基于电磁矢量传感器阵列相干源DOA估计的研究
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摘要
阵列信号处理是空域信号分析和处理的一种重要手段,它广泛应用于雷达、声纳、通信、地震勘探和医学成像等多个领域。阵列信号处理的本质是利用空间按一定规则布置的传感器阵列和多通道来接收获取信号的时域和空域等多维信息,达到检测信号和提取其参数的目的。对于空间电磁波信号而言,波达方向和极化状态是其重要的特征参数,携带了空间电磁波信号的重要信息。信号波达方向描述了信号源在空间中的位置,极化状态描述了电磁波的矢量运动特征,是电磁波本身固有属性。传统的标量传感器阵列能够估计信号的功率、频率、时间延迟和到达方向,但不能估计出波信号的极化状态。电磁矢量传感器阵列不仅能获得信号的空间到达角信息,而且也能得到信号的极化信息。和传统标量传感器阵列相比较,电磁矢量传感器阵列具有以下几个优点：具有较强的抗干扰能力；具有稳健的监测能力；具有较高的系统分辨能力；具有极化多址能力。
在实际工程中,经常会碰到相干源的问题。在雷达或声纳系统中,当目标信号存在多径或有多个目标信号时,接收到的回波是相干的。关于相干源的波达方向估计问题一直是雷达、通信和声纳等系统中的关键问题之一。当来波信号相干时,经典的MUSIC算法和ESPRIT算法中关键的协方差矩阵不满秩,从而无法划分信号子空间和噪声子空间,导致算法失效。在此,本文利用电磁矢量传感器阵列的优秀性能,讨论研究了相干信号源DOA和极化参数的估计问题。
针对循环平稳信号中的相干源问题,本文首先利用极化均匀线阵,结合空域平滑技术,介绍了循环MUSIC平滑算法。其后,研究了在Toeplitz矩阵重构基础上的相干源DOA估计方法。对相干循环平稳信号源的DOA给予了有效估计,而且在不影响阵列孔径的情况下,进一步提高了估计性能。
最后,分析了非均匀线阵的信号模型,讨论了非均匀线阵的阵元配置、阵列信号的估计模糊的问题,并结合电磁矢量传感器平滑的循环MUSIC算法,研究了在稀疏线性阵列下的循环相干信号的DOA和极化参数估计问题,并进行仿真实验予以验证。
Array signal processing is important means of the signal analysis.It is widely applied in radar, sonar, communication, seismic exploration and medical imaging etc. Array signal processing is using plenty of sensors in different locations in the space composition to form a sensor array, through which signals of the space are received and processed to get the temporal and spatial multi-dimensional signal. That's how detection and extraction of its parameters is completed. The polarization state and DOA are the most important characteristic parameters for space of electromagnetic signals and they carry important information of electromagnetic signals. Signal DOA describes the position of signal source in space, while the polarization describes the characteristics of electromagnetic wave motion vector, which is the intrinsic property of electromagnetic wave. The traditional scalar sensor array can estimate the signal power, frequency, time delay and to estimate direction, but not the polarization. Electromagnetic vector sensor array can not only obtain the angle of signal in the space, but also can get information of signal polarization. Compared with traditional scalar sensor array, electromagnetic vector sensor array, has several advantages:strong anti-jamming ability, stable capability. The system has high resolution and polarization multi-access ability.
In practical engineer project, we often encounter with coherent sources. In radar or sonar system, when there is target with multipath or multiple target signals, receipt of the echo is key issues of coherence estimation problem. When the wave signals are coherent, the covariance of the classical MUSIC algorithm and the ESPRIT algorithm cannot divide signal subspace and noise sub-space, which causes algorithm failure. So this paper studies the DOA of coherent sources and the polarization parameters estimation problem.
Firstly, based on the polarized uniform linear array, we combined with spatial smoothing technique, described the cycle MUSIC smoothing algorithm for the coherent cyclostationary signals. Subsequently, the basis of Toeplitz matrix regrouping DOA coherent sources estimate method is studied. The smooth circulation of coherent sources estimate DOA gives effective estimates, and in the circumstances, the pore arrays to further improve the performance.
