二维波达方向估计方法研究
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摘要
二维波达方向(DOA)估计方法广泛应用于雷达、声纳、通信和地震学等领域。近年来提出了很多二维波达方向的估计方法,其中具有代表性的为基于空域信号二维特征结构的高分辨技术。然而,对于采用多维搜索的二维DOA估计技术,计算量很大而不易于实际应用;对于采用分维处理的二维DOA估计技术,由于需要对参数进行配对,在低信噪比、小的角间距下或者复杂的信号传播环境情况下,就会出现配对错误,从而不能获得正确的参数估计。
本文的主要工作是对常用阵列的二维DOA估计特性进行研究,针对不同的阵列和信号,分析了已有算法的不足,提出了几种无需参数配对的计算量较低的二维DOA估计方法。本文的主要创新之处概括如下:
1.针对双平行均匀线性阵列,提出了一种解耦二维DOA估计方法。与现有的基于双平行线阵的算法不同,该方法不仅能估计更多信号的二维DOA,还获得了更高的估计精度。根据双平行均匀阵列的特点,进一步给出了基于多项式求根的二维到达角估计方法。给出了双平行阵列的CRB(Cramer-Rao Bound),最后采用前后向空间平滑技术把其推广到处理相关信号源的情况。
2.针对基于双平行均匀线性阵列的现有DOA矩阵法存在的一维角度兼并问题,通过合理设计阵列流形,提出了一种基于联合对角化技术的DOA矩阵方法。该方法较好的解决了现有DOA矩阵法存在的一维角度兼并问题,并且无需二维谱峰搜索和参数配对,改善了阵列的角估计性能。然后,新方法被推广到应用于由任意triplets(三元子阵)组成的阵列,通过调整triplets间的距离可以获得更高的分辨力。
3.在一些应用中,信号常常具有不同的谱。利用信号的时域信息,可以有效的扩展阵列孔径,避免阵列校正等等。针对原空时DOA矩阵法不能估计在某些曲面内的信号的缺点,提出了一种基于联合对角化空时协方差矩阵的二维DOA估计方法。通过联合对角化全部或部分空时DOA矩阵,新方法比原空时DOA矩阵法获得了两方面的性能增强。第一,解决了原空时DOA矩阵法在某些曲面存在的角度兼并问题;第二,在低信噪比下,其估计性能得到了改善。最后把该方法推广到任意阵列的二维DOA估计。
4.对于非高斯信号,高阶统计量包含了有效的统计信息,并且具有许多良好性质,如抑制任意加性高斯噪声、阵列校正与孔径扩展等。针对相互独立的非高斯窄带信号,提出了基于联合对角化技术的累量域二维DOA矩阵方法。利用阵列的结构,该方法构造几个子阵,然后通过联合对角化获得二维角估计。其适合存在一维角兼并的情况。
5.在实际中所遇到的很多信号和噪声都是非高斯的。在非高斯情况下,若仍采用高斯假设,则信号处理的性能会大打折扣。为了使设备在此复杂情况下正常工作,必须研究适合冲击噪声环境下的算法。为此,提出了三种基于联合对角化分数低阶矩阵的二维DOA估计方法,该方法适合于存在一维角度兼并的信号,且无需二维谱峰搜索和参数配对,弥补了传统的二阶或四阶统计模型及相应的处理算法不能用于冲击噪声环境的缺陷,增强了子空间算法的稳健性,改善了阵列的二维角估计性能。
The problem of two-dimensional (2-D) directions of arrival (DOAs) estimation has attracted a lot of attention, especially in fields such as radar, sonar, communications, and seismology. Many 2-D DOAs estimation methods have been proposed recently, the popular high-resolution techniques used to distinguish multiple closely spaced sources are eigenstructure based techniques. However, multidimensional searching based 2-D DOA estimation techniques require searching spectral peaks in a 2-D domain and are thus not amenable to real-time implementation. Another class of methods that adopt two one-dimensional processing requires complex pair matching. The aligning accuracy of pair matching degrades significantly in the case of low SNR, small angular separation, and other severe propagation environments.
The main contributions of this dissertation are studying the property of some widely used arrays and proposing several 2-D DOAs estimation algorithms with neither pair matching nor peak searching. The main creative works are concluded as the following:
Firstly, a novel decoupled method for 2-D DOAs estimation using two parallel ULAs is proposed. It decouples the 2-D DOAs estimation problem into two one-dimensional estimation problems and thus reduces the computation complexity. It can estimate more 2-D parameters of source signals with distinct angles than DOA matrix method and obtained more accurate estimates. Then it is solved by polynomial-rooting. A relevant Cramer-Rao bound (CRB) of the proposed method is derived and forward/backward spatial smoothing techniques are adopted to extend the proposed method to estimate 2-D DOAs of multiple highly correlated and coherent signals.
