基于空间谱估计的阵列误差校正方法研究
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摘要
空间谱估计技术特点明显:波达方向估计精度高,分辨能力强,并且可以同时估计多个信号等。这类算法需要已知正确的阵列流型,但是阵列误差会导致实际的阵列流型和理论值存在误差,这就使得空间谱估计技术性能下降甚至失效。因此阵列误差是空间谱估计技术走向实用的瓶颈,阵列误差校正方法也就成为一个重要的研究热点。
本文针对上述问题,研究和分析阵列误差校正方法。主要工作如下:首先,从空间谱估计角度介绍阵列误差校正方法的基础,接着基于MUSIC算法介绍阵列误差的模型及阵列误差对算法的影响。文中将阵列误差校正方法分为两个大类:一类通过估计阵列误差的方法实现误差校正,包括有源校正方法和自校正方法。另一类研究对阵列误差不敏感的稳健算法。稳健算法在不需要估计阵列误差的前提下,就能实现良好的估计性能。最后本文通过仿真实验,验证有源校正、自校正和稳健算法对阵列误差估计的准确性,以及对波达方向估计的有效性。
The merits of spatial spectrum estimation algorithms are quite obvious,including the high precision of DOA, the high resolution performance and the ability to measure a lot of signals simultaneously. However, in order to obtain these merits, this kind of method requires quite accurate array manifold. The array perturbations would lead to the serious deviations between the real array manifold and the ideal one, which make the performance of algorithms sharply reduced, and in some conditions, the algorithms even become useless. Thus, array calibration methods have attracted much attention and play a significant role in the area of array signal processing.
Calibration algorithms have been divided into two major parts. On one hand, some algorithms calibrate the array perturbations through finding the best estimations of the array perturbations. There were two major branches in this field: self-calibration method (auto calibration method) and calibration with a set of calibration sources. On the other hand, some algorithms could obtain well performance of finding the DOA without estimating the perturbations which are named robust algorithm.
In this thesis, the author studied on array calibration methods for spatial spectrum estimation. The main works in this paper as follows, at the beginning, the author has introduced the basic information on array calibration methods and the classical MUSIC algorithm. Secondly, the analysis has been made in order to build the models of array perturbations. In this part, the author pays much attention on the influence from gain/phase errors and mutual coupling errors. Thirdly, several specific algorithms have been discussed. At last, some simulations and graphs have been made in order to illustrate the influence from perturbations and verify the performance of calibration algorithms.
本文针对上述问题,研究和分析阵列误差校正方法。主要工作如下:首先,从空间谱估计角度介绍阵列误差校正方法的基础,接着基于MUSIC算法介绍阵列误差的模型及阵列误差对算法的影响。文中将阵列误差校正方法分为两个大类:一类通过估计阵列误差的方法实现误差校正,包括有源校正方法和自校正方法。另一类研究对阵列误差不敏感的稳健算法。稳健算法在不需要估计阵列误差的前提下,就能实现良好的估计性能。最后本文通过仿真实验,验证有源校正、自校正和稳健算法对阵列误差估计的准确性,以及对波达方向估计的有效性。
The merits of spatial spectrum estimation algorithms are quite obvious,including the high precision of DOA, the high resolution performance and the ability to measure a lot of signals simultaneously. However, in order to obtain these merits, this kind of method requires quite accurate array manifold. The array perturbations would lead to the serious deviations between the real array manifold and the ideal one, which make the performance of algorithms sharply reduced, and in some conditions, the algorithms even become useless. Thus, array calibration methods have attracted much attention and play a significant role in the area of array signal processing.
Calibration algorithms have been divided into two major parts. On one hand, some algorithms calibrate the array perturbations through finding the best estimations of the array perturbations. There were two major branches in this field: self-calibration method (auto calibration method) and calibration with a set of calibration sources. On the other hand, some algorithms could obtain well performance of finding the DOA without estimating the perturbations which are named robust algorithm.
