Polar motion prediction using the combination of SSA and Copula-based analysis

Abstract

The real-time estimation of polar motion (PM) is needed for the navigation of Earth satellite and interplanetary spacecraft. However, it is impossible to have real-time information due to the complexity of the measurement model and data processing. Various prediction methods have been developed. However, the accuracy of PM prediction is still not satisfactory even for a few days in the future. Therefore, new techniques or a combination of the existing methods need to be investigated for improving the accuracy of the predicted PM. There is a well-introduced method called Copula, and we want to combine it with singular spectrum analysis (SSA) method for PM prediction. In this study, first, we model the predominant trend of PM time series using SSA. Then, the difference between PM time series and its SSA estimation is modeled using Copula-based analysis. Multiple sets of PM predictions which range between 1 and 365 days have been performed based on an IERS 08 C04 time series to assess the capability of our hybrid model. Our results illustrate that the proposed method can efficiently predict PM. The improvement in PM prediction accuracy up to 365 days in the future is found to be around 40% on average and up to 65 and 46% in terms of success rate for the and , respectively.

A new hybrid method to improve the ultra-short-term prediction of LOD

“…Further information about Copula can be found, e.g., in Joe (1997) and Nelsen (2006). For many years, the Copula method has been used for modeling the dependence structure between random variables in different types of studies, such as Economics (Rachev and Mittnik 2000;Patton 2006Patton , 2009, Biomedicine (Wang and Wells 2000;Escarela and Carriere 2003), Hydrology (Bárdossy and Li 2008;Bárdossy and Pegram 2009;Verhoest et al 2015), Meteorology (Laux et al 2011;Vogl et al 2012), Hydro-geodesy, and Geodesy (Modiri et al 2015(Modiri et al , 2018. Six different bivariate Copula families are used in this research: the Archimedean 12, Archimedean 14, Clayton, Frank, Gumbel, and Joe.…”

“…The difference between the observed LOD and Copula LOD estimated data is modeled using the SSA method. After that, the EAM Z is predicted as described in detail in Modiri et al (2018). The prediction algorithm is demonstrated through the following steps: as it is shown in Fig.…”

“…We explored the combination of Copula-based analysis and singular spectrum analysis (SSA) to predict LOD. In Modiri et al (2018), we applied the combination of SSA and Copula for the first time as a novel deterministic-stochastic tool for PM prediction. In this method, deterministic part is estimated by SSA, whereas Copula is used for modeling the stochastic part.…”

“…SSA is a subspace-based technique which makes use of empirical functions derived from the data to model the time series in a pre-specified level of details. It can be used for trend extraction and extrapolation (Alexandrov 2009;Modiri et al 2018), periodicity detection, seasonal adjustment, smoothing, noise reduction (Golyandina et al 2001;Ghil et al 2002) as well as for change point detection (Moskvina and Zhigljavsky 2003;Hoseini et al 2020). First, we derive the dependence structure between LOD and EAM Z .…”

Smoothing and predicting celestial pole offsets using a Kalman filter and smoother

“…However, there are other sources of EOP predictions and different forecast methods are applied by many scientific institutions. Autoregression (Kosek et al 2008), auto-covariance (Kosek et al 2008), least-squares colocation (Hozakowski 1990), neural networks (Kalarus and Kosek 2004;Schuh et al 2002), wavelets and fuzzy inference systems (Akyilmaz et al 2011), Kalman filter (Freedman et al 1994, spectral analysis and least-squares extrapolation (Akulenko et al 2002), combination of least squares plus auto-regression (Kosek et al 1998(Kosek et al , 2008Xu et al 2012), combination of singular spectrum analysis and Copula-based analysis (Modiri et al 2018), modelling and forecasting excitation functions (Chin et al 2004) are the most common algorithms for EOP prediction.…”