The deviation in the phase of SAR echoes due to INS error

Quadratic phase error (QPE) of SAR (Synthetic aperture radar) echo accumulated during SAR integration interval, determines SAR image resolution. QPE depends on quadratic position error of SAR antenna. Though INS (Inertial navigation system)/GPS (Globe position system) integrated navigation system is widely used in SAR motion compensation, in each coherent time, however only INS data is used for the measurement of SAR antenna position and GPS data is avoided due to its highfrequency errors. So INS errors play main role in the SAR image resolution. There are many sources of INS errors, such as gyro drift, accelerometer bias etc. In order to find the analytical relation between INS errors and QPE of SAR we have written their transfer functions in Laplace domain. These transfer functions depict the different effects of different INS errors on QPE of SAR. Time domain simulations and SAR imaging simulations prove the analytical conclusions. In this paper the analytical relations have been verified by computer simulations. The results in this paper are useful for developing SAR motion compensation system with high performance and cost ratio.