Aiming at the random error of MEMS gyroscope is the main factor that restricts its precision and application range, the Kalman filter estimation method based on regression moving average (ARMA) model is proposed in this paper. Firstly, based on the results of Allan variance analysis, the quantization noise, angle random walk and zero bias instability are the main parts of the MEMS gyroscope random noise. Then, the stability of MEMS gyroscope random noise is tested by using time series analysis. Finally, based on the random drift of the autoregressive moving average (ARMA) model, a discrete Kalman filter equation is built to actualize its error estimation and compensation. The results of static vehicle and dynamic environment of digital noise reduction and Kalman filtering compensation experiments show that the Kalman filter estimation method based on the ARMA model has more obvious advantages in MEMS Gyroscope random error compensation.