高频雷达空时联合超分辨算法研究
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摘要
空间谱估计具有超(高)的空间信号的分辨能力,因此也常常被称为“超(高)分辨谱估计”。本文首先讨论了空间谱估计的理论模型,然后分析了三种基于特征分解的线性预测算法(包括最大熵算法,最大方差算法以及自回归模型算法),之后对超分辨算法中最为经典的多重信号分类算法进行了深入研究。而这些算法都可以归结为子空间算法中的噪声子空间算法。
子空间算法中另外一类就是旋转不变子空间算法。本文对基于最小二乘(LS)法和总体最小二乘(TLS)法的两类算法做出了在角度和成功概率等评价标准上的性能比较。
上述算法均是针对方位的一维信号参数的估计。而同时对角度和多普勒频率的进行联合估计则更贴近实际。因此本文从一维参数估计的讨论出发,讨论了空域和时域处理等效性,并选用了噪声子空间类算法做了空时联合的扩展分析。
在文中也详细的介绍了会影响多重信号分类(MUSIC)算法性能的因素。之后论文从计算机仿真出发,分析了阵元间距以及相干源信号对MUSIC的影响,并仿真验证了前后向平滑这种改进算法对相干信源有着良好的分辨能力。在实际海面,杂波会对超分辨算法的有效性造成很大的困扰。在文章中,特别采用高阶累积量的方法对MUSIC算法进行改进。这种改进不仅可以获得比二阶矩更好的性能,而且使得上述研究的超分辨算法无论在高斯白噪声环境还是在有色高斯噪声环境下均有很好的来波方向估计(DOA)性能。在文中,也基于这些改善,利用实测数据检验了MUSIC算法的性能。
仿真是检验算法正确性的重要方法。论文中对每一种算法都做了仿真研究。在论文中,天线阵主要采用了线阵和面阵。研究结果表明,噪声子空间算法不仅在一维角度估计方面有良好性能,同时,通过对结果的定性分析,基于特征分解的噪声子空间算法完全能对二维参数(方位角和频率)进行联合估计。同时,本文选取了角度/频率绝对偏差,角度/频率方差以及成功概率对四种算法进行了定量分析。从比较结果来看,MUSIC从各个方面都优于其他算法。
Spatial spectrum estimation is called super-resolution spectrum estimation for the reason that it has super (high) resolution for spatial signal. Based on the study of theoretical model, the dissertation first analyzes three linear prediction algorithms including maximum entropy algorithm based on character decomposition, the maximum variance algorithm and auto regression algorithm, and then studies multiple signal classification method, which is a classical super resolution algorithm. The entire above algorithms can be concluded into noise subspace algorithm.
Another kind of subspace algorithm is estimation of signal parameters via rotational invariance techniques.This dissertation compares the algorithms of LS and TLS to evaluate the performance in the angle detection and success probability.
All the above algorithms are one-dimensional signal parameters estimation aiming at Azimuth. However, 2-D estimation considering angle and doppler frequency is more applicable. This dissertation begins with the discussion of one-dimensional estimation, and discusses about the equivalent of time domain and spatial domain in dealing with signals. As to the above nosie space algorithms, the dissertation does further research on the space-time joint estimation.
For the actual situation, the dissertation introduces the factors influencing the performance of MUSIC in detail and analyzes the effect of array element spacing and wideband signals on MUSIC. And it is verified that forward-back smoothing algorithm can distinguish coherent signals well.
On real sea surface, clutter affects the resolution of the super resolution algorithm. At the end of the dissertation, higher-order statistics method is employed in improving MUSIC, which has better performance than second-order moment method, and it gains better DOA performance with super-resolution algorithm no matter in the environment of non-correlated Gaussian noise or correlated Gaussian noise.
The dissertation simulates every algorithm, and selects linear array and area array as antenna array element. In this dissertation, real data are also employed to test the performance of MUSIC algorithm.
From the simulation results, Noise subspace algorithm based on character decomposition can gain good performance in angle estimation and 2-D estimation for angle and frequency. As the test of the four algorithms, Absolute deviation and variance of angle/frequency and success probability are used to do quantitative analysis. From the result, MUSIC is better than other algorithms from all aspects.
