Studying atmospheric turbulence effects on aircraft motion for airborne SAR motion compensation requirements

It is necessary to study the influence of atmospheric disturbance on aircraft motion for the motion compensation sensitivity requirements of airborne SAR. Most motion compensation study for airborne SAR is focusing on the effects of assuming motion errors on SAR images from the early years of airborne SAR development. In this paper, based on power spectra density (PSD) method, the spectra of aircraft motion that containing all the response motion information due to atmospheric disturbance can be calculated from the given spectra of the atmospheric turbulence and the transfer function between aircraft motion and atmospheric turbulence. As an example, one common atmospheric turbulence model is applied to get the lateral/longitudinal uncontrolled and controlled aircraft motion. At low frequency domain, our results show that the controlled aircraft motion is suppressed in comparison with the uncontrolled aircraft motion as wished; whereas, at high frequency domain, there is no difference between the spectra of controlled and uncontrolled aircraft motion, i.e., each has a scaling behavior with a scaling exponent corresponding exactly to the atmospheric turbulence model. Based on these aircraft motion analysis, an acceptable residual motion error is predicted from the motion compensation requirements, which suggests that motion compensation for airborne SAR is unavoidable and should pay more attention on the medium frequency range.