Abstract
In this letter, a novel angular jerk estimator (AJE) in the time-frequency (TF) domain is proposed. For this purpose, the properties of the short-time Fourier transform (STFT) are taken into consideration, which allows for computation of the instantaneous angular jerk for each time and frequency <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(</b> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</b> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">,</b> ω <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">)</b> coordinate. Additionally, apart from the introduced AJE, two novel forms of the instantaneous chirp rate (CR) and the instantaneous frequency (IF) estimators are provided, which is an improvement on the capabilities of these tools when compared to approaches existing in the literature. The proposed estimators are presented in analytic form, tested from the perspective of their precision, and compared to the Cramer-Rao Lower Bound (CRLB) as well as validated under numerical experiments.
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