Secondly, a novel joint diagonalization based DOA matrix method is proposed to estimate the higher 2-D DOAs of uncorrelated narrowband signals. The method constructs three subarrays by exploiting the special structure of the array, thereby obtaining the 2-D DOAs of the array based on joint diagonalization directly with neither peak search nor pairing. The new method can handle sources with common 1-D angles. Then the method is extended to a sensor array consists of triplets of identical sensors. The new array structure achieves very accurate estimates since the estimation accuracy can be improved by adjusting the array aperture.
Thirdly, in some applications, the sources are stationary with different spectral contents. We can achieve array aperture extending, array calibration, and so on by exploiting the temporal structure of the signals. We propose a 2-D DOAs estimation method based on a joint diagonalization of several spatio-temporal covariance matrices. It is shown that performing a joint diagonalization of a combined set of these matrices provides an improved estimate of the 2-D DOAs over the aforementioned techniques in two aspects. First, signals with common 1-D angles or in any curved surface can be resolved. Second, robustness is increased at low signal to noise ratios (SNRs). At last, the method is extended to 2-D DOAs estimation with arbitrary array configuration.
Fourthly, for non-Gaussian signals, higher-order (HO) statistics have many excellent properties such as suppress non-Gaussian noise, array calibration, array aperture extending and so on. Two novel joint diagonalization fourth-order cumulant DOA matrix methods are proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in arbitrary Gaussian noise environment. Based on the special structure of the array, the methods constructs several subarrays by exploiting fourth-order cumulant, thereby obtaining the 2-D DOAs of the array directly with neither peak searching nor pair matching. The new method can handle sources with common 1-D angles.
Finally, there are also many phenomena in signal processing which are decidedly non-Gaussian. Non-Gaussianity often results in significant performance degradation for system optimized under the Gaussian assumption. In order that the devices work well and exert fighting efficiency sufficiently in this bad situations, an exact and appropriate mathematical model needs to be established for impulsive interference or noise, what's more, signal processing methods and techniques are studied in the impulsive noise environments. Three novel joint diagonalization fractional lower-order moment (FLOM) DOA matrix methods are proposed, which can estimate the 2-D DOAs of the signals directly with neither peak searchings nor pair matchings. Moreover, they can handle sources with common 1-D angles. The new methods are robust against SαS noises and remedy the lack of the traditional subspace-based techniques employing second-order or HO moments cannot be applied in the implusive noise environments.
本文的主要工作是对常用阵列的二维DOA估计特性进行研究,针对不同的阵列和信号,分析了已有算法的不足,提出了几种无需参数配对的计算量较低的二维DOA估计方法。本文的主要创新之处概括如下:
1.针对双平行均匀线性阵列,提出了一种解耦二维DOA估计方法。与现有的基于双平行线阵的算法不同,该方法不仅能估计更多信号的二维DOA,还获得了更高的估计精度。根据双平行均匀阵列的特点,进一步给出了基于多项式求根的二维到达角估计方法。给出了双平行阵列的CRB(Cramer-Rao Bound),最后采用前后向空间平滑技术把其推广到处理相关信号源的情况。
2.针对基于双平行均匀线性阵列的现有DOA矩阵法存在的一维角度兼并问题,通过合理设计阵列流形,提出了一种基于联合对角化技术的DOA矩阵方法。该方法较好的解决了现有DOA矩阵法存在的一维角度兼并问题,并且无需二维谱峰搜索和参数配对,改善了阵列的角估计性能。然后,新方法被推广到应用于由任意triplets(三元子阵)组成的阵列,通过调整triplets间的距离可以获得更高的分辨力。
3.在一些应用中,信号常常具有不同的谱。利用信号的时域信息,可以有效的扩展阵列孔径,避免阵列校正等等。针对原空时DOA矩阵法不能估计在某些曲面内的信号的缺点,提出了一种基于联合对角化空时协方差矩阵的二维DOA估计方法。通过联合对角化全部或部分空时DOA矩阵,新方法比原空时DOA矩阵法获得了两方面的性能增强。第一,解决了原空时DOA矩阵法在某些曲面存在的角度兼并问题;第二,在低信噪比下,其估计性能得到了改善。最后把该方法推广到任意阵列的二维DOA估计。
4.对于非高斯信号,高阶统计量包含了有效的统计信息,并且具有许多良好性质,如抑制任意加性高斯噪声、阵列校正与孔径扩展等。针对相互独立的非高斯窄带信号,提出了基于联合对角化技术的累量域二维DOA矩阵方法。利用阵列的结构,该方法构造几个子阵,然后通过联合对角化获得二维角估计。其适合存在一维角兼并的情况。
5.在实际中所遇到的很多信号和噪声都是非高斯的。在非高斯情况下,若仍采用高斯假设,则信号处理的性能会大打折扣。为了使设备在此复杂情况下正常工作,必须研究适合冲击噪声环境下的算法。为此,提出了三种基于联合对角化分数低阶矩阵的二维DOA估计方法,该方法适合于存在一维角度兼并的信号,且无需二维谱峰搜索和参数配对,弥补了传统的二阶或四阶统计模型及相应的处理算法不能用于冲击噪声环境的缺陷,增强了子空间算法的稳健性,改善了阵列的二维角估计性能。
