Aiming at the problem of whitening of colored noise in auto-regressive moving average（ ARMA） model while modeling the micro-electro-mechanical system（ MEMS） gyroscope random noise

colored noise is used as control term of system state equation to modify decoupling adaptive Kalman filtering algorithm

and the effect of noise compensation of MEMS gyro is improved. Experimental results show that after modified algorithm filtering

mean square deviation of noise is reduced by 85. 1 % and random noise term is reduced by 41. 9 %. Compared with standard Kalman filtering algorithm

decoupling adaptive Kalman filtering algorithm

random noise is reduced by 30. 5 %

and 10. 1 %

separately

and can reduce random noise of MEMS gyroscope more efficiently.