Approximate least squares estimators of a two-dimensional chirp model and their asymptotic properties

Abstract

In this paper, we address the problem of parameter estimation of a two-dimensional (2D) chirp model under the assumption that the errors are stationary. We define a periodogram-type function, which is based on the extension of the 2D periodogram function, defined for a 2D sinusoidal model, to the 2D chirp model. We put forward an alternative to the least squares estimators (LSEs), called the approximate least squares estimators (ALSEs). The proposed estimators take less time to compute and at the same time, they are asymptotically equivalent to the LSEs. Moreover the asymptotic properties of these estimators are obtained under slightly weaker assumptions than those required for the LSEs. Finally, we propose a sequential method for the estimation of the unknown parameters of a multiple component 2D chirp model. This method significantly reduces the computational difficulty involved in finding the usual LSEs and the ALSEs. To see how the proposed method works, we perform some simulation studies and analyze a data set for illustrative purposes.