectrum estimationalgorithms, two DOA estimation methods based on delay correlation function are proposed.Non-zero delay correlation function of received data contains the DOA information of signals,and has a restraining influence on the noise. Considering this principle, the rotationalinvariance of delay correlation functions among different antennas of the uniform linear array(ULA) has been found. An ESPRIT (Estimation of Signal Parameters via RotationalInvariance Techniques) algorithm based on delay correlation processing is proposed. For anarbitrary array, a MUSIC (Multiple Signal Classification) algorithm based on delaycorrelation processing is developed. To improve the real-time performance of the algorithm,the mutative scale chaos optimization algorithm is used to simplify the construction oftwo-dimensional spectral function and the spectral peak searching. The performances of these two algorithms are tested with the computer simulation.
In actual direction finding system, the performance of classical MUSIC algorithm maybe deteriorated due to the effect of non-uniform noise received by the array. To solve thisproblem, a new method for DOA estimation is proposed under the condition of non-uniformnoise. Firstly, by processing the covariance matrix with three transformation matrixes, twoparts of data without and with noise are obtained respectively. Then, the noise covariancematrix is estimated with the two parts of data. Finally, the non-uniform noise is changed towhite noise with equivalent value by standardizing the received data with the estimated noisecovariance matrix. Tthe non-uniform noise background for DOA estimation turns into thewhite noise background, which could minimize the effect of non-uniform noise on theperformance of algorithm. Simulation results testify to the performance of proposed algorithmunder non-uniform noise background and experimental results in actual direction findingsystem prove the engineering practicability of the proposed algorithm.
The non-circular characteristics of signals can be used to improve the performance ofdirection finding. According to the characteristics of non-circular signals, two DOAestimation algorithms are designed. The first method is the ESPRIT algorithm of non-circularsignals based on the matrix regrouping. Sub-matrixes that have the same amount of elementsin array with rotational invariance relationship are constructed through theconjugatereconstruction of received data. Then the influence of Gaussian white noise on thealgorithm is restrained by delaying correlation processing, the simulation results show that theperformance of the proposed algorithm are better than the ESPRIT algorithm. The second oneis a robust non-circular signal DOA estimation method on the basis of fourth-order cumulant.Fourth-order cumulant could extend array aperture and suppress Gaussian noise. In view ofthese characteristics, two fourth-order cumulant matrixes are constructed, and the DOAestimation is completed on the basis of the rotational invariance of the two matrixes. Then, therobustness of this algorithm with the channel amplitude and phase error model is analyzedand the conclusions are as follows: if only any two of the reception channels arefairlyconsistent, the accurate DOA estimation could be acquired without error correction. Theangular accuracy and the resolution are improved obviously from predictions, and theproposed algorithm is robust to amplitude-phase error.
引文
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