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.