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

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 $O_p(N^{-1})$ of the initial estimator to $O_p(N^{-3/2})$ for one-lag differential signal condition and from $O_p(N^{-2})$ of the initial estimator to $O_p(N^{-5/2})$ 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 $N$. 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.