A Computationally Efficient algorithm to estimate the Parameters of a Two-Dimensional Chirp Model with the product term

TL;DR

This paper introduces a new computationally efficient method for estimating parameters in two-dimensional chirp models, achieving asymptotic optimality and comparable convergence rates to least squares estimators.

Contribution

The paper proposes a novel estimator for 2D chirp models that is computationally efficient, asymptotically optimal, and has the same convergence rate as traditional least squares methods.

Findings

Proposed estimators are computationally efficient.

Estimators achieve asymptotic optimality.

Numerical simulations support theoretical properties.

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. These methods however are either statistically sub-optimal or computationally burdensome, specially for two dimensional (2D) chirp models. In this paper, we consider the problem of parameter estimation of 2D chirp models and propose a computationally efficient estimator and establish asymptotic theoretical properties of the proposed estimators. And the proposed estimators are observed to have the same rates of convergence as the least squares estimators (LSEs). Furthermore, the proposed estimators of chirp rate parameters are shown to be asymptotically optimal. Extensive and detailed numerical simulations are conducted, which support theoretical results of the proposed estimators.