总体最小二乘拟合的盖氏圆盘信源数估计法
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摘要
针对调整因子设置不当造成在信源数估计时盖氏圆盘法(Gerschgorin Disks Estimation,GDE)性能下降的问题,提出一种基于总体最小二乘拟合的盖氏圆盘法(Total Least Squares-Gerschgorin Disks Estimation,TLS-GDE)。该方法以圆盘半径作为拟合点进行直线拟合,若拟合点含信号圆盘半径,则拟合偏差较大,利用这一特性制定了比值阶跃准则,进行信源数判决,解决了盖氏圆盘法对调整因子依赖的问题。最后,仿真结果表明,该方法鲁棒性较好,在低信噪比下性能要优于GDE算法,更具有实用价值。
Aiming at the problem that the performance of the Gerschgorin disks method was degraded when the adjustment factor was set improperly in source number estimation,this paper proposed a modified Gerschgorin disks method based on total least squares fitting. This method kept the radius of the disk as the fitting points of straight line so that the fitting discrepancy of the signal disk radius was much larger than that of the noise disk radius,and a ratio-step criterion was developed to estimate the source number so that no artificial adjustment factor was set. The performance of the TLS-GDE algorithm was verified by simulation. The results show that the robustness of the TLS-GDE is improved and the performance of the TLS-GDE is better than that of the GDE in low SNR.
Aiming at the problem that the performance of the Gerschgorin disks method was degraded when the adjustment factor was set improperly in source number estimation,this paper proposed a modified Gerschgorin disks method based on total least squares fitting. This method kept the radius of the disk as the fitting points of straight line so that the fitting discrepancy of the signal disk radius was much larger than that of the noise disk radius,and a ratio-step criterion was developed to estimate the source number so that no artificial adjustment factor was set. The performance of the TLS-GDE algorithm was verified by simulation. The results show that the robustness of the TLS-GDE is improved and the performance of the TLS-GDE is better than that of the GDE in low SNR.
引文
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[6]艾健健,刘成城,赵拥军.利用随机矩阵理论的MDL信源数估计算法[J].信号处理,2015,31(2):186-193.Ai J J,Liu C C,Zhao Y J.MDL Algorithm for Source Enumeration Using Random Matrix Theory[J].Journal of Signal Processing,2015,31(2):186-193.(in Chinese)
[7]叶中付,向利,徐旭.基于信息论准则的信源个数估计算法改进[J].电波科学学报,2007,22(4):593-598.Ye Z F,Xiang L,Xu X,Improvement of source number estimation based on information theoretic criteria[J].Chinese Journal of Radio Science,2007,22(4):593-598.(in Chinese)
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[9]叶中付,李春辉,贾红江,等.空间非平稳噪声下的信源数估计算法[J].兵工学报,2009,30(7):873-878.Ye Z F,Li C H,Jia H J,Estimation of the Number of Signal Source in Spatially Nonstationary Noise[J].Acta Armamentarii,2009,30(7):873-878.(in Chinese)
[10]胡隽.盖氏圆准则信源数估计算法的分析与改进[J].系统工程理论与实践,2007,27(10):124-131.Hu J.Research and Improvement on the Estimator Using Gerschgorin Disks[J].Systems Engineering-Theory&Practice,2007,27(10):124-131.(in Chinese)
[11]Zhong Z F,Wen B Y,Wang Q D,et al.A new method using Gerschgorin disks for source number estimation[C]∥International Conference on Machine Learning and Cybernetics,Vol.4,2004:2086-2089.
[12]董姝敏,梁国龙.改进的盖尔圆源数目估计方法[J].哈尔滨工程大学学报:英文版,2013,34(4):440-444.Dong S M,Liang G L.A modified Gerschgorin disks estimation method for source number estimation[J].Journal of Harbin Engineering University,2013,34(4):440-444.(in Chinese)
[13]Lan X.A source number estimation method based on total least squares fitting[C]∥International Conference on Mechatronic Sciences,Electric Engineering and Computer.IEEE,2013:1275-1278.
[14]Golub G H,Loan C F V.An Analysis of the Total Least Squares Problem[J].Siam Journal on Numerical Analysis,1980,17(6):883-893.
[2]Wax M,Ziskind I.Detection of the number of coherent signals by the MDL principle[J].IEEE Transactions on Acoustics Speech&Signal Processing,1989,37(8):1190-1196.
[3]Wu H T,Yang J F,Chen F K.Source number estimators using transformed Gerschgorin radii[J].Signal Processing IEEE Transactions on,1995,43(6):1325-1333.
[4]Shan T J,Paulraj A,Kailath T.On smoothed rank profile tests in eigenstructure methods for directions-of-arrival estimation[J].IEEE Transactions on Acoustics Speech&Signal Processing,1987,35(10):1377-1385.
[5]Chen,W,Reilly,et al.Detection of the number of signals in noise with banded covariance matrices[J].Radar,Sonar and Navigation,IEE Proceedings,2000,143(5):289-294.
[6]艾健健,刘成城,赵拥军.利用随机矩阵理论的MDL信源数估计算法[J].信号处理,2015,31(2):186-193.Ai J J,Liu C C,Zhao Y J.MDL Algorithm for Source Enumeration Using Random Matrix Theory[J].Journal of Signal Processing,2015,31(2):186-193.(in Chinese)
[7]叶中付,向利,徐旭.基于信息论准则的信源个数估计算法改进[J].电波科学学报,2007,22(4):593-598.Ye Z F,Xiang L,Xu X,Improvement of source number estimation based on information theoretic criteria[J].Chinese Journal of Radio Science,2007,22(4):593-598.(in Chinese)
[8]Wu H T,Yang J F,Chen F K.Source number estimators using transformed Gerschgorin radii[J].Signal Processing IEEE Transactions on,1995,43(6):1325-1333.
[9]叶中付,李春辉,贾红江,等.空间非平稳噪声下的信源数估计算法[J].兵工学报,2009,30(7):873-878.Ye Z F,Li C H,Jia H J,Estimation of the Number of Signal Source in Spatially Nonstationary Noise[J].Acta Armamentarii,2009,30(7):873-878.(in Chinese)
[10]胡隽.盖氏圆准则信源数估计算法的分析与改进[J].系统工程理论与实践,2007,27(10):124-131.Hu J.Research and Improvement on the Estimator Using Gerschgorin Disks[J].Systems Engineering-Theory&Practice,2007,27(10):124-131.(in Chinese)
[11]Zhong Z F,Wen B Y,Wang Q D,et al.A new method using Gerschgorin disks for source number estimation[C]∥International Conference on Machine Learning and Cybernetics,Vol.4,2004:2086-2089.
[12]董姝敏,梁国龙.改进的盖尔圆源数目估计方法[J].哈尔滨工程大学学报:英文版,2013,34(4):440-444.Dong S M,Liang G L.A modified Gerschgorin disks estimation method for source number estimation[J].Journal of Harbin Engineering University,2013,34(4):440-444.(in Chinese)
[13]Lan X.A source number estimation method based on total least squares fitting[C]∥International Conference on Mechatronic Sciences,Electric Engineering and Computer.IEEE,2013:1275-1278.
[14]Golub G H,Loan C F V.An Analysis of the Total Least Squares Problem[J].Siam Journal on Numerical Analysis,1980,17(6):883-893.