Ship Velocity Estimation in Airborne Along-Track Interferometric SAR Imagery Based on the Fractional Fourier Transform

Abstract

Synthetic aperture radar (SAR) was originally exploited to image stationary scenes. However, it is important to derive target information of velocity for many applications. The fractional Fourier transform (FrFT) is a generalization of the classical Fourier transform and is well-known as a useful tool to estimate the chirp rate of linear frequency-modulated (LFM) signals. Motion compensation is critical to moving target imaging. It is difficult for us to obtain the actual motion parameters in real scenarios. Based on the moving target echo model in airborne along-track interferometric SAR (ATI-SAR) and expression of the ATI phase, a method is proposed to estimate the ship velocity by combining the ATI phase with FrFT. First, we use the FrFT to evaluate the chirp rate of the moving target echo. Then, we construct an equation to estimate the ship velocity using the chirp rate estimation, peak response time, and ATI phase. Finally, the simulation experiments are used to validate the effectiveness of the proposed method.

[Retracted] Using Color Difference Compensation Method to Balance and Repair the Image of Art Design

“…Lighting color compensation methods can be divided into two categories: mapping and nonmapping. e mapping theories mainly include von Kries color coefficient law [10], gamut mapping theory, lookup table method, and spectral sharpening theory [11]. Nonmapping theories [12] mainly include retinal cortex theory, neural network model, supervised color constant algorithm, color space-based method, and light compensation method based on a finitedimensional linear model.…”

Restoration of Authentic Position of Unidentified Vessels in SAR Imagery: A Deep Learning Based Approach

“…As the velocity and acceleration of moving target defined the Doppler frequency, the movement of the target was able to be restored by analyzing the difference and offset between the sub-look images: images generated from severed Doppler spectrum [37], [38]. Various studies succeeded to implement the velocity measurement without rendering sub-look images by directly measuring the azimuth frequency modulated (FM) rate; one of the studies restored the azimuth velocity term while surmising the effect of acceleration on velocity measurement separately [36], the other ameliorated the algorithm to the extent where it could be applied to airborne ATI [39], [40]. Both analyses implemented fractional Fourier transform (FrFT), a generalized conformation of conventional Fourier transform conducted with respect to a given angle [41].…”

“…Maneuvering target in SAR images generated a modification 1), where the exact quantity of azimuth shift was demonstrated in (2), derived by the linear term of (1) [39], [47].…”

“…The velocity and acceleration of target in the SAR antenna coverage modify the slant range between the antenna and the target [39]. As illustrated in (1), the linear term of the equation is imprinted as the physical azimuth shift, where the quadratic term determines the Doppler rate, or azimuth FM rate.…”

“…In contrast, FrFT relocates the time domain to joint time-frequency domain, which is defined as a rotation of two-dimensional time-frequency coordinate axes. It implies that (i) FrFT signifies joint time-frequency information of different state and phase as the axes rotation angle α is modified and (ii) FrFT is reduced into conventional Fourier Transform in certain α of π/2 [39]. A detailed elaboration is demonstrated in (8) and ( 9), where j, δ and n respectively indicates imaginary unit of √ , Dirac delta function and an integer.…”