Furthermore, the signal sparse linear array model is also analyzed, the inhomogeneous linear array elements configuration and the estimation of the fuzzy array signals are discussed. At last, based on the cycle of electromagnetic vector sensor smoothing algorithm, DOA and polarized coherent signal parameter estimation problem is discussed under the sparse linear array with simulation experiment verified.
在实际工程中,经常会碰到相干源的问题。在雷达或声纳系统中,当目标信号存在多径或有多个目标信号时,接收到的回波是相干的。关于相干源的波达方向估计问题一直是雷达、通信和声纳等系统中的关键问题之一。当来波信号相干时,经典的MUSIC算法和ESPRIT算法中关键的协方差矩阵不满秩,从而无法划分信号子空间和噪声子空间,导致算法失效。在此,本文利用电磁矢量传感器阵列的优秀性能,讨论研究了相干信号源DOA和极化参数的估计问题。
针对循环平稳信号中的相干源问题,本文首先利用极化均匀线阵,结合空域平滑技术,介绍了循环MUSIC平滑算法。其后,研究了在Toeplitz矩阵重构基础上的相干源DOA估计方法。对相干循环平稳信号源的DOA给予了有效估计,而且在不影响阵列孔径的情况下,进一步提高了估计性能。
最后,分析了非均匀线阵的信号模型,讨论了非均匀线阵的阵元配置、阵列信号的估计模糊的问题,并结合电磁矢量传感器平滑的循环MUSIC算法,研究了在稀疏线性阵列下的循环相干信号的DOA和极化参数估计问题,并进行仿真实验予以验证。
Array signal processing is important means of the signal analysis.It is widely applied in radar, sonar, communication, seismic exploration and medical imaging etc. Array signal processing is using plenty of sensors in different locations in the space composition to form a sensor array, through which signals of the space are received and processed to get the temporal and spatial multi-dimensional signal. That's how detection and extraction of its parameters is completed. The polarization state and DOA are the most important characteristic parameters for space of electromagnetic signals and they carry important information of electromagnetic signals. Signal DOA describes the position of signal source in space, while the polarization describes the characteristics of electromagnetic wave motion vector, which is the intrinsic property of electromagnetic wave. The traditional scalar sensor array can estimate the signal power, frequency, time delay and to estimate direction, but not the polarization. Electromagnetic vector sensor array can not only obtain the angle of signal in the space, but also can get information of signal polarization. Compared with traditional scalar sensor array, electromagnetic vector sensor array, has several advantages:strong anti-jamming ability, stable capability. The system has high resolution and polarization multi-access ability.
In practical engineer project, we often encounter with coherent sources. In radar or sonar system, when there is target with multipath or multiple target signals, receipt of the echo is key issues of coherence estimation problem. When the wave signals are coherent, the covariance of the classical MUSIC algorithm and the ESPRIT algorithm cannot divide signal subspace and noise sub-space, which causes algorithm failure. So this paper studies the DOA of coherent sources and the polarization parameters estimation problem.
Firstly, based on the polarized uniform linear array, we combined with spatial smoothing technique, described the cycle MUSIC smoothing algorithm for the coherent cyclostationary signals. Subsequently, the basis of Toeplitz matrix regrouping DOA coherent sources estimate method is studied. The smooth circulation of coherent sources estimate DOA gives effective estimates, and in the circumstances, the pore arrays to further improve the performance.
Furthermore, the signal sparse linear array model is also analyzed, the inhomogeneous linear array elements configuration and the estimation of the fuzzy array signals are discussed. At last, based on the cycle of electromagnetic vector sensor smoothing algorithm, DOA and polarized coherent signal parameter estimation problem is discussed under the sparse linear array with simulation experiment verified.
引文
[1]庄钊文,肖顺平,王雪松.雷达极化信息处理及应用[M].北京：国防工业出版社,1999.
[2]王永良,陈辉,彭应宁,万群著.空间谱估计理论与算法[M].北京：清华大学出版,2004.
[3]Kim H, Viberg M. Two decades of array signal processing research[J]. IEEE Signal Processing Magazine,1996,13(4):67-94
[4]J. P. Burg. Maximum entropy spectral analysis[C]. Presented at the 37th Meeting Soc. Exploration Geophysicists, Oklahoma, OK,1967.
