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Journal of Applied Mathematics
Volume 2014, Article ID 903426, 14 pages
http://dx.doi.org/10.1155/2014/903426
Research Article

A Computationally Efficient Iterative Algorithm for Estimating the Parameter of Chirp Signal Model

1School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
2Institute of Statistics, Hubei University of Economics, Wuhan 430205, China
3Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China

Received 10 April 2014; Revised 15 June 2014; Accepted 16 June 2014; Published 22 July 2014

Academic Editor: Filomena Cianciaruso

Copyright © 2014 Jiawen Bian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The parameter estimation of Chirp signal model in additive noises when all the noises are independently and identically distributed (i.i.d.) has been considered. A novel iterative algorithm is proposed to estimate the frequency rate of the considered model by constructing the iterative statistics with one-lag and multilag differential signals. It is observed that the estimator for the iterative algorithm is consistent and works quite well in terms of biases and mean squared errors. Moreover, the convergence rate of the estimator is improved from of the initial estimator to for one-lag differential signal condition and from of the initial estimator to for multilag differential signal condition, respectively, by only three iterations. The range of the lag is discussed and the optimal lag is obtained for the multilag differential signal condition when the lag is of order . The estimator of frequency rate with optimal lag is very close to Cramer-Rao lower bound (CRLB) as well as the asymptotic variance of least-squares estimator (LSE) at moderate signal-to-noise ratio (SNR). Finally, simulation experiments are performed to verify the effectiveness of the algorithm.