On approximate least squares estimators of parameters of one-dimensional chirp signal. Issue 5 (3rd September 2018)

• Record Type: Journal Article
• Authors: Grover, Rhythm; Kundu, Debasis; Mitra, Amit
• Is Part Of: Statistics. Volume 52:Issue 5(2018)
• Page Start: 1060
• Page End: 1085
• Publication Date: 2018-09-03
• Subjects: Chirp signals -- stationary -- least squares estimators -- approximate least squares estimators -- consistent; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1470631
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: Chirp signals are quite common in many natural and man-made systems such as audio signals, sonar, and radar. Estimation of the unknown parameters of a signal is a fundamental problem in statistical signal processing. Recently, Kundu and Nandi [Parameter estimation of chirp signals in presence of stationary noise. Stat Sin. 2008;75:187–201] studied the asymptotic properties of least squares estimators (LSEs) 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 (ALSEs) to estimate the unknown parameters and study the asymptotic properties of these estimators under the same error assumptions. It is observed that the ALSEs are strongly consistent and asymptotically equivalent to the LSEs. Similar to the periodogram estimators, these estimators can also be used as initial guesses to find the LSEs of the unknown parameters. We perform some numerical simulations to see the performance of the proposed estimators and compare them with the LSEs and the estimators proposed by Lahiri et al. [Efficient algorithm for estimating the parameters of two dimensional chirp signal. Sankhya B. 2013;75(1):65–89]. We have analysed two real data sets for illustrative purposes.