子空间算法中另外一类就是旋转不变子空间算法。本文对基于最小二乘(LS)法和总体最小二乘(TLS)法的两类算法做出了在角度和成功概率等评价标准上的性能比较。
上述算法均是针对方位的一维信号参数的估计。而同时对角度和多普勒频率的进行联合估计则更贴近实际。因此本文从一维参数估计的讨论出发,讨论了空域和时域处理等效性,并选用了噪声子空间类算法做了空时联合的扩展分析。
在文中也详细的介绍了会影响多重信号分类(MUSIC)算法性能的因素。之后论文从计算机仿真出发,分析了阵元间距以及相干源信号对MUSIC的影响,并仿真验证了前后向平滑这种改进算法对相干信源有着良好的分辨能力。在实际海面,杂波会对超分辨算法的有效性造成很大的困扰。在文章中,特别采用高阶累积量的方法对MUSIC算法进行改进。这种改进不仅可以获得比二阶矩更好的性能,而且使得上述研究的超分辨算法无论在高斯白噪声环境还是在有色高斯噪声环境下均有很好的来波方向估计(DOA)性能。在文中,也基于这些改善,利用实测数据检验了MUSIC算法的性能。
仿真是检验算法正确性的重要方法。论文中对每一种算法都做了仿真研究。在论文中,天线阵主要采用了线阵和面阵。研究结果表明,噪声子空间算法不仅在一维角度估计方面有良好性能,同时,通过对结果的定性分析,基于特征分解的噪声子空间算法完全能对二维参数(方位角和频率)进行联合估计。同时,本文选取了角度/频率绝对偏差,角度/频率方差以及成功概率对四种算法进行了定量分析。从比较结果来看,MUSIC从各个方面都优于其他算法。
Spatial spectrum estimation is called super-resolution spectrum estimation for the reason that it has super (high) resolution for spatial signal. Based on the study of theoretical model, the dissertation first analyzes three linear prediction algorithms including maximum entropy algorithm based on character decomposition, the maximum variance algorithm and auto regression algorithm, and then studies multiple signal classification method, which is a classical super resolution algorithm. The entire above algorithms can be concluded into noise subspace algorithm.
Another kind of subspace algorithm is estimation of signal parameters via rotational invariance techniques.This dissertation compares the algorithms of LS and TLS to evaluate the performance in the angle detection and success probability.
All the above algorithms are one-dimensional signal parameters estimation aiming at Azimuth. However, 2-D estimation considering angle and doppler frequency is more applicable. This dissertation begins with the discussion of one-dimensional estimation, and discusses about the equivalent of time domain and spatial domain in dealing with signals. As to the above nosie space algorithms, the dissertation does further research on the space-time joint estimation.
For the actual situation, the dissertation introduces the factors influencing the performance of MUSIC in detail and analyzes the effect of array element spacing and wideband signals on MUSIC. And it is verified that forward-back smoothing algorithm can distinguish coherent signals well.
On real sea surface, clutter affects the resolution of the super resolution algorithm. At the end of the dissertation, higher-order statistics method is employed in improving MUSIC, which has better performance than second-order moment method, and it gains better DOA performance with super-resolution algorithm no matter in the environment of non-correlated Gaussian noise or correlated Gaussian noise.
The dissertation simulates every algorithm, and selects linear array and area array as antenna array element. In this dissertation, real data are also employed to test the performance of MUSIC algorithm.
From the simulation results, Noise subspace algorithm based on character decomposition can gain good performance in angle estimation and 2-D estimation for angle and frequency. As the test of the four algorithms, Absolute deviation and variance of angle/frequency and success probability are used to do quantitative analysis. From the result, MUSIC is better than other algorithms from all aspects.
