On estimating parameters of a multi-component Chirp Model with equal chirp rates

TL;DR

This paper develops and compares efficient estimators for multi-component chirp models with equal chirp rates, demonstrating their strong theoretical properties and practical effectiveness in radar signal analysis.

Contribution

It introduces two new computationally efficient estimators with proven consistency and asymptotic normality for this specific chirp model, addressing limitations of previous methods.

Findings

Sequential combined estimator of chirp rate is asymptotically efficient.

All proposed estimators show satisfactory computational and theoretical performance.

Application to radar data effectively recovers ISAR images from noisy signals.

Abstract

Multi-component chirp signal models with equal chirp rates appear in various radar applications, e.g., synthetic aperture radar, echo signal of a rapid mobile target, etc. Many sub-optimal estimators have been developed for such models, however, these suffer from the problem of either identifiability or error propagation effect. In this paper, we have developed theoretical properties of the least squares estimators (LSEs) of the parameters of multi-component chirp model with equal chirp rates, where the model is contaminated with linear stationary errors. We also propose two computationally efficient estimators as alternative to LSEs, namely sequential combined estimators and sequential plugin estimators. Strong consistency and asymptotic normality of these estimators have been derived. Interestingly, it is observed that sequential combined estimator of the chirp rate parameter is asymptotically efficient. Extensive numerical simulations have been performed, which validate satisfactory computational and theoretical performance of all three estimators. {We have also analysed a simulated radar data with the help of our proposed estimators of multi-component chirp model with equal chirp rates, which performs efficiently in recovery of inverse synthetic aperture radar (ISAR) image of a target from a noisy data.