Performance of Chirp Parameter Estimation in the Fractional Fourier Domains and an Algorithm for Fast Chirp-Rate Estimation

This article addresses the problem of fast and accurate chirp signal parameter estimation in fractional Fourier domains. By employing a perturbation analysis, it is shown that the fractional Fourier transform can be used as an effective tool to yield an asymptotically minimum-variance unbiased estim...

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Bibliographic Details
Published in:IEEE transactions on aerospace and electronic systems 2020-10, Vol.56 (5), p.3685-3700
Main Authors: Aldimashki, Omair, Serbes, Ahmet
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
Chirp
Chirp rate
Chirp signals
Computational efficiency
Computing costs
Domains
Estimation
Fourier transforms
fractional fourier transform (FrFT)
golden section search (GSS)
linear-frequency-modulated (LFM) parameter estimation
Lower bounds
Parameter estimation
Perturbation methods
Radar
radon–wigner transform
Time-frequency analysis
Transforms
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Summary:This article addresses the problem of fast and accurate chirp signal parameter estimation in fractional Fourier domains. By employing a perturbation analysis, it is shown that the fractional Fourier transform can be used as an effective tool to yield an asymptotically minimum-variance unbiased estimator of the chirp parameters. Furthermore, it is shown that the asymptotic performance of the fractional-Fourier-transform-based chirp-rate estimator depends only on the actual chirp rate, not the initial frequency. Consequently, the chirp-rate estimation can be done in only one-dimensional search space, which greatly reduces the computational cost. In order to validate theoretical outcomes, we propose a fast and powerful method for the estimation of chirp rates in the fractional Fourier domains based on the golden section search. Extensive computer simulations confirm the theoretical results by demonstrating that the estimation performance of the chirp rate achieves the Cramer-Rao lower bound for both single- and multicomponent chirps. Consequently, we assert that the proposed method of chirp parameter estimation in the fractional Fourier domains is the minimum-variance unbiased estimator, requiring minimal computational cost.
ISSN:0018-9251
1557-9603
DOI:10.1109/TAES.2020.2981268