引文
1 Mark A. Richards. Fundamentals of Radar Signal Processing. Publishing House of Electronics Industry,2008:292~294
2王永良,陈辉,彭应宁,万群.空间谱估计理论与算法.清华大学出版社, 2004:1~2,9~10,68~70,467~477
3汪金华.小型阵列超分辨算法研究.哈尔滨工业大学硕士论文. 2007:3~4
4 Krim H, Viberg M. Two decades of array signal processing research. IEEE Signal Processing Magazine. 1996: 67~84
5 Kay S. M, Marple S. L. Spectrum analysis-a modern perspective. Proc of the IEEE. 1981: 11
6 Burg J.P. Macimum entropy spectral analysis. Proc. of the 37th meeting of the Annual Int. SEG Meeting. Oklahoma City. 1967
7 Capon J. High-resolution frequency-wavenumber spectrum analysis. Proc. of IEEE. 1969,57(8):1408~1418
8 Kumaresan R, Tufts D. W. Estimating the angles of arrival of multiple plne waves. IEEE Trans. On AES. 1983,19(1):134~139
9 Schmidt R.O. Multipe emitter location and signal parameter estimation. IEEE Trans AP-34(3) .1986:276~280
10孙超,李斌.加权子空间拟合算法理论与应用.西北工业大学出版社, 1994:26~27
11 Chen Y.M, Lee J.H, Yeh C.C. Bearing estimation without calibration for randomly perturbed arrays. IEEE Trans on SP. 39(1):194~196
12 Stoica P, Nehorai A. Music, Maximum likelihood, and Cramer-Rao bound. In Proc ICASSP, 1988:2296~2299
13梁清泉.基于高阶累积量的波达方向估计技术的.西北工业大学硕士论文. 2002:1~10
14金梁,殷勤业,汪仪林.广义谱相关子空间拟合DOA估计原理.电子学报. 2000, (1):60~61
15 Mathews C.P. Eigen-structure techniques for 2-D angle estimation with uniform circular arrays. IEEE on SP, 1994, 42(9):2395~2401
16 Swindlehurt A, Kailath T. Azimuth/elevation direction finding using regular array geometries. IEEE Trans on AEW, 1993, 29(1):145~155
17 Yin Q, Newcomb R, Zou L. Estimation of 2-D angles of arrival via parallel linear arrays. In proc. ICASSP, Nanjing, China, 1989, 2803~2806
18 Zoltowski M.D, Mathews C.P. Real-time frequency and 2-D angle estimation with sub-Nyquist apatio-sampling. Proc, ICASSP, 1993, 117~120
19 Zoltowski M.D, Mathews C.P. Real-time frequency and 2-D angle estimation with sub Nyquista patio-temporal sampling. IEEE Trans, on SP, 1994, 42 (10):2781~2797
20 Roy R, Kailath T. ESPRIT-a subspace totation approach to estimation of parameters of cissoid in noise. IEEE Trans, on ASSP, 1986, 34 (10):1340~1342
21陈辉,王永良.空间谱估计算法结构及仿真分析.系统工程与电子技术. 2001, 23(8):76~76
22张林让,保铮,杨克虎.基于时域投影的空时二维超分辨技术.西安电子科技大学学报(雷达处理信号专辑). 1997, 24:62~67
23贾永康,保铮.利用多普勒信息的波达方向最大似然估计方法电子学报. 1997, 25(6):71~76
24赵伟娟.多基地固定站高频超视距地波雷达主控机软件研制.哈尔滨工业大学硕士论文. 2008:1~5
25殷勤业,邹理和.一种高分辨率二维信号参量估计方法.通信学报. 1997, 12(4):1~3
26黄浩学,吴嗣亮.基于均匀圆阵的信号源DOA和多普勒频率估计算法.电子学报, 2007,29(5):619~620
27张辉.二维空间谱估计与自适应波束形成技术研究.解放军信息工程大学博士论文. 2007:9~10
28韩卫杰.改进MUSIC算法在DOA估计中的研究.西南交通大学硕士论文. 2006:24~26
29汪晋宽,顾德英.空间自适应信号处理.东北大学出版社, 2003:182~183