[5]J. Capon. High-resolution frequency-wavenumber spectrum analysis[J]. Proc. IEEE 57(8): 1408-1418, Aug.1969.
[6]V. F. Pisarenko. The Retrieval of Harmonics From a Covariance Function[J]. Geophys J.Roy. Astron.Soc,1973,33:.247-266.
[7]R.O. Schmidt. Multiple Emitter Location and Signal Parameter Estimation[J]. IEEE Trans, on AP, 1986,34(3):276-280.
[8]R. Roy, T. Kailath. ESPRIT-A subspace rotation approach to estimation of parameters of cissoids in noise[J]. IEEE Trans. on ASSP,1986,34(10):1340-1342.
[9]Cadzow J A, Kim Y S, Shiue D C. General direction-of-arrival estimation:a signal subspace approach[J]. IEEE Trans. on AES,1989,25(1):31-46.
[10]R. Kumaresan, D. W. Tufts. Estimating the Angle-of-Arrival of Multiple Plane Waves[J]. IEEE Trans. on AES,1983,19(1):135-139.
[11]A. J. Baraell. Improving the resolution of eigen-structure based direction finding algorithms[J]. Proc. ICASSP, Boston,1983, pp.336-339.
[12]Rao B D, Hari K V S. Performance analysis of Root-MUSIC[J]. IEEE Trans. on ASSP,1989, 37(12):1939-1949.
[13]R.Roy, T.Kailath. Total Least Squares ESPRIT[C]. Proc.,21st Asilomar Conf., Circuits, Sys Computer, Monterey CA, Nov,1987.
[14]S. Y. Kuang, Arun K S, Rao. D V B. State pace and SVD based approximation methods for the harmonic retrieval problem[J]. J. Opt. Soc. Amer.,1983,73(12):1799-1811.
[15]Stoica P, Nehorai A. MUSIC, Maximum likelihood, and Carmer-Rao bound[C].In Proc. ICASSP. 1988,2296-2299.
[16]Cadzow J A. A high resolution direction-of-arrival algorithm for narrow-band coherent and incoherent sources[J]. IEEE Trans. on Acoustics,Speech,and Signal Processing.1988,36(7): 965-979.
[17]Huang Lai, Kristine Bell. DOA Estimation Using Vector Sensor Arrays [C]. Signals, Systems and Computers,2008 42nd Asilomar Conference. Pacific Grove,2008.pp.293-297.
[18]XU G H, KAILATH.Direction-of-Arrival Estimation via Exploitation on of Cyclostationary-A Combination of Temporal and Spatial Processing[J]. IEEE Trans. on Signal Processing.1992,40(17): 1775-1785.
[19]Pascal Charge, Yide Wang, An Extended Cyclic MUSIC Algorithm. IEEE Trans. SP,2003,51(7):. 1695-1701.
[20]汪仪林,殷勤业,金梁,姚敏立.利用信号的循环平稳特性进行相干源的波达方向估计[J].电子学报,1999,27(9)：86-89.
[21]黄知涛,周一宇,姜文利.基于循环平稳特性的源信号到达角估计方法[J].电子学报,2002,30(3)：372-375.
[22]J. Xin, A. Sano. Linear Prediction Approach to Direction Estimation of Cyclostationary Signals in Multipath Environment[J]. IEEE Trans. on SP,2001,49(4):710-720.
[23]S. U. Pillai, B. H. Kwon, Forward/Backward Spatial Smoothing Techniques for Coherent Singnal Identification, IEEE Trans. On ASSP, T1989,37(1):8-15.
[24]Wang H, Kavch M. On the performance of signal-subspace processing-Part Ⅱ:coherent wide-band systems. IEEE Trans. On ASSP,1989,35(11):1583-1591.
[25]Hung H, Kavch M. On the statistical sufficiency of the coherently averaged covariance matrix for the estimation of the parameters of wideband sources. ICASSP,1987,12:33-36. 45(10):1467-1474.
[26]Yang J F, Kaven M. Wideband adaptive arrays based on the coherent signal-subspace transformation. ICASSP.1987.12:2011-2014.
[27]Shaw A K, Kumaresan R. Estimation of angles of arrivals of broadband signals. ICASSP,1987.12: 2296-2299.
