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High-resolution airborne synthetic aperture radar (SAR) imaging requires long synthetic aperture time (LSAT). However, the LSAT invalidates the Fresnel approximation in the traditional autofocusing method, leaving a residual signal phase in the motion error. To solve the problem, a signal-reconstructionbased phase gradient autofocus (SR-PGA) and a sub-image resampling (SIR) methods are proposed. They are developed on the hyperbolic model. First, a sub-aperture division strategy divides the full-aperture high-order error into multiple low-order sub-aperture errors. Then, the SR-PGA is developed to estimate the sub-aperture error (SPE), in which the precise deramping is reconstructed to eliminate the residual signal phase in the SPE. Third, the SIR is proposed to eliminate residual Doppler-variant shift of the adjacent sub-images, improving the accuracy of the SPE combination. Finally, simulation and actual data processing verify the effectiveness and validity of the algorithm.

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