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.

Automated summary

In this paper, two computationally efficient algorithms are proposed to estimate the parameters of the elementary chirp model, based on two different initial estimators. The proposed estimators are consistent and have the same asymptotic distribution as the least squares estimators, with lower computational intensity. Sequential efficient procedures are also proposed to estimate the parameters of the multi-component elementary chirp model, with asymptotic properties coinciding with the least squares estimators. The importance of these efficient algorithms lies in their ability to produce efficient frequency rate estimators in a fixed number of iterations and achieve Cramer-Rao lower bounds asymptotically.