系数矩阵正交矢量谱估计
NEW SPECTRAL ESTIMATION APPROACHES IN LPEF COEFFICIENT MATRIX SPACE
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摘要: 邹理和(1984)提出,用线性预测误差滤波器系数矩阵对K个二维复正弦波加白噪声的信号作谱估计,有着良好的特性。本文将证明,二维线性预测误差滤波器系数矩阵空间具有和相关阵空间非常类似的结构。在系数阵空间同样存在正交矢量谱估计方法。采用相关阵SVD逼近技术,可使系数阵正交矢量方法不仅具有很高分辨率,而且具有很好的统计稳定性。最后将二维的结果移植到一维,并在一维中进行了计算机模拟,模拟结果表明新方法比现用的一些方法为佳。Abstract: For the case of sinusoids plus white noise, it will be proved that the construction of the LPEF (Linear Prediction Error Filter) coefficient matrix space is quite similar to that of the correlation matrix space. Therefore, the orthogonal vector techniques can be applied to the LPEF coefficient matrix space for spectral estimation. With the SVD approximation approach used for the correlation matrix, the present approach has not only the property of high resolution, but also the property of high statistic stability. finally, a one dimensional LPEF coefficient matrix is formed and the spectral estimation is simulated by computer. The results are compared with those obtained by other approaches.
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Li He Zou(邹理和) On Resolution of 2-D Spectral Estimation as Applied to Sinusoids in White Noise,Ph. D. Dissertation, Princeton University, 1984.[2]S.M. Kay, S. L. Marple, Jr. PIEE, 69(1981), 1380-1419.[3]G. Bienvenu, Eigensystem Properties of Sampled Space Coherent Signal and Interference, Proc. ICASSP,1984.[4]T.K.Citron, T. Kailath, An Improved Eigenvector Beamformer, Proc. ICASSP, 1984.Angzhao Di, L.Tiao, Matrix Decomposition and Multiple Source Location, Proc. ICASSP, 1984.[5]D. W. Tufts, R. Kumaresan, Proc. IEEE, 70(1982), 975-989.[6]O. I. Frost, Power Spectrum Estimation, In 1976 NATO Advanced Study Institute on Signal Processing with Emphasis on Underwater Acoustic Portovence, Italy, 1976.[7]H.C. Lin, Trans, IEEE on AP, AP-30(1982).[8]D. R. Farrier, PIEE, 131(1984).[9]C. L. Lawson, R.J. Hanson, Solving Least Squares Problems, Englewood Cliffs, NJ, Prentice Hall, 1974. -
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