Fiber optical gyro (FOG) is a new developed inertial measurement unit for inertial navigation systems. Its performance geatly depends on the photoelectric devices such as optical sources, integrated chips and photoelectric detectors used. The main noise mechanisms of high precision fiber optic gyros are presented and the Allan variance analysis of two gyros with different precision is made. The content of white noise and fractal noise in a FOG is judged according to the estimated noise parameters of the FOG. Thus, the precision of the FOG is verified and the improved schemes for FOGs with different precision are given so as to provide theoretical guidance for the improvement of the precision of FOGs.