In this thesis, the author studied on array calibration methods for spatial spectrum estimation. The main works in this paper as follows, at the beginning, the author has introduced the basic information on array calibration methods and the classical MUSIC algorithm. Secondly, the analysis has been made in order to build the models of array perturbations. In this part, the author pays much attention on the influence from gain/phase errors and mutual coupling errors. Thirdly, several specific algorithms have been discussed. At last, some simulations and graphs have been made in order to illustrate the influence from perturbations and verify the performance of calibration algorithms.
引文
[1] B. Friedlander, A. J. Weiss. Effect of modeling errors on the resolution threshold of the MUSIC algorithm. IEEE Trans. on Signal Processing. 1994, Vol.42. 1519-1526.
[2] Li F, R. J. Vaccaro. Sensitivity analysis of DOA estimation algorithm to sensor errors. IEEE Trans. on Aerospace and Electronic Systems. 1992, 708~717.
[3] B. Friedlander. Sensitivity analysis of the maximum likelihood direction finding algorithm. IEEE Trans. on Aerospace and Electronic Systems, 1990, 953~968.
[4]苏卫民,顾红,倪晋麟.通道失配对MUSIC空间谱及其分辨力的影响.电子学报,1998. Vol.26 (9), 142-145.
[5] R. Hamza, K. Buckley. An analysis of weighted eigenspace methods in the presence of sensor errors, IEEE Trans. on Signal Processing, 1995, Vol.43, 1140-1150.
[6] A. L. Swindlehurst, T. Kailath, A performance analysis of subspace-based methods in the presence of model errors: The MUSIC algorithm. IEEE Trans. on Signal Processing, 1992, Vol.40 (7), 1758-1774.
[7] B. Friedlander. A sensitivity analysis of the MUSIC algorithm IEEE Trans. on Acous -tics, Speech and Signal Processing. 1990, Vol.38 (10), 1740-1751.
[8]王永良,陈辉,彭应宁等.空间谱估计理论与算法.北京.清华大学出版社. 2004, 1-8.
[9]魏平.高分辨阵列测向系统研究.电子科技大学硕士论文. 1996.
[10] C. C. Yeh, M. L. Leou, D. R. Ucci. Bearing estimations with mutual coupling prese- nt. IEEE Trans. on Antennas and Propagation. 1989, Vol.37, 1332-1335.
[11] T. Svantesson. Modeling and estimation of mutual coupling in a uniform linear arra -y of dipoles. Acoustics, Speech and Signal Processing. ICASSP '99. Proceedings., 1999 IEEE International Conference, vol.5, 2961-2964.
[12] E. Hung. A critical study of a self-calibration direction-finding method for array. IEEE Trans. on Signal Processing. 1994, Vol.42(2), 471-474.
[13] H. Krim, M. Viberg. Two decades of array signal processing research. IEEE Signal Processing Magazine: the parametric approach. 1996, Vol.13 (4), 67-94.
[14] J. G. Ables. Maximum entropy spectral analysis. Astronomy and Astrophysics Sup -plement, Vol. 15, 383-393.
[15] Capon J. High resolution frequency wavenumber spectrum analysis. Proceedings of the IEEE. 1969, Vol.57 (8), 1408-1418.
[16] Schmidt R O. Multiple emitter location and signal parameter estimation. IEEE Trans. on Antennas and Propagation, 1986, Vol.34 (3), 276-280.
[17] A. J. Weiss, B. Friedlander, Manifold interpolation for diversely polarized arrays. IEE Proceedings. Radar, Sonar and Navigation. Vol.141 (1) , 19-24.
[18] R. O. Schmidt. Multilinear array manifold interpolation. IEEE Trans. on Signal Processing, 1994, 857~866.
[19] K. R. Danderkar, H. Ling, G. Xu. Experimental study of mutual coupling compen -sation in smart antenna applications. IEEE Trans. on Wireless Communications, 2002, vol.1 (3), 480-487.
[20]韩芳明,张守宏,潘复平.阵列误差对MUSIC算法性能的影响与校正.西安电子科技大学学报.2003, Vol.30 (5).
