阵列信号二维到达角估计算法理论及其应用研究
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摘要
基于相位干涉仪测向体制的传统反辐射导弹(ARM:Anti Radiation Missile)被动雷达导引头(PRS:Passive Radar Seeker)存在着精度不高、分辨率差、不能处理同时到达信号等缺点。本文致力于将性能优良的基于阵列信号处理的谱估计算法应用到被动雷达导引头实际工程中,以实现高精度、超分辨、高实时性的二维到达角(DOA:Direction of Arrival)估计。主要研究工程应用中所需要解决的信源数估计问题、基于极化敏感阵列测向算法问题、阵列结构性能优化问题以及谱估计算法的快速实现问题。
谱估计算法的优良性能是建立在精确已知信源数的基础上,因此正确估计信源数是实现精确测向的基础。第三章研究了不同条件下的信源数估计方法。当实际系统的性能理想时,在高斯白噪声背景下,可以通过基于信息论准则的方法实现信源数估计,该方法简便有效；在色噪声背景下,可以通过基于协方差矩阵对角加载的信息论方法或者盖尔圆盘定理的方法估计信源数。当实际系统性能不够理想,存在阵元间互耦以及通道不一致性时,噪声会变成空间色噪声,对此提出了基于改进参数空间的信息论准则的方法来估计信源数。计算机仿真和实测数据实验验证了该方法的有效性。
以多重信号分类(MUSIC:Multiple Signal Classification)算法为代表的谱估计算法具有高精度、超分辨的性能。而在实际工程中,由于只能有限快拍采样,以及存在互耦、不一致性等问题使得算法对单个信号具有很高的精度,但对多个信号的分辨力不高。第四章研究了利用极化敏感阵列来提高谱估计算法的分辨率,实现二维超分辨测向。首先基于MUSIC算法形成了空域-极化域联合谱,并通过理论分析和计算机仿真分析了联合谱的超分辨性能。其次介绍了基于总体最小二乘准则的借助旋转不变技术估计信号参数(TLS-ESPRIT:Totla Least Squares-Estimation of Signal Parameters via Rotational Invariance Techniques)算法的联合谱估计。最后提出了基于极化旋转矩阵的MUSIC算法。该方法将四维谱搜索降为二维谱搜索,极大地提高了实时性,同时保持了联合谱的超分辨性能,通过计算机仿真表明了该方法的有效性。
在阵列信号测向中,不同的算法会有不同的到达角(DOA:Direction of Arrival)估计性能,同时阵列结构对算法的最终性能也有重要的影响。第五章通过阵列流形的微分几何研究了不同阵列的精度性能以及分辨性能,并且利用微分几何在理论上探讨了阵列设计的方法。然后对测向中影响最严重的一阶模糊问题进行了研究,对任意平面阵推导了一个阵列不存在一阶模糊的充分条件,能够指导工程中充分利用阵列孔径而不产生一阶模糊。
基于阵列信号处理的谱估计算法具有高精度、超分辨的良好性能,但其代价是相比于传统的测向体制它的算法复杂得多,因而运算量大、实时性差。为了保证实时性,第六章在原有被动探测及测向的实验平台上,通过硬件和算法软件的设计,研制了一个基于MUSIC算法的高速测向器。该测向器在硬件上采用四片ADI公司高性能浮点DSP TS201S共享总线紧耦合并行处理的设计,软件流程上提出了利用导向矢量查表计算空间谱值的方法,最后能够实现快速实时测向。进行了测向器测角精度和实时性指标的测试实验,测试结果为研制新型被动雷达导引头提供了非常有价值的参考。
The conventional anti radiation missile (ARM) passive radar seeker (PRS) has the disadvantages including low precision, poor resolution and disability to handle simultaneous signals based on phase interferometer mechanism. This dissertation applys spectral estimation algorithm based on array signal processing to PRS, in order to achieve two-dimensional high-precision, super-resolution, real-time direction of arrival (DOA) estimation. The problems in practices including source number estimation, utility of polarization sensitive array, array geometry designing optimization and fast implementation of spectral estimation algorithm are mainly researched in this thesis.
The excellent performance of spectral estimation algorithm is under the assumption of knowing the source number precisely, so the correct estimation of source number is the precondition to achieve precise DOA estimation. Source number estimation methods under different conditions is studied. While the practical system is ideal, source number can be estimated by information theory criteria method with the Gaussian white noise background, or by diagonal loading to the covariance matrix information criteria or Gerschgorin disk theorem with the colored noise background. When the practical system is not ideal, the noise will become spatial colored in respect of the existence of mutual coupling and channel mismatch. To deal with this case, a new method called improving the parameter space of information criteria is proposed. Simulation and experimental measurement results illustrate the effectiveness of the new method.
