Analysis and prediction of EOP time series using LSHE+ARMA method

Document Type : Research


1 College of Engineering, University of Tehran Tenran, Iran

2 ُSchool of Geospatial and Surveying Engineering - college of Engineering - University of Tehran

3 , Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Iran


The rotation of the solid Earth with respect to inertial space is not constant due to the changes of external gravitational forces and internal dynamics. Earth orientation parameters (EOP), including, the Earth’s polar motion (PM), Anomalies in the Earth’s angular velocity and celestial pole offsets (CPO), describe these irregularities in the Earth’s rotation. Anomalies in the axis defined by the celestial intermediate pole (CIP) with respect to the Z axis of the terrestrial reference system are named as PM. The CPO are expressed as the deviations, dX and dY, between the observed CIP and the conventional CIP position. The difference between the smoothed principal form of universal time UT1 and the coordinated universal time UTC denotes the Earth’s rotation angle, which, together with the xp, yp terrestrial pole coordinates, forms a set of Earth orientation parameters (EOP). In addition to the other EOP, the length of day (LOD) is used to model the Anomalies in the Earth’s rotation rate. LOD is the difference between the duration of the day measured by space geodesy and nominal day of 86,400 s duration.

Generally, EOP are the parameters that provide the rotation of the International Terrestrial Reference System (ITRS) to the International Celestial Reference System (ICRS) as a function of time. However the EOP are computed using the modern space geodetic techniques such as Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI) and the Global Navigation Satellite System (GNSS), they are unavailable to the real-time applications due to the data processing complexities. Accurate and rapid EOP predictions are required for different fields like precise orbit determinations of artificial Earth satellites, positional astronomy, space navigation and geophysical phenomena.

There are many different methods for analysis and prediction of EOP time series including deep learning methods, least square (LS) with autoregressive (AR) and also Singular Spectrum Analysis as a non-parametric method.

In this research Least Square Harmonic Estimation analysis is used to investigate the frequencies of EOP. First, The solid and ocean tide terms are modeled based on IERS technical notes. These effects are removed from LOD time series. The remained time series are named as LODR time series. The univariate time series analysis is then applied to the LODR time series and multivariate analysis is used for detecting the PM periodic patterns. Applying these methods to the 40 years observations of EOP (since 1 January 1980 to 31 December 2020) revealed the Chandler, annual, semi Chandler, semi-annual and annual signals as the main periodic signals in the EOP time series. The functional model is then formed using all detected signals in order to model the deterministic variations of EOP time series.

In order to model the remained non-deterministic variations, an ARMA (Autoregressive Moving Average) model is fitted to the least square residuals. The Akaike's Information Criterion (AIC) is used to investigate the optimized order of ARMA model.

The EOP is then predicted for the first 20 days of 2021, using the pre-identified functional model for the deterministic part and the ARMA model for the non-deterministic part of the time series variations. For the prediction of LOD time series, after creating the functional model of LODR time series, the solid and ocean tide terms are added to the functional model of LODR.

Finally, in order to validate the accuracy of the proposed method, a comparison is made with an EOP prediction study that used the ANN (Artificial Neural Network) and ANFIS (Adaptive Network Based Fuzzy Inference System) methods for short term prediction of EOP.

The result shows that the accuracy of the proposed method is better than the previous study and the method can be used for accurate prediction of EOP time series.


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