Modeling and filtering methods of fiber optic gyroscope(FOG) random noise based on auto-regressive (AR) model were analyzed and contrasted, and the Kalman filtering algorithm based on AR model was improved. A new method of whitening colored noise for Kalman filter was introduced to solve the problem of traditional methods in which there must be a colored noise between system noise and observation noise. Test results demonstrate that the proposed filtering method can effectively reduce FOG random noise and improve accuracy of the attitude determination.