[21] Anne Ferreol, Pascal Larzabal, Mats Viberg. On the Asymtotic Performance Anal -ysis of Subspace DOA Estimation in the Presence of Modeling Errors: case of music, IEEE trans. on Signal Processing. 2006, Vol.54 (3), 907-919.
[22] K. M. Pasala, E. M. Freil. Mutual coupling effects and their reduction in wideband direction of arrival estimation. IEEE Trans on Aerospace and Electronic Systems. 1994, Vol.30, 1116-1122.
[23] Y. Rockah, P. Schultheiss. Array shape calibration using sources in unknown locations--Part I: Far-field sources. IEEE Trans. on Acoustics, Speech and Signal Processing. 1987, Vol.35(3). 286-299.
[24]贾永康,保铮,吴洹.一种阵列天线阵元位置,幅度及相位误差的有源校正方法.电子学报. 1996, Vol.24 (3), 47-52.
[25]王鼎,李长胜,吴瑛.均匀圆阵互耦和幅相差有源校正分离迭代算法.探测与控制学报. 2009, Vol.31 (1), 64-69.
[26]王鼎,李长胜,吴瑛.均匀线阵互耦和幅相差有源校正改进算法.系统工程与电子技术. 2009, Vol.31 (9), 34-41.
[27] C. M. S. See. Sensor array calibration in the presence of mutual coupling, gain and phase mismatch, Electron Lett, 1994, 373-374.
[28] A. G. Jaffer. Constrained Mutual Coupling Estimation for Array Calibration. Signa -ls, Systems and Computers. 2001, vol.2. 1273-1277.
[29] Signals, Systems and Computers, Conference Record of the Thirty-Fifth Asilomar Conference. 2001, vol.2. 1273-1277.
[30] B. Friedlander, A. J. Weiss. Array shape calibration using sources in unknown loca -tions: A Maximum Likelihood Approach. IEEE Trans. on Signal Processing, 1989, 1958~1966.
[31] Zhang M, Zhu Z D. Array shape calibration using sources in known locations. Processing of the IEEE National Aerospace and Electronic Conference, NAECO 1993, 70~73.
[32] K. Stavropoulos, Manikas. A Array calibration in the presence of unknown sensor characteristics and mutual coupling. Proceedings of the European Signal Processing Conference. EUSIP 2000,1417-1420.
[33] Ng B. C, WeeSer. Array shape calibration using sources in unknown locations. Sing -apore ICCS/ISITA '92. 'Communications on the Move'. Nov 1992, vol.2 836-840.
[34] E. K. L. Hung. Matrix-construction calibration method for antenna arrays IEEE Trans. on Aerospace and Electronic Systems. Jul 2000,Vol.36(3),819-828.
[35] C. M. S. See. Method for array calibration in high-resolution senor array processing IEE Proceeding-Radar, Sonar Navig. 1995,Vol.142(3), 90-96.
[36] Min Lin, Luxi Yang. Blind Calibration and DOA Estimation With Uniform Circular Arrays in the Presence of Mutual Coupling. IEEE Trans. on Antennas and Wireless Propagation Letters. 2006, Vol.5, 315-318.
[37] Fabrizio Sellone, Alberto Serra. A Novel Online Mutual Coupling Compensation Algorithm for Uniform and Linear Arrays, IEEE Trans. on Signal Processing, 2007, Vol. 55(2), 560-573.
[38] B. Friedlander, A. J. Weiss. Direction Finding in the Presence of Mutual Coupling. IEEE Trans. on Antennas and Propagation.1991, Vol. 39(3), 273-284.
[39] Yufeng Zhang, Chao liu, Xu Xu. Direction of Arrival Estimation in the Presence of Array Perturbations. ICETC, 2010. Vol5. 12-16.
[40] Pierre J, Kaveh M. Experimental performance of calibration and direction-finding algorithms. Proceedings of IEEE ICASSP’91.1991, 1365-1368.
[41] Benjamin Friedlander, A. J. Weiss. Eigenstructure methods for direction finding with sensor gain and phase uncertainties. Circuits, System, Signal Processing. 1990, Vol.9 (3). 271-300.
