A state amplification based method is proposed for real-time filtering of MEMS random error, which is used to overcome the disadvantage of civil MEMS gyroscopes of low precision, and to solve the problem of traditional MEMS that random error time series modeling needs zero-mean processing and cannot be modeled online.In the method, the mean of time series is considered as an unknown parameter, and an intercept term is added to the traditional ARMA model.A classical Kalman filter and an adaptive Kalman filter are designed by using the state amplification method based on this model, in which the filter has no zero-mean requirement for the measured data.Static and rocking experiments show that this method can significantly improve the accuracy of MEMS gyroscopes.