Computationally Efficient Algorithm for Frequency Estimation of a Two-Dimensional Sinusoidal Model

In this paper, we propose a computationally faster yet conceptually simple methodology to estimate the parameters of a two-dimensional (2-D) sinusoidal model in the presence of additive white noise. We develop the large sample properties like consistency and asymptotic normality of these low-complexity estimators, and they are observed to be theoretically as efficient as the ordinary least squares estimators. To assess the numerical performance, we conduct extensive simulation studies. The results indicate that the proposed estimators can successfully replace the least squares estimators for sample size as small as 20 ×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} 20 and for signal-to-noise ratio (SNR) as small as 12 dB.