30 Efron A, Tufts D. Estimation of frequencies of multiple two-dimensional sinusoids: improved methods of linera prediction. IEEE Internatioal Conference on ICASSP, 1985, 1777~1779
31 Shan T.J, Wax M, Kailath T. Adaptive beamforming for coherent signals, IEEE Trans on ASSP, 1985, 33(3):527~536
32 Shan T.J, Wax M, Kailath T. On spatial smoothing for estimation of coherent signals. IEEE Trans on ASSP, 1985, 33(4):806~811
33 Pillai S.U, Kwon B.H. Forward/backward spatial smoothing for coherent signal identification. IEEE Trans on ASSP, 1989, 37(1):8~15
34 Pillai S.U, Kwon B.H. Performance analysis of MUSIC-type high resolution estimators for direction finding in correlated and coherent scenes. IEEE Trans on ASSP, 1989, 37(8):1176~1189
35 Rao B.D, Hari K. V. S. Effect of spatial smootihing on the performance of MUSIC and the minimum-norm method. IEE Proc F, 1990, 137(6):449~458
36 Rao B.D, Hari K. V. S. Effect of spatial smootihing on statespace methods/ ESPRIT. In Proc IEEE 5th workshop spectrum estimation modeling, 1990, 10:377~381
37徐利民,吴瑛.一种改进二维超分辨分维估计方法.现代电子技术, 2003, 7:58~59
38苏洪涛,张守宏,保铮.空时超分辨算法在高频地波超视距雷达中的应用.电子学报. 2006, 3:436~438
39李廷伟.高阶统计量及在阵列信号处理中的应用.国防科学技术大学硕士论文. 2005:5~7
40郑明辉.高阶谱应用中参数估计问题分析.福建工程学院学报. 2007, 4:358~360
41李长柏.基于高阶谱和循环谱的舰船噪声多源特征分离研究.西北工业大学硕士论文. 2005:40~45
42李盛,吕泽均,张扬.基于四阶累积量的到达频率差估计算法.电视技术. 2006,2:172~174
43高勋章,黎湘,庄钊文.基于四阶混合累积量的雷达目标二维超分辨成像.电子与信息学报. 2005,10:1555~1557
44康晓涛,石要武,张丽丽.谐波恢复的互高阶累积量Hankel矩阵法.电子学报. 2005,1:67~69
2王永良,陈辉,彭应宁,万群.空间谱估计理论与算法.清华大学出版社, 2004:1~2,9~10,68~70,467~477
3汪金华.小型阵列超分辨算法研究.哈尔滨工业大学硕士论文. 2007:3~4
4 Krim H, Viberg M. Two decades of array signal processing research. IEEE Signal Processing Magazine. 1996: 67~84
5 Kay S. M, Marple S. L. Spectrum analysis-a modern perspective. Proc of the IEEE. 1981: 11
6 Burg J.P. Macimum entropy spectral analysis. Proc. of the 37th meeting of the Annual Int. SEG Meeting. Oklahoma City. 1967
7 Capon J. High-resolution frequency-wavenumber spectrum analysis. Proc. of IEEE. 1969,57(8):1408~1418
8 Kumaresan R, Tufts D. W. Estimating the angles of arrival of multiple plne waves. IEEE Trans. On AES. 1983,19(1):134~139
9 Schmidt R.O. Multipe emitter location and signal parameter estimation. IEEE Trans AP-34(3) .1986:276~280
10孙超,李斌.加权子空间拟合算法理论与应用.西北工业大学出版社, 1994:26~27
11 Chen Y.M, Lee J.H, Yeh C.C. Bearing estimation without calibration for randomly perturbed arrays. IEEE Trans on SP. 39(1):194~196
12 Stoica P, Nehorai A. Music, Maximum likelihood, and Cramer-Rao bound. In Proc ICASSP, 1988:2296~2299
13梁清泉.基于高阶累积量的波达方向估计技术的.西北工业大学硕士论文. 2002:1~10
14金梁,殷勤业,汪仪林.广义谱相关子空间拟合DOA估计原理.电子学报. 2000, (1):60~61
15 Mathews C.P. Eigen-structure techniques for 2-D angle estimation with uniform circular arrays. IEEE on SP, 1994, 42(9):2395~2401
