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

TL;DR

This paper introduces approximate least squares estimators for one-dimensional chirp signals, demonstrating their consistency and asymptotic equivalence to traditional estimators, with validation through simulations and real data analysis.

Contribution

It proposes periodogram-type approximate least squares estimators for chirp signals and analyzes their asymptotic properties, offering a computationally efficient alternative to traditional methods.

Findings

Estimators are strongly consistent.

Estimators are asymptotically equivalent to least squares estimators.

Numerical simulations and real data analysis validate the proposed methods.

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.