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The Position and Orientation System is integrated measurement equipment for airborne remote sensing system. The calibration of gyro biases is an effective way to reduce azimuth misalignment and navigation error of strapdown inertial navigation system (SINS). According to the analytic-coarse-alignment principle, the sensitivities of Euler angles with respect to inertial sensor biases are analyzed uniquely. The errors of Earth rotation rate in body frame caused by initial misalignment are obtained. Based on the transformation model of gyro biases, a novel analytic calibration of gyro biases with arbitrary double position is proposed. The simulation and experiment results show that the method can accurately calibrate the gyro biases, improve the precision of initial alignment and inertial navigation for SINS, and verify the efficiency of the proposed method.