[28]Chen Y M, Lee J H, Yeh C C. Bearing estimation without calibration for randomly perturbed arrays. IEEE Trans. On SP,39(1):194-197.
[29]Linebarger D A. Tedundancy averaging with large arrays. IEEE Trans. On SP,1993, 41(4):1907-1710.
[30]Kung S Y, Lo C K, Foka R. A toeplitz approximation approach to coherent source direction finding. ICASSP,1986,11:193-196.
[31]Codaralc(美)著,左群声等译.无线通信天线手册[M].北京：国防工业出版社,2004.
[32]R T Compton, JR. On the performance of a polarization sensitive adaptive array[J].IEEE Trans.1981,AP-29(5):718-725.
[33]A Nehorai, E Paldi. Vector sensor processing for electromagnetic source localization [C]. in 25th Asilomar Conference on Signals, Systems and Computers, (Pacific Grove, CA), Nov 1991,1: 566-572.
[34]A Nehorai, E Paldi. Vector sensor array processing for electromagnetic source localization [J]. IEEE Trans. On Signal Processing,1994, SP-42(2):376-398.
[35]A Nehorai, K. C. Ho, B. T. G. Tan. Minimun-Noise-Variance Beamformer with an Electromagetic Vector Sensor. Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing,1998,4(12-15):2021-202.
[36]Kah-Chye Tan, Kwok-Chiang Ho, Arye Nehorai. Linear independence of steering vectors of an electromagnetic vector sensor[J]. IEEE Trans. on SP,1996,44(12):3099-3107.
[37]K.T Wong, M.D Zoltowski. Uni-vector-sensor ESPRIT for multisource azimuth, elevation, and polarization estimation[J]. IEEE Teans. On Antennas and Propagat(S0018-926X),1997,45(10): 1467-1474.
[38]K. T Wong, M. D.Zoltowski. Closed-from direction-finding and polarization estimation with arbitrarily spaced electromagnetic vector-sensors at unknown locations [J]. IEEE Trans. on Antennas and Propagat (S0018-926X),2000,48(5):671-681.
[39]Jinn Li, R.T. Compton, Jr. Angle and polarization estimation using ESPRIT with a polarization sensitive array. IEEE Trans. on AP,1991,39(9):1376-1383.
[40]Jian Li, R. T. Compton, Jr. Two-dimentional angle and polarization estimation using the ESPRIT algorithm[J]. IEEE Transactions on Antennas and Propagation,1992,40(5):550-555.
[41]Jian Li. On arrays with small loops and short dipoles[C].IEEE International Conference on Acoustics,Speech,and Signal Processing,ICASSP1993.Apr.1993,vol.4:27-30.
[42]Michael D. Zoltowski, Kainam Thomas Wong. ESPRIT-Based 2-D Direction Finding with a Sparse Uniform Array of Electromagnetic Vector Sensors[J]. IEEE Trans. on Signal Processing.2000, 48(8):2195-2204.
[43]K. T. Wong, Linshan Li, M. D. Zoltowski. Root-MUSIC-Based Direction Finding and Polarization estimation using diversely polarized possibly collocated antennas[M]. Antennas and Wireless Propagation Letters.2004.
[44]徐振海.极化敏感阵列信号处理的研究[D].国防科学技术大学博士论文.2004.
[45]许友根,刘志文.电磁矢量传感器阵列相干信号源波达方向和极化参数的同时估计：空间平滑方法[J].通信学报.2004,25(5)：28-38
[46]黄家才.极化阵列信号处理的理论与方法研究[D].吉林大学博士学位论文,2006.
[47]黄家才,石要武,陶建武.多径循环平稳信号二维波达方向估计——极化域平滑法[J].电子与信息学报.2007,29(5)：1110-1114.
[48]陈四根.阵列信号处理相关技术研究[D].哈尔滨工程大学,2004.
[49]张贤达,保铮.非平稳信号处理.北京：国防工业出版社,1998：324-390.
[50]W. A. Gardner. Simplification of MUSIC and ESPRIT by exploitation of cyclostationarity[J]. Proc. IEEE.1988,76(7):845-847.
[51]郭跃,王宏远,周陬.阵元间距对MUSIC算法的影响[J].电子学报,2007,35(9)：1675-1679.
