Abstract
In this paper, we consider the two-dimensional (2-D) superimposed exponential signals in independently and identically distributed (i.i.d.) multiplicative and additive noise. We use a three step iterative(TSI) algorithm to estimate the frequencies of the considered model. It is observed that the estimator is consistent and works quite well in terms of biases and mean squared errors. Moreover, the convergence rate of the estimators attain \(O_p(M^{-3/2}N^{-1/2})\) and \(O_p(M^{-1/2}N^{-3/2})\) for each pair of frequencies. It attains the convergence rate of the least squares estimators (LSEs) in presence of only additive noise.
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References
Francos, J.M., Narashimhan, A., Woods, J.W.: Maximum-likelihood Estimation of Textures Using a Wold Decomposition Model. IEEE Trans. Image Process. 4(12), 1655–1666 (1995)
Ward, J.: Space-Time Adaptive Processing for Airborne Radar. Lincoln Lab., MIT, Lexington, MA, Tech. Rep. 1015 (1994)
Rao, C.R., Zhao, L., Zhou, B.: Maximum Likelihood Estimation of 2-D Superimposed Exponential Signals. IEEE Trans. Signal Process. 42(7), 1795–1802 (1994)
Kunda, D., Mitra, A.: Asymptotic Properties of the Least Squares Estimators of 2-D Exponential Signals. Multidimensional Systems and Signal Processing 7, 135–150 (1996)
Lang, S.W., McClellan, J.H.: The Extension of Pisarenko’s Method to Multiple Dimensions. In: Proc. Int. Conf. Acoustics, Speech, Signal Processing, Paris, France, pp. 125–128 (1982)
Kumaresan, R., Tufts, D.W.: A Two-dimensional Technique for Frequency-Wavenumber Estimation. Proc. IEEE 69(11), 1515–1517 (1981)
Ibrahim, H.M., Gharieb, R.R.: Estimating Two-dimensional Frequencies by a Cumulant Based FBLP Method. IEEE Trans. Signal Process. 47(1), 262–266 (1999)
Giannakis, G.B., Zhou, G.: Harmonics in Multiplicative and Additive Noise: Parameter Estimation Using Cyclic Statistics. IEEE Trans. Signal Process. 43(9), 2217–2221 (1995)
Besson, B., Castanie, F.: On Estimating the Frequency of a Sinusoid in Auto-regressive Multiplicative Noise. Signal Processing 30, 65–83 (1993)
Swami, A.: Multiplicative Noise Models: Parameter Estimation Using Cumulants. Signal Processing 36, 355–373 (1994)
Wang, F., Wang, S., Dou, H.: Two-dimensional Parameter Estimation Using Two-dimensional Cyclic Statistics. Acta Electronica Sinica 31(10), 1522–1525 (2003)
Yang, S., Li, H.: Two-dimensional Harmonics Parameters Estimation Using Third-order Cyclicmoments. Acta Electronica Sinica 33(10), 1808–1811 (2005)
Yang, S., Li, H.: 2-D Harmonic Retrieval in Multiplicative and Additive Noise Based on Chirp Z-tranform. In: Proc. Int. Conf. Signal Processing, Beijing, China, pp. 16–20 (2006)
Nandi, S., Kundu, D.: An Efficient and Fast Algorithm for Estimating the Parameters of Sinusoidal Signals. Sankhya 68(2), 283–306 (2006)
Bai, Z.D., Rao, C.R., Chow, M., Kundu, D.: An Efficient Algorithm for Estimating the Parameters of Superimposed Exponential Signals. J. Statist. Plan. Infer. 110, 23–34 (2003)
Mangulis, V.: Handbook of Series for Scientists and Engineers. Academic Press, New York (1965)
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Bian, J., Li, H., Peng, H., Xing, J. (2009). An Efficient and Fast Algorithm for Estimating the Frequencies of 2-D Superimposed Exponential Signals in Presence of Multiplicative and Additive Noise. In: Wang, H., Shen, Y., Huang, T., Zeng, Z. (eds) The Sixth International Symposium on Neural Networks (ISNN 2009). Advances in Intelligent and Soft Computing, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01216-7_20
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DOI: https://doi.org/10.1007/978-3-642-01216-7_20
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