The spectral estimation algorithms represented by multiple signal classification (MUSIC) algorithm have the performance of high-precision and super-resolution. However, in practices, it has been proved that due to the limited snapshots, the existence of mutual coupling and channel mismatch and some other factors, the algorithms perform well with high precision only when dealing with single source, and would result in quite poor resolution when dealing with multiple sources. How to improve the resolution of spectral estimation algorithms to achieve high-resolution performance by using polarization sensitive arrays is proposed and studied. With polarization sensitive array, the spatial and polarizational joint spectrum is defined by using MUSIC algorithm. And the super-resolution performance of the joint spectrum was analysed through theoretical analysis and simulation. Then the joint spectrum estimation based on TLS-ESPRIT algorithm is introduced. Finally, a new algorithm called MUSIC algorithm based on polarization rotation matrix is proposed. This method reduces four-dimensional spectrum search to two-dimensional, which greatly improves the real-time performance while maintains the super-resolution of joint spectrum. The simulation results show the effectiveness of this method.
In array signal direction finding, different algorithms lead to different performance of direction of arrival (DOA) estimation. Meanwhile, the array geometry has important impact on the final performance of direction finding algorithm. The precision and resolution performance of different array geometry is studied by array differential geometry, and also array designing method is discussed theoretically. And the rank-1 ambiguity issue which has the most serious effectiveness in direction finding is studied. A sufficient condition of non-existing of rank-1 ambiguity is derived based on arbitrary planar array, which can guide to making full use of array aperture without creating rank-1 ambiguity in practical projects.
The spectral estimation algorithm based on array signal processing has excellent performance of high-precision and super-resolution, but it is much more computational complicated than conventional DF mechanism. It needs a large quantity of computation, and as a result, its real-time performance is comparably much poorer. In order to guarantee real-time performance, a design of high-speed DF device based on MUSIC algorithm is developed. The DF device works with an existed experimental PRS platform. It makes use of four ADI' high performance floating point DSPs TS201S in hardware design of the DF device. And the four DSPs combine a parallel digital signal processor by sharing bus and tightly coupling. In software design, a method of computing spectrum by steering vector table search is proposed. And thus the DF device achieves very high speed. The experimental test results about accuracy and real-time performance of the DF device provide a very valuable reference for developing new PRS.
谱估计算法的优良性能是建立在精确已知信源数的基础上,因此正确估计信源数是实现精确测向的基础。第三章研究了不同条件下的信源数估计方法。当实际系统的性能理想时,在高斯白噪声背景下,可以通过基于信息论准则的方法实现信源数估计,该方法简便有效；在色噪声背景下,可以通过基于协方差矩阵对角加载的信息论方法或者盖尔圆盘定理的方法估计信源数。当实际系统性能不够理想,存在阵元间互耦以及通道不一致性时,噪声会变成空间色噪声,对此提出了基于改进参数空间的信息论准则的方法来估计信源数。计算机仿真和实测数据实验验证了该方法的有效性。
以多重信号分类(MUSIC:Multiple Signal Classification)算法为代表的谱估计算法具有高精度、超分辨的性能。而在实际工程中,由于只能有限快拍采样,以及存在互耦、不一致性等问题使得算法对单个信号具有很高的精度,但对多个信号的分辨力不高。第四章研究了利用极化敏感阵列来提高谱估计算法的分辨率,实现二维超分辨测向。首先基于MUSIC算法形成了空域-极化域联合谱,并通过理论分析和计算机仿真分析了联合谱的超分辨性能。其次介绍了基于总体最小二乘准则的借助旋转不变技术估计信号参数(TLS-ESPRIT:Totla Least Squares-Estimation of Signal Parameters via Rotational Invariance Techniques)算法的联合谱估计。最后提出了基于极化旋转矩阵的MUSIC算法。该方法将四维谱搜索降为二维谱搜索,极大地提高了实时性,同时保持了联合谱的超分辨性能,通过计算机仿真表明了该方法的有效性。
在阵列信号测向中,不同的算法会有不同的到达角(DOA:Direction of Arrival)估计性能,同时阵列结构对算法的最终性能也有重要的影响。第五章通过阵列流形的微分几何研究了不同阵列的精度性能以及分辨性能,并且利用微分几何在理论上探讨了阵列设计的方法。然后对测向中影响最严重的一阶模糊问题进行了研究,对任意平面阵推导了一个阵列不存在一阶模糊的充分条件,能够指导工程中充分利用阵列孔径而不产生一阶模糊。
基于阵列信号处理的谱估计算法具有高精度、超分辨的良好性能,但其代价是相比于传统的测向体制它的算法复杂得多,因而运算量大、实时性差。为了保证实时性,第六章在原有被动探测及测向的实验平台上,通过硬件和算法软件的设计,研制了一个基于MUSIC算法的高速测向器。该测向器在硬件上采用四片ADI公司高性能浮点DSP TS201S共享总线紧耦合并行处理的设计,软件流程上提出了利用导向矢量查表计算空间谱值的方法,最后能够实现快速实时测向。进行了测向器测角精度和实时性指标的测试实验,测试结果为研制新型被动雷达导引头提供了非常有价值的参考。
