Statistica Sinica 27 (2017), 1779-1792

ON PARAMETER ESTIMATION OF TWO-DIMENSIONAL

POLYNOMIAL PHASE SIGNAL MODEL

Ananya Lahiri and Debasis Kundu

Chennai Mathematical Institute and Indian Institute of Technology Kanpur

Abstract: Two-dimensional (2-D) polynomial phase signals occur in different areas of image processing. When the degree of the polynomial is two they are called chirp signals. In this paper, we consider the least squares estimators of the unknown parameters of the 2-D polynomial phase signal model in the presence of stationary noise, and derive their properties. The proposed least squares estimators are strongly consistent and we obtained their asymptotic distributions. It is observed that asymptotically the least squares estimators are normally distributed. We perform some simulation experiments to observe their behavior.

Key words and phrases: Asymptotic distribution, least squares estimators, linear processes, polynomial phase signals, strong consistency.