A Height Nonlinear Velocity Field Algorithm for CORS Station Based on GARCH Model

Abstract

In this study, the basic concept of height nonlinear velocity field modeling in the CORS station is described. The noise results in a large deviation between the observation and predicted height. An ARCH testing method for heteroscedasticity of CORS height residual square series was proposed and the non-stationary characteristic of CORS height residual square time series was proved. A CORS height nonlinear velocity field reconstruction method based on the GARCH model was proposed. First, a nonlinear LS periodic fitting model was established for CORS height series data. Then, a GARCH model was established for the fitted non-stationary residual series. Finally, the signal term, linear trend term, and GARCH model noise term of nonlinear LS modeling were combined to reconstruct the nonlinear velocity field of the CORS height. The RMSE of nonlinear LS cycle modeling for 25 CORS stations worldwide ranged from 5 to 10 mm. The differences between the velocity, approximate annual and semi-annual amplitudes, and SOPAC results were 0.73 mm/a, 0.94 mm, and 0.51 mm, respectively. Compared with the centimeter amplitude of the CORS station height, the accuracy of the nonlinear model established in this study met the requirements. The results of height nonlinear velocity field reconstruction at 25 CORS stations worldwide showed that the mean square error of prediction of the one-year height movement reached 9 mm, and the average prediction accuracy of the semi-annual was 7 mm. Compared with the calculation accuracy of the current global CORS elevation component of 3–5 mm, the prediction error in this study was about 3 mm. The expected goal was achieved regarding the accuracy of the CORS station height nonlinear velocity field model.