[42] N. Fistas, A. Manikas. A new general global array calibration method. IEEE. ICASSP. 1994, 73-76.
[43] Ng A P C. Direction of arrival estimates in the presence of wavelength, gain and phase errors. IEEE Trans. on Signal Processing. 1995, Vol.43(1). 225-232.
[44]魏平,肖先赐,阵列测向系统中模型误差的校正方法.电子科技大学学报. 1995, Vol.24(7), 121-126.
[45] D. Mcarthur, J. P. Reilly. An efficient self-calibrating direction-of-arrival estimator. Statistical Signal and Array Processing. IEEE Seventh SP Workshop. 1994, 129-132.
[46] Zhongfu Ye, Chao Liu. 2-D DOA Estimation in the Presence of Mutual Coupling IEEE Trans. on Antennas and Propagation. 2008, Vol.56, No.10, 3150-3158.
[47] Buhong Wang, Yongliang Wang. A robust DOA estimation algorithm for uniform linear array in the presence of mutual coupling. IEEE Antennas and propagation Society International Symposium. 2003, Vol.3. 924-927.
[48]王布宏,王永良,陈辉等.均匀线阵互耦条件下的鲁棒DOA估计及互耦自校正.中国科学E辑.技术科学. 2004, Vol.34 (2), 229-240.
[49]侯颖妮,冯西安,黄建国.一类高分辨方位估计算法的稳健性研究.计算机仿真. 2007, Vol.24 (6). 92-95.
[50] A. L. Swindlehust, T. Kailath. A performance analysis of subspace-based methods in the presence of model errors: Multidimensional algorithm. IEEE Trans. on Signal Processing, 1993, Vol.41 (9). 2882-2890.
[51] M. C. Dogan, J.M. Mendel. Applications of cumulants to array processing. I. apertu -re extension and array calibration. IEEE Trans. on Signal Processing. 1995, Vol. 43(5). 1200-1216.
[52] A. J. Weiss, B. Friedlander.“Almost Blind”Steering Vector Estimation Using Second-order Moment. IEEE Trans. on Signal Processing. 1996,Vol. 44(4). 2724-2732.
[53] Lo J T H, S. L. Marple. Observeability conditions for multiple signal direction find -ing and array sensor localization. IEEE Trans. on Signal Processing, 1992, Vol. 40(11). 2641-2650.
[2] Li F, R. J. Vaccaro. Sensitivity analysis of DOA estimation algorithm to sensor errors. IEEE Trans. on Aerospace and Electronic Systems. 1992, 708~717.
[3] B. Friedlander. Sensitivity analysis of the maximum likelihood direction finding algorithm. IEEE Trans. on Aerospace and Electronic Systems, 1990, 953~968.
[4]苏卫民,顾红,倪晋麟.通道失配对MUSIC空间谱及其分辨力的影响.电子学报,1998. Vol.26 (9), 142-145.
[5] R. Hamza, K. Buckley. An analysis of weighted eigenspace methods in the presence of sensor errors, IEEE Trans. on Signal Processing, 1995, Vol.43, 1140-1150.
[6] A. L. Swindlehurst, T. Kailath, A performance analysis of subspace-based methods in the presence of model errors: The MUSIC algorithm. IEEE Trans. on Signal Processing, 1992, Vol.40 (7), 1758-1774.
[7] B. Friedlander. A sensitivity analysis of the MUSIC algorithm IEEE Trans. on Acous -tics, Speech and Signal Processing. 1990, Vol.38 (10), 1740-1751.
[8]王永良,陈辉,彭应宁等.空间谱估计理论与算法.北京.清华大学出版社. 2004, 1-8.
[9]魏平.高分辨阵列测向系统研究.电子科技大学硕士论文. 1996.
[10] C. C. Yeh, M. L. Leou, D. R. Ucci. Bearing estimations with mutual coupling prese- nt. IEEE Trans. on Antennas and Propagation. 1989, Vol.37, 1332-1335.