16 Swindlehurt A, Kailath T. Azimuth/elevation direction finding using regular array geometries. IEEE Trans on AEW, 1993, 29(1):145~155
17 Yin Q, Newcomb R, Zou L. Estimation of 2-D angles of arrival via parallel linear arrays. In proc. ICASSP, Nanjing, China, 1989, 2803~2806
18 Zoltowski M.D, Mathews C.P. Real-time frequency and 2-D angle estimation with sub-Nyquist apatio-sampling. Proc, ICASSP, 1993, 117~120
19 Zoltowski M.D, Mathews C.P. Real-time frequency and 2-D angle estimation with sub Nyquista patio-temporal sampling. IEEE Trans, on SP, 1994, 42 (10):2781~2797
20 Roy R, Kailath T. ESPRIT-a subspace totation approach to estimation of parameters of cissoid in noise. IEEE Trans, on ASSP, 1986, 34 (10):1340~1342
21陈辉,王永良.空间谱估计算法结构及仿真分析.系统工程与电子技术. 2001, 23(8):76~76
22张林让,保铮,杨克虎.基于时域投影的空时二维超分辨技术.西安电子科技大学学报(雷达处理信号专辑). 1997, 24:62~67
23贾永康,保铮.利用多普勒信息的波达方向最大似然估计方法电子学报. 1997, 25(6):71~76
24赵伟娟.多基地固定站高频超视距地波雷达主控机软件研制.哈尔滨工业大学硕士论文. 2008:1~5
25殷勤业,邹理和.一种高分辨率二维信号参量估计方法.通信学报. 1997, 12(4):1~3
26黄浩学,吴嗣亮.基于均匀圆阵的信号源DOA和多普勒频率估计算法.电子学报, 2007,29(5):619~620
27张辉.二维空间谱估计与自适应波束形成技术研究.解放军信息工程大学博士论文. 2007:9~10
28韩卫杰.改进MUSIC算法在DOA估计中的研究.西南交通大学硕士论文. 2006:24~26
29汪晋宽,顾德英.空间自适应信号处理.东北大学出版社, 2003:182~183
30 Efron A, Tufts D. Estimation of frequencies of multiple two-dimensional sinusoids: improved methods of linera prediction. IEEE Internatioal Conference on ICASSP, 1985, 1777~1779
31 Shan T.J, Wax M, Kailath T. Adaptive beamforming for coherent signals, IEEE Trans on ASSP, 1985, 33(3):527~536
32 Shan T.J, Wax M, Kailath T. On spatial smoothing for estimation of coherent signals. IEEE Trans on ASSP, 1985, 33(4):806~811
33 Pillai S.U, Kwon B.H. Forward/backward spatial smoothing for coherent signal identification. IEEE Trans on ASSP, 1989, 37(1):8~15
34 Pillai S.U, Kwon B.H. Performance analysis of MUSIC-type high resolution estimators for direction finding in correlated and coherent scenes. IEEE Trans on ASSP, 1989, 37(8):1176~1189
35 Rao B.D, Hari K. V. S. Effect of spatial smootihing on the performance of MUSIC and the minimum-norm method. IEE Proc F, 1990, 137(6):449~458
36 Rao B.D, Hari K. V. S. Effect of spatial smootihing on statespace methods/ ESPRIT. In Proc IEEE 5th workshop spectrum estimation modeling, 1990, 10:377~381
37徐利民,吴瑛.一种改进二维超分辨分维估计方法.现代电子技术, 2003, 7:58~59
38苏洪涛,张守宏,保铮.空时超分辨算法在高频地波超视距雷达中的应用.电子学报. 2006, 3:436~438
39李廷伟.高阶统计量及在阵列信号处理中的应用.国防科学技术大学硕士论文. 2005:5~7
40郑明辉.高阶谱应用中参数估计问题分析.福建工程学院学报. 2007, 4:358~360
41李长柏.基于高阶谱和循环谱的舰船噪声多源特征分离研究.西北工业大学硕士论文. 2005:40~45
42李盛,吕泽均,张扬.基于四阶累积量的到达频率差估计算法.电视技术. 2006,2:172~174
43高勋章,黎湘,庄钊文.基于四阶混合累积量的雷达目标二维超分辨成像.电子与信息学报. 2005,10:1555~1557
44康晓涛,石要武,张丽丽.谐波恢复的互高阶累积量Hankel矩阵法.电子学报. 2005,1:67~69