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A state space approach for the modeling of nonstationary time series is presented. Based on the concept of smoothness priors constraint, the overall model is fitted by using the Kalman filler and Akaike's AIC criterion. Whenever an autoregressive (AR) model with time-varying coefficient is fitted in state space model, it can be used for the time-varying spectrum estimation. Some numerical results of gyro drift models are obtained for analysis of high-precision gyro. As the trend, irregular and periodic components of the observed time series can be modeled simultaneously, it is statistically more accurate and efficient than that modeled separately.