[11] T. Svantesson. Modeling and estimation of mutual coupling in a uniform linear arra -y of dipoles. Acoustics, Speech and Signal Processing. ICASSP '99. Proceedings., 1999 IEEE International Conference, vol.5, 2961-2964.
[12] E. Hung. A critical study of a self-calibration direction-finding method for array. IEEE Trans. on Signal Processing. 1994, Vol.42(2), 471-474.
[13] H. Krim, M. Viberg. Two decades of array signal processing research. IEEE Signal Processing Magazine: the parametric approach. 1996, Vol.13 (4), 67-94.
[14] J. G. Ables. Maximum entropy spectral analysis. Astronomy and Astrophysics Sup -plement, Vol. 15, 383-393.
[15] Capon J. High resolution frequency wavenumber spectrum analysis. Proceedings of the IEEE. 1969, Vol.57 (8), 1408-1418.
[16] Schmidt R O. Multiple emitter location and signal parameter estimation. IEEE Trans. on Antennas and Propagation, 1986, Vol.34 (3), 276-280.
[17] A. J. Weiss, B. Friedlander, Manifold interpolation for diversely polarized arrays. IEE Proceedings. Radar, Sonar and Navigation. Vol.141 (1) , 19-24.
[18] R. O. Schmidt. Multilinear array manifold interpolation. IEEE Trans. on Signal Processing, 1994, 857~866.
[19] K. R. Danderkar, H. Ling, G. Xu. Experimental study of mutual coupling compen -sation in smart antenna applications. IEEE Trans. on Wireless Communications, 2002, vol.1 (3), 480-487.
[20]韩芳明,张守宏,潘复平.阵列误差对MUSIC算法性能的影响与校正.西安电子科技大学学报.2003, Vol.30 (5).
[21] Anne Ferreol, Pascal Larzabal, Mats Viberg. On the Asymtotic Performance Anal -ysis of Subspace DOA Estimation in the Presence of Modeling Errors: case of music, IEEE trans. on Signal Processing. 2006, Vol.54 (3), 907-919.
[22] K. M. Pasala, E. M. Freil. Mutual coupling effects and their reduction in wideband direction of arrival estimation. IEEE Trans on Aerospace and Electronic Systems. 1994, Vol.30, 1116-1122.
[23] Y. Rockah, P. Schultheiss. Array shape calibration using sources in unknown locations--Part I: Far-field sources. IEEE Trans. on Acoustics, Speech and Signal Processing. 1987, Vol.35(3). 286-299.
[24]贾永康,保铮,吴洹.一种阵列天线阵元位置,幅度及相位误差的有源校正方法.电子学报. 1996, Vol.24 (3), 47-52.
[25]王鼎,李长胜,吴瑛.均匀圆阵互耦和幅相差有源校正分离迭代算法.探测与控制学报. 2009, Vol.31 (1), 64-69.
[26]王鼎,李长胜,吴瑛.均匀线阵互耦和幅相差有源校正改进算法.系统工程与电子技术. 2009, Vol.31 (9), 34-41.
[27] C. M. S. See. Sensor array calibration in the presence of mutual coupling, gain and phase mismatch, Electron Lett, 1994, 373-374.
[28] A. G. Jaffer. Constrained Mutual Coupling Estimation for Array Calibration. Signa -ls, Systems and Computers. 2001, vol.2. 1273-1277.
[29] Signals, Systems and Computers, Conference Record of the Thirty-Fifth Asilomar Conference. 2001, vol.2. 1273-1277.
[30] B. Friedlander, A. J. Weiss. Array shape calibration using sources in unknown loca -tions: A Maximum Likelihood Approach. IEEE Trans. on Signal Processing, 1989, 1958~1966.
[31] Zhang M, Zhu Z D. Array shape calibration using sources in known locations. Processing of the IEEE National Aerospace and Electronic Conference, NAECO 1993, 70~73.
[32] K. Stavropoulos, Manikas. A Array calibration in the presence of unknown sensor characteristics and mutual coupling. Proceedings of the European Signal Processing Conference. EUSIP 2000,1417-1420.
