Approximate least squares estimators of a two-dimensional chirp model

Abstract

In this paper, we propose a method based on maximizing a periodogram-type function for parameter estimation of a two-dimensional (2-D) mono-component chirp signal model. The obtained estimators are called approximate least squares estimators (ALSEs). We also put forward a sequential algorithm for parameter estimation of a more general version of the model with multiple number of components. The main focus of the paper has been on developing the large-sample properties of the proposed estimators. Derived theoretical results show that the proposed estimators are strongly consistent and asymptotically normally distributed. Moreover, it is shown that the derived asymptotic distribution is identical to that of the traditional least squares estimators (LSEs). The numerical performance of the ALSEs and sequential ALSEs is demonstrated through extensive simulation studies. The results are positioned parallel to that obtained using the least squares method and 2-D multilag High Order Ambiguity function (2D-ml-HAF) for a comparative study. These simulations make use of the true values as the initial guesses in the optimization algorithm as using a fine grid search for this purpose is practically infeasible. We also provide a practical alternative for modeling of real world signals in an another set of simulation experiments. This involves a combination of two methods- 2D-ml-HAF estimators and genetic algorithm (GA). The results show that the proposed combination is a reasonable scheme to find initial guesses and provides satisfactory performance for varying signal-to-noise ratio (SNR).