The random errors of a micro electro mechanical system (MEMS) gyroscope was analyzed and modeled to improve gyroscope performance. Time series analysis was used to fit the gyroscope measurement data which had been preprocessed. State vector augmenting method was proposed to design Kalman filter. In order to verify the validity of the method, rate test and oscillating test had been done. After filtering, in the case of static and constant angular rate, the mean value and standard deviation were 55% and 12% of that before filtering respectively. However, the effect decreased when it turns to oscillating environment. Adaptive Kalman filter was adopted to solve the problem. The choosing principle of fading factor was discussed and the filtering performance of constant fading factor was compared with that of adaptive factor. The results showed that, in the case of oscillating, both of them could get a remarkable performance improvement, and the filtering performance of the adaptive fading factor is higher than that of the constant one.