Abstract: The measurement accuracy of MEMS (Micro-ElectroMechanical Systems) gyroscope is low and the noise is high, so it is urgent to process the output signal of MEMS gyroscope digitally. Aiming at the problem that the traditional Kalman filtering method relies heavily on the initial value of the covariance at the initial stage of signal processing, based on the real-time output signal of gyroscope, the data is analyzed online, error types are identified, and the output angular velocity of gyroscope is described by using the dynamic time series model, and the autoregressive first-order model of gyroscope signal is constructed in real time. Based on the autoregressive first-order model, the covariance, state prediction error and measurement error of Kalman filter are analyzed, and the real-time optimization method of steady-state Kalman filter is deeply studied, and the optimal variance and optimal Kalman gain at every moment are directly calculated, so that the optimal estimation at every moment can be achieved in steady-state condition. The dependence of traditional Kalman filter on the initial value of covariance is eliminated. Using MPU6050 as MEMS gyroscope test prototype, the test results show that compared with the traditional Kalman filtering method, the steady-state Kalman filtering method can improve the average value of the output result by 93.33% and the standard difference by 96.87% in the initial filtering stage, realizing the optimal estimation of MEMS gyroscope signal and meeting the requirements of real-time filtering and rapid optimization of MEMS gyroscope.