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An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

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Języki publikacji
EN
Abstrakty
EN
This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton–Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton–Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.
Rocznik
Strony
117--129
Opis fizyczny
Bibliogr. 40 poz., tab., wykr.
Twórcy
autor
  • School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China
autor
  • School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China
autor
  • Department of Statistics and Applied Mathematics, Hubei University of Economics, Wuhan, 430205, China
autor
  • School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China
autor
  • School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China
Bibliografia
  • [1] Bai, Z.D., Rao, C.R., Chow M. and Kundu, D. (2003). An efficient algorithm for estimating the parameters of superimposed exponential signals, Journal of Statistical Planning and Inference 110(1–2): 23–34.
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  • [3] Bian, J., Li, H. and Peng, H. (2009). An efficient and fast algorithm for estimating the frequencies of superimposed exponential signals in zero-mean multiplicative and additive noise, Journal of Statistical Computation and Simulation 74(12): 1407–1423.
  • [4] Bian, J., Li, H. and Peng, H. (2009). An efficient and fast algorithm for estimating the frequencies of superimposed exponential signals in multiplicative and additive noise, Journal of Information and Computational Science 6(4): 1785–1797.
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  • [7] Chan, K.W. and So, H.C. (2004). Accurate frequency estimation for real harmonic sinusoids, IEEE Signal Processing Letters 11(7): 609–612.
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  • [10] Gawron, P., Klamka, J. and Winiarczyk, R. (2012). Noise effects in the quantum search algorithm from the viewpoint of computational complexity, International Journal of Applied Mathematics and Computer Science 22(2): 493–499, DOI: 10.2478/v10006-012-0037-2.
  • [11] Ghogho, M., Swami, A. and Garel, B. (1999). Performance analysis of cyclic statistics for the estimation of harmonics in multiplicative and additive noise, IEEE Transactions on Signal Processing 47(12): 3235–3249.
  • [12] Ghogho, M., Swami, A. and Nandi, A.K. (1999). Non-linear least squares estimation for harmonics in multiplicative and additive noise, Signal Processing 78(1): 43–60.
  • [13] Giannakis, G.B. and Zhou, G. (1995). Harmonics in multiplicative and additive noise: Parameter estimation using cyclic statistics, IEEE Transactions on Signal Processing 43(9): 2217–2221.
  • [14] Hartley, H.O. (1961). The modified Gauss–Newton method for the fitting of non-linear regression functions by least squares, Technometrics 3(2): 269–280.
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  • [17] Kannan, N. and Kundu, D. (1994). On modified EVLP and ML methods for estimating superimposed exponential signals, Signal Processing 39(3): 223–233.
  • [18] Koko, J. (2004). Newton’s iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition, International Journal of Applied Mathematics and Computer Science 14(1): 13–18.
  • [19] Kundu, D. (1997). Asymptotic theory of the least squares estimators of sinusoidal signals, Statistics 30(3): 221–238.
  • [20] Kundu, D., Bai, Z., Nandi, S. and Bai, L. (2011). Super efficient frequency estimation, Journal of Statistical Planning and Inference 141(8): 2576–2588.
  • [21] Kundu, D. and Mitra, A. (1995). Consistent method of estimating superimposed exponential signals, Scandinavian Journal of Statistics 22(1): 73–82.
  • [22] Kundu, D. and Mitra, A. (1999). On asymptotic behavior of the least squares estimators and the confidence intervals of the superimposed exponential signals, Signal Processing 72(2): 129–139.
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  • [27] Peng, H., Li, H. and Bian, J. (2009). Asymptotic behavior of least squares estimators for harmonics in multiplicative and additive noise, Journal of Information and Computational Science 6(4): 1847–1860.
  • [28] Prasath, V.B.S. (2011). A well-posed multiscale regularization scheme for digital image denoise, International Journal of Applied Mathematics and Computer Science 21(4): 769–777, DOI: 10.2478/v10006-011-0061-7.
  • [29] Quinn, B.G. (1994). Estimating frequency by interpolation using Fourier coefficients, IEEE Transactions on Signal Processing 42(5): 1264–1268.
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  • [32] Sadler, B., Giannakis, G. and Shamsunder, S. (1995). Noise subspace techniques in non-Gaussian noise using cumulants, IEEE Transactions on Aerospace and Electronic Systems 31(3): 1009–1018.
  • [33] Swami, A. (1994). Multiplicative noise models: Parameter estimation using cumulants, Signal Processing 36(3): 355–373.
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  • [40] Zhou, G. and Giannakis, G.B. (1995). Harmonics in multiplicative and additive noise: Performance analysis of cyclic estimators, IEEE Transactions on Signal Processing 43(6): 1445–1460.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ec9bd4c5-01ff-4373-b486-99a9fd949f9e
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