Simplified and approximation autofocus back-projection algorithm for SAR

Due to accuracy limited inertial measurement unit systems, residual synthetic aperture radar (SAR) motion errors need to be compensated by autofocus method. Back-projection (BP) algorithm is a time-domain imaging process suitable for arbitrary trajectory and imaging on digital elevation model. However, traditional SAR autofocus algorithm requires a Fourier transform relationship between image domain and phase history domain. This study introduces an autofocus algorithm based on phase-error estimation. By selecting the image sharpness as target cost function, the exact phase error is directly estimated in closed form by solving the fourth-order polynomial with simplified approach. Another straightforward approximation autofocus method is also proposed to simplify calculation with high accuracy. The vast storage requirement for filtered BP data is reduced through a trade between time and space. Computer simulation and airborne experimental results validate the efficiency and efficacy of the proposed method.