The problem of two-dimensional (2-D) directions of arrival (DOAs) estimation has attracted a lot of attention, especially in fields such as radar, sonar, communications, and seismology. Many 2-D DOAs estimation methods have been proposed recently, the popular high-resolution techniques used to distinguish multiple closely spaced sources are eigenstructure based techniques. However, multidimensional searching based 2-D DOA estimation techniques require searching spectral peaks in a 2-D domain and are thus not amenable to real-time implementation. Another class of methods that adopt two one-dimensional processing requires complex pair matching. The aligning accuracy of pair matching degrades significantly in the case of low SNR, small angular separation, and other severe propagation environments.
The main contributions of this dissertation are studying the property of some widely used arrays and proposing several 2-D DOAs estimation algorithms with neither pair matching nor peak searching. The main creative works are concluded as the following:
Firstly, a novel decoupled method for 2-D DOAs estimation using two parallel ULAs is proposed. It decouples the 2-D DOAs estimation problem into two one-dimensional estimation problems and thus reduces the computation complexity. It can estimate more 2-D parameters of source signals with distinct angles than DOA matrix method and obtained more accurate estimates. Then it is solved by polynomial-rooting. A relevant Cramer-Rao bound (CRB) of the proposed method is derived and forward/backward spatial smoothing techniques are adopted to extend the proposed method to estimate 2-D DOAs of multiple highly correlated and coherent signals.
Secondly, a novel joint diagonalization based DOA matrix method is proposed to estimate the higher 2-D DOAs of uncorrelated narrowband signals. The method constructs three subarrays by exploiting the special structure of the array, thereby obtaining the 2-D DOAs of the array based on joint diagonalization directly with neither peak search nor pairing. The new method can handle sources with common 1-D angles. Then the method is extended to a sensor array consists of triplets of identical sensors. The new array structure achieves very accurate estimates since the estimation accuracy can be improved by adjusting the array aperture.
Thirdly, in some applications, the sources are stationary with different spectral contents. We can achieve array aperture extending, array calibration, and so on by exploiting the temporal structure of the signals. We propose a 2-D DOAs estimation method based on a joint diagonalization of several spatio-temporal covariance matrices. It is shown that performing a joint diagonalization of a combined set of these matrices provides an improved estimate of the 2-D DOAs over the aforementioned techniques in two aspects. First, signals with common 1-D angles or in any curved surface can be resolved. Second, robustness is increased at low signal to noise ratios (SNRs). At last, the method is extended to 2-D DOAs estimation with arbitrary array configuration.
Fourthly, for non-Gaussian signals, higher-order (HO) statistics have many excellent properties such as suppress non-Gaussian noise, array calibration, array aperture extending and so on. Two novel joint diagonalization fourth-order cumulant DOA matrix methods are proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in arbitrary Gaussian noise environment. Based on the special structure of the array, the methods constructs several subarrays by exploiting fourth-order cumulant, thereby obtaining the 2-D DOAs of the array directly with neither peak searching nor pair matching. The new method can handle sources with common 1-D angles.
Finally, there are also many phenomena in signal processing which are decidedly non-Gaussian. Non-Gaussianity often results in significant performance degradation for system optimized under the Gaussian assumption. In order that the devices work well and exert fighting efficiency sufficiently in this bad situations, an exact and appropriate mathematical model needs to be established for impulsive interference or noise, what's more, signal processing methods and techniques are studied in the impulsive noise environments. Three novel joint diagonalization fractional lower-order moment (FLOM) DOA matrix methods are proposed, which can estimate the 2-D DOAs of the signals directly with neither peak searchings nor pair matchings. Moreover, they can handle sources with common 1-D angles. The new methods are robust against SαS noises and remedy the lack of the traditional subspace-based techniques employing second-order or HO moments cannot be applied in the implusive noise environments.
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