The conventional anti radiation missile (ARM) passive radar seeker (PRS) has the disadvantages including low precision, poor resolution and disability to handle simultaneous signals based on phase interferometer mechanism. This dissertation applys spectral estimation algorithm based on array signal processing to PRS, in order to achieve two-dimensional high-precision, super-resolution, real-time direction of arrival (DOA) estimation. The problems in practices including source number estimation, utility of polarization sensitive array, array geometry designing optimization and fast implementation of spectral estimation algorithm are mainly researched in this thesis.
The excellent performance of spectral estimation algorithm is under the assumption of knowing the source number precisely, so the correct estimation of source number is the precondition to achieve precise DOA estimation. Source number estimation methods under different conditions is studied. While the practical system is ideal, source number can be estimated by information theory criteria method with the Gaussian white noise background, or by diagonal loading to the covariance matrix information criteria or Gerschgorin disk theorem with the colored noise background. When the practical system is not ideal, the noise will become spatial colored in respect of the existence of mutual coupling and channel mismatch. To deal with this case, a new method called improving the parameter space of information criteria is proposed. Simulation and experimental measurement results illustrate the effectiveness of the new method.
The spectral estimation algorithms represented by multiple signal classification (MUSIC) algorithm have the performance of high-precision and super-resolution. However, in practices, it has been proved that due to the limited snapshots, the existence of mutual coupling and channel mismatch and some other factors, the algorithms perform well with high precision only when dealing with single source, and would result in quite poor resolution when dealing with multiple sources. How to improve the resolution of spectral estimation algorithms to achieve high-resolution performance by using polarization sensitive arrays is proposed and studied. With polarization sensitive array, the spatial and polarizational joint spectrum is defined by using MUSIC algorithm. And the super-resolution performance of the joint spectrum was analysed through theoretical analysis and simulation. Then the joint spectrum estimation based on TLS-ESPRIT algorithm is introduced. Finally, a new algorithm called MUSIC algorithm based on polarization rotation matrix is proposed. This method reduces four-dimensional spectrum search to two-dimensional, which greatly improves the real-time performance while maintains the super-resolution of joint spectrum. The simulation results show the effectiveness of this method.
In array signal direction finding, different algorithms lead to different performance of direction of arrival (DOA) estimation. Meanwhile, the array geometry has important impact on the final performance of direction finding algorithm. The precision and resolution performance of different array geometry is studied by array differential geometry, and also array designing method is discussed theoretically. And the rank-1 ambiguity issue which has the most serious effectiveness in direction finding is studied. A sufficient condition of non-existing of rank-1 ambiguity is derived based on arbitrary planar array, which can guide to making full use of array aperture without creating rank-1 ambiguity in practical projects.
The spectral estimation algorithm based on array signal processing has excellent performance of high-precision and super-resolution, but it is much more computational complicated than conventional DF mechanism. It needs a large quantity of computation, and as a result, its real-time performance is comparably much poorer. In order to guarantee real-time performance, a design of high-speed DF device based on MUSIC algorithm is developed. The DF device works with an existed experimental PRS platform. It makes use of four ADI' high performance floating point DSPs TS201S in hardware design of the DF device. And the four DSPs combine a parallel digital signal processor by sharing bus and tightly coupling. In software design, a method of computing spectrum by steering vector table search is proposed. And thus the DF device achieves very high speed. The experimental test results about accuracy and real-time performance of the DF device provide a very valuable reference for developing new PRS.
引文
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