Abstract: MEMS gyroscopes are widely applied in the underwater vehicles.Since the random sequences contain the trend terms, which are nonstationary.We cannot use ARMA model to analyze the gyroscopes data.Thus, exploring an effective method of the trend extraction is extremely important.This paper proposes the method of the trend extraction based on smoothness prior approach.The polynomial trend fitting method and the empirical mode decomposition method are also introduced.These algorithms are applied in analyzing the experimental data.Normality test for the residual data is selected as the judgment conditions.The results verify that these methods can extract the trend.However, various methods have their advantages and disadvantages.Thus, we need choose the optimal method based on the different applications conditions.