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

Hengjing Zhang1, Huanling Liu2, Dongdong Cui3

  • 1School of Geomatics, Liaoning Technical University, Fuxin 123000, China.

Sensors (Basel, Switzerland)
|October 14, 2022
PubMed
Summary

This study introduces a new GARCH model to reconstruct nonlinear velocity fields for Continuously Operating Reference Station (CORS) heights, improving accuracy by accounting for noise and non-stationarity. The method significantly enhances prediction accuracy for CORS height movements.

Keywords:
CORS height time seriesGARCHheight predictionnonlinear velocity field

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Area of Science:

  • Geodesy
  • Geophysics
  • Time Series Analysis

Background:

  • Noise in Continuously Operating Reference Station (CORS) height data causes significant deviations between observed and predicted values.
  • The non-stationary characteristics of CORS height residual square time series require advanced modeling techniques.

Purpose of the Study:

  • To develop and validate a nonlinear velocity field reconstruction method for CORS height data.
  • To address the impact of heteroscedasticity and non-stationarity in CORS height residuals.
  • To improve the accuracy of CORS height predictions.

Main Methods:

  • Proposed an ARCH testing method to identify heteroscedasticity in CORS height residual square series.
  • Developed a nonlinear Least Squares (LS) periodic fitting model for CORS height data.
  • Applied a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to the fitted non-stationary residual series.
  • Reconstructed the nonlinear velocity field by combining signal, linear trend, and GARCH noise terms.

Main Results:

  • Root Mean Square Error (RMSE) for nonlinear LS cycle modeling across 25 CORS stations ranged from 5 to 10 mm.
  • Differences between estimated velocity, annual/semi-annual amplitudes, and SOPAC results were within acceptable limits (0.73 mm/a, 0.94 mm, 0.51 mm).
  • Prediction mean square error for one-year height movement reached 9 mm, with average semi-annual prediction accuracy at 7 mm, achieving prediction errors of approximately 3 mm.

Conclusions:

  • The proposed nonlinear velocity field reconstruction method using a GARCH model effectively addresses noise and non-stationarity in CORS height data.
  • The accuracy of the established nonlinear model meets the requirements for CORS station height analysis, outperforming previous methods in prediction accuracy.
  • The study successfully achieved its goal of accurately modeling the nonlinear velocity field of CORS station heights worldwide.