[33] Ng B. C, WeeSer. Array shape calibration using sources in unknown locations. Sing -apore ICCS/ISITA '92. 'Communications on the Move'. Nov 1992, vol.2 836-840.
[34] E. K. L. Hung. Matrix-construction calibration method for antenna arrays IEEE Trans. on Aerospace and Electronic Systems. Jul 2000,Vol.36(3),819-828.
[35] C. M. S. See. Method for array calibration in high-resolution senor array processing IEE Proceeding-Radar, Sonar Navig. 1995,Vol.142(3), 90-96.
[36] Min Lin, Luxi Yang. Blind Calibration and DOA Estimation With Uniform Circular Arrays in the Presence of Mutual Coupling. IEEE Trans. on Antennas and Wireless Propagation Letters. 2006, Vol.5, 315-318.
[37] Fabrizio Sellone, Alberto Serra. A Novel Online Mutual Coupling Compensation Algorithm for Uniform and Linear Arrays, IEEE Trans. on Signal Processing, 2007, Vol. 55(2), 560-573.
[38] B. Friedlander, A. J. Weiss. Direction Finding in the Presence of Mutual Coupling. IEEE Trans. on Antennas and Propagation.1991, Vol. 39(3), 273-284.
[39] Yufeng Zhang, Chao liu, Xu Xu. Direction of Arrival Estimation in the Presence of Array Perturbations. ICETC, 2010. Vol5. 12-16.
[40] Pierre J, Kaveh M. Experimental performance of calibration and direction-finding algorithms. Proceedings of IEEE ICASSP’91.1991, 1365-1368.
[41] Benjamin Friedlander, A. J. Weiss. Eigenstructure methods for direction finding with sensor gain and phase uncertainties. Circuits, System, Signal Processing. 1990, Vol.9 (3). 271-300.
[42] N. Fistas, A. Manikas. A new general global array calibration method. IEEE. ICASSP. 1994, 73-76.
[43] Ng A P C. Direction of arrival estimates in the presence of wavelength, gain and phase errors. IEEE Trans. on Signal Processing. 1995, Vol.43(1). 225-232.
[44]魏平,肖先赐,阵列测向系统中模型误差的校正方法.电子科技大学学报. 1995, Vol.24(7), 121-126.
[45] D. Mcarthur, J. P. Reilly. An efficient self-calibrating direction-of-arrival estimator. Statistical Signal and Array Processing. IEEE Seventh SP Workshop. 1994, 129-132.
[46] Zhongfu Ye, Chao Liu. 2-D DOA Estimation in the Presence of Mutual Coupling IEEE Trans. on Antennas and Propagation. 2008, Vol.56, No.10, 3150-3158.
[47] Buhong Wang, Yongliang Wang. A robust DOA estimation algorithm for uniform linear array in the presence of mutual coupling. IEEE Antennas and propagation Society International Symposium. 2003, Vol.3. 924-927.
[48]王布宏,王永良,陈辉等.均匀线阵互耦条件下的鲁棒DOA估计及互耦自校正.中国科学E辑.技术科学. 2004, Vol.34 (2), 229-240.
[49]侯颖妮,冯西安,黄建国.一类高分辨方位估计算法的稳健性研究.计算机仿真. 2007, Vol.24 (6). 92-95.
[50] A. L. Swindlehust, T. Kailath. A performance analysis of subspace-based methods in the presence of model errors: Multidimensional algorithm. IEEE Trans. on Signal Processing, 1993, Vol.41 (9). 2882-2890.
[51] M. C. Dogan, J.M. Mendel. Applications of cumulants to array processing. I. apertu -re extension and array calibration. IEEE Trans. on Signal Processing. 1995, Vol. 43(5). 1200-1216.
[52] A. J. Weiss, B. Friedlander.“Almost Blind”Steering Vector Estimation Using Second-order Moment. IEEE Trans. on Signal Processing. 1996,Vol. 44(4). 2724-2732.
[53] Lo J T H, S. L. Marple. Observeability conditions for multiple signal direction find -ing and array sensor localization. IEEE Trans. on Signal Processing, 1992, Vol. 40(11). 2641-2650.