Estimation methods for elementary chirp model parameters

TL;DR

This paper introduces new estimation techniques for elementary chirp model parameters, providing theoretical properties, practical initial value strategies, and sequential procedures that perform well in noisy or complex scenarios.

Contribution

It develops sequential estimation methods with proven consistency and normality, addressing challenges in initial value selection for multi-component chirp models.

Findings

Sequential estimators outperform traditional methods in noisy environments.

Proposed estimators are strongly consistent and asymptotically normal.

Numerical experiments confirm the effectiveness of the methods.

Abstract

In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one-component elementary chirp model. It is proved that the proposed estimators are strongly consistent and follow the normal distribution asymptotically. We also suggest how to obtain proper initial values for these methods. The problem of finding initial values is a difficult problem when the number of components in the model is large, or when the signal-to-noise ratio is low, or when two frequency rates are close to each other. We propose sequential procedures to estimate the multiple-component elementary chirp model parameters. We prove that the theoretical properties of sequential least squares estimators and sequential approximate least squares estimators coincide with those of least squares estimators and approximate least squares estimators, respectively. To evaluate the performance of the proposed estimators, numerical experiments are performed. It is observed that the proposed sequential estimators perform well even in situations where least squares estimators do not perform well. We illustrate the performance of the proposed sequential algorithm on a bat data.