[52]闫禄,解明祥,柳宝鹏.非均匀阵列模糊问题及测向性能分析[J].舰船电子工程,2010,30(2)：50-52.
[53]刘亮,陶建武.基于稀疏非均匀COLD阵列的极化信号DOA估计[J].系统工程与电子技术,2009,31(10)：2376-2379.
[2]王永良,陈辉,彭应宁,万群著.空间谱估计理论与算法[M].北京：清华大学出版,2004.
[3]Kim H, Viberg M. Two decades of array signal processing research[J]. IEEE Signal Processing Magazine,1996,13(4):67-94
[4]J. P. Burg. Maximum entropy spectral analysis[C]. Presented at the 37th Meeting Soc. Exploration Geophysicists, Oklahoma, OK,1967.
[5]J. Capon. High-resolution frequency-wavenumber spectrum analysis[J]. Proc. IEEE 57(8): 1408-1418, Aug.1969.
[6]V. F. Pisarenko. The Retrieval of Harmonics From a Covariance Function[J]. Geophys J.Roy. Astron.Soc,1973,33:.247-266.
[7]R.O. Schmidt. Multiple Emitter Location and Signal Parameter Estimation[J]. IEEE Trans, on AP, 1986,34(3):276-280.
[8]R. Roy, T. Kailath. ESPRIT-A subspace rotation approach to estimation of parameters of cissoids in noise[J]. IEEE Trans. on ASSP,1986,34(10):1340-1342.
[9]Cadzow J A, Kim Y S, Shiue D C. General direction-of-arrival estimation:a signal subspace approach[J]. IEEE Trans. on AES,1989,25(1):31-46.
[10]R. Kumaresan, D. W. Tufts. Estimating the Angle-of-Arrival of Multiple Plane Waves[J]. IEEE Trans. on AES,1983,19(1):135-139.
[11]A. J. Baraell. Improving the resolution of eigen-structure based direction finding algorithms[J]. Proc. ICASSP, Boston,1983, pp.336-339.
[12]Rao B D, Hari K V S. Performance analysis of Root-MUSIC[J]. IEEE Trans. on ASSP,1989, 37(12):1939-1949.
[13]R.Roy, T.Kailath. Total Least Squares ESPRIT[C]. Proc.,21st Asilomar Conf., Circuits, Sys Computer, Monterey CA, Nov,1987.
[14]S. Y. Kuang, Arun K S, Rao. D V B. State pace and SVD based approximation methods for the harmonic retrieval problem[J]. J. Opt. Soc. Amer.,1983,73(12):1799-1811.
[15]Stoica P, Nehorai A. MUSIC, Maximum likelihood, and Carmer-Rao bound[C].In Proc. ICASSP. 1988,2296-2299.
[16]Cadzow J A. A high resolution direction-of-arrival algorithm for narrow-band coherent and incoherent sources[J]. IEEE Trans. on Acoustics,Speech,and Signal Processing.1988,36(7): 965-979.
[17]Huang Lai, Kristine Bell. DOA Estimation Using Vector Sensor Arrays [C]. Signals, Systems and Computers,2008 42nd Asilomar Conference. Pacific Grove,2008.pp.293-297.
[18]XU G H, KAILATH.Direction-of-Arrival Estimation via Exploitation on of Cyclostationary-A Combination of Temporal and Spatial Processing[J]. IEEE Trans. on Signal Processing.1992,40(17): 1775-1785.
[19]Pascal Charge, Yide Wang, An Extended Cyclic MUSIC Algorithm. IEEE Trans. SP,2003,51(7):. 1695-1701.
[20]汪仪林,殷勤业,金梁,姚敏立.利用信号的循环平稳特性进行相干源的波达方向估计[J].电子学报,1999,27(9)：86-89.
[21]黄知涛,周一宇,姜文利.基于循环平稳特性的源信号到达角估计方法[J].电子学报,2002,30(3)：372-375.
[22]J. Xin, A. Sano. Linear Prediction Approach to Direction Estimation of Cyclostationary Signals in Multipath Environment[J]. IEEE Trans. on SP,2001,49(4):710-720.
[23]S. U. Pillai, B. H. Kwon, Forward/Backward Spatial Smoothing Techniques for Coherent Singnal Identification, IEEE Trans. On ASSP, T1989,37(1):8-15.
