This is a kind of trend that the synthetic aperture radar (SAR) system needs miniaturization. With dramatically reduced cost, size, precision and weight, micro electromechanical system inertial measurement unit system (MEMS IMU) has played a major role in SAR motion compensation. It has to take measures to improve the measurement precision of the relative motion within a short time in view of a large random error in MEMS IMU. Firstly, the influence of measurement error on SAR imaging has been analyzed. Secondly, ARMA model has been set up by analyzed the unsystematic error using time series theory. And then, the Kalman equation has been designed and it has been used to filter the IMU raw data. It turns out that the method can be used to reduce the random error which can be helpful to reduce the influence of random noise on SAR motion compensation in a synthetic aperture time Airborne SAR flight test data processing result has proved that the method proposed in this paper can effectively decrease the random error, improve the SAR focusing image quality.