A computationally efficient algorithm to estimate the parameters of a two-dimensional chirp model with the product term

Abstract

Chirp signal models and their generalizations have been used to model many natural and man-made phenomena in signal processing and time series literature. In recent times, several methods have been proposed for parameter estimation of these models. However, these methods are either statistically sub-optimal or computationally burdensome, especially for two dimensional chirp models. In this paper, we consider the problem of parameter estimation of two dimensional chirp models and propose a computationally efficient estimator and establish asymptotic theoretical properties of the proposed estimators. Moreover, the proposed estimators are observed to have the same rates of convergence as the least squares estimators. Further, the proposed estimators of chirp rate parameters are shown to be asymptotically optimal. Extensive and detailed numerical simulations are conducted, which support the theoretical results of the proposed estimators.