[24]Wang H, Kavch M. On the performance of signal-subspace processing-Part Ⅱ:coherent wide-band systems. IEEE Trans. On ASSP,1989,35(11):1583-1591.
[25]Hung H, Kavch M. On the statistical sufficiency of the coherently averaged covariance matrix for the estimation of the parameters of wideband sources. ICASSP,1987,12:33-36. 45(10):1467-1474.
[26]Yang J F, Kaven M. Wideband adaptive arrays based on the coherent signal-subspace transformation. ICASSP.1987.12:2011-2014.
[27]Shaw A K, Kumaresan R. Estimation of angles of arrivals of broadband signals. ICASSP,1987.12: 2296-2299.
[28]Chen Y M, Lee J H, Yeh C C. Bearing estimation without calibration for randomly perturbed arrays. IEEE Trans. On SP,39(1):194-197.
[29]Linebarger D A. Tedundancy averaging with large arrays. IEEE Trans. On SP,1993, 41(4):1907-1710.
[30]Kung S Y, Lo C K, Foka R. A toeplitz approximation approach to coherent source direction finding. ICASSP,1986,11:193-196.
[31]Codaralc(美)著,左群声等译.无线通信天线手册[M].北京：国防工业出版社,2004.
[32]R T Compton, JR. On the performance of a polarization sensitive adaptive array[J].IEEE Trans.1981,AP-29(5):718-725.
[33]A Nehorai, E Paldi. Vector sensor processing for electromagnetic source localization [C]. in 25th Asilomar Conference on Signals, Systems and Computers, (Pacific Grove, CA), Nov 1991,1: 566-572.
[34]A Nehorai, E Paldi. Vector sensor array processing for electromagnetic source localization [J]. IEEE Trans. On Signal Processing,1994, SP-42(2):376-398.
[35]A Nehorai, K. C. Ho, B. T. G. Tan. Minimun-Noise-Variance Beamformer with an Electromagetic Vector Sensor. Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing,1998,4(12-15):2021-202.
[36]Kah-Chye Tan, Kwok-Chiang Ho, Arye Nehorai. Linear independence of steering vectors of an electromagnetic vector sensor[J]. IEEE Trans. on SP,1996,44(12):3099-3107.
[37]K.T Wong, M.D Zoltowski. Uni-vector-sensor ESPRIT for multisource azimuth, elevation, and polarization estimation[J]. IEEE Teans. On Antennas and Propagat(S0018-926X),1997,45(10): 1467-1474.
[38]K. T Wong, M. D.Zoltowski. Closed-from direction-finding and polarization estimation with arbitrarily spaced electromagnetic vector-sensors at unknown locations [J]. IEEE Trans. on Antennas and Propagat (S0018-926X),2000,48(5):671-681.
[39]Jinn Li, R.T. Compton, Jr. Angle and polarization estimation using ESPRIT with a polarization sensitive array. IEEE Trans. on AP,1991,39(9):1376-1383.
[40]Jian Li, R. T. Compton, Jr. Two-dimentional angle and polarization estimation using the ESPRIT algorithm[J]. IEEE Transactions on Antennas and Propagation,1992,40(5):550-555.
[41]Jian Li. On arrays with small loops and short dipoles[C].IEEE International Conference on Acoustics,Speech,and Signal Processing,ICASSP1993.Apr.1993,vol.4:27-30.
[42]Michael D. Zoltowski, Kainam Thomas Wong. ESPRIT-Based 2-D Direction Finding with a Sparse Uniform Array of Electromagnetic Vector Sensors[J]. IEEE Trans. on Signal Processing.2000, 48(8):2195-2204.
[43]K. T. Wong, Linshan Li, M. D. Zoltowski. Root-MUSIC-Based Direction Finding and Polarization estimation using diversely polarized possibly collocated antennas[M]. Antennas and Wireless Propagation Letters.2004.
[44]徐振海.极化敏感阵列信号处理的研究[D].国防科学技术大学博士论文.2004.
[45]许友根,刘志文.电磁矢量传感器阵列相干信号源波达方向和极化参数的同时估计：空间平滑方法[J].通信学报.2004,25(5)：28-38
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