In order to improve the accuracy and reliability of GPS data, a method based on the least squares adjustment principle, the least squares adjustment with three times the unit weight error tolerance criteria and robust estimation of gross error detection Inter Quartile Range(IQR) criteria is proposed to detect, eliminate, classify and compare the data in gross error. And time series fitting model and spectral analysis are used to study the elevation components data of the International GNSS Service(IGS) station in the MATLAB platform. By studying the elevation data of Beijing Fangshan station, we can see that the residuals time series of GPS point elevation component are similar to the sine function, of which the period is approximately 1 year, with an amplitude of 0.03. Elevation components from the image data analysis present an obvious linearity, as well as a periodicity, which demonstrates that the principle of least squares, error tolerance and IQR criteria can well reflect the linearity, periodicity and residual spectral features of the elevation data.