On approximate least squares estimators of parameters on one-dimensional chirp signal

Abstract

Chirp signals are quite common in many natural and man-made systems like audio signals, sonar, radar etc. Estimation of the unknown parameters of a signal is a fundamental problem in statistical signal processing. Recently, Kundu and Nandi \cite{2008} studied the asymptotic properties of least squares estimators of the unknown parameters of a simple chirp signal model under the assumption of stationary noise. In this paper, we propose periodogram-type estimators called the approximate least squares estimators to estimate the unknown parameters and study the asymptotic properties of these estimators under the same error assumptions. It is observed that the approximate least squares estimators are strongly consistent and asymptotically equivalent to the least squares estimators. Similar to the periodogram estimators, these estimators can also be used as initial guesses to find the least squares estimators of the unknown parameters. We perform some numerical simulations to see the performance of the proposed estimators and compare them with the least squares estimators and the estimators proposed by Lahiri et al., \cite{2013}. We have analysed two real data sets for illustrative purposes.