On Efficient Parameter Estimation of Elementary Chirp Model.

Elementary chirp signals can be found in various fields of science and engineering. We propose two computationally efficient algorithms based on the choice of two different initial estimators to estimate the parameters of the elementary chirp model. It is observed that the proposed efficient estimators are consistent; they have the identical asymptotic distribution as that of the least squares estimators and they are also less computationally intensive. We also propose sequential efficient procedures to estimate the parameters of the multi-component elementary chirp model. The asymptotic properties of the sequential efficient estimators coincide with the least squares estimators. The important point about the efficient and sequential efficient algorithms is that these algorithms produce efficient frequency rate estimators in a fixed number of iterations. Another important point is that the under normal error assumption the theoretical variances of the proposed estimators achieve the Cramer-Rao lower bounds asymptotically. Simulation experiments are performed to see the performance of the proposed estimators, and it is observed that they are computationally efficient, take less time in computation than the other existing methods and perform well when two frequency rates are close to each other upto a reasonably low degree of separation. On an EEG dataset, we demonstrate the performance of the proposed algorithm.