Differential Learning: A method for polar motion time series prediction

Nowadays, many applications such as Global Navigation Satellite Systems (GNSS) or spacecraft tracking require a rapid determination, or even predictions, of the Earth Orientation Parameters (EOP). However, due to the measurement techniques utilized to estimate EOP, the latency can be considerably longer than required, which especially hinders real-time applications, resulting in a need for accurate EOP prediction methods.

With the resurgence of machine learning in the last decade, time series prediction is increasingly studied in this context. We propose a learning algorithm for the prediction of polar motion components (xp, yp). The algorithm is based on the concept of Ordinary Differential Equation (ODE) fitting. Within this investigation, a general formula for ODE fitting based on multivariate time series is proposed, with special focus on second order ODEs. The mathematical relations are derived and presented in both linear and non-linear forms, particularly with LSTM and Elman neural networks. In addition, a sensitivity analysis framework is proposed for the linear case, which is used for the determination of the importance of features. 

We compared the prediction performance of our method with those from three different studies. First, the conditions of the first Earth Orientation Prediction Comparison Campaign (EOPPCC) are followed. In this case, the ultra-short term predictions (up to 10 days) can be improved on average by 62.5% and 45.6% for xp and yp, respectively,  compared to the best performing EOPPCC method. Second, the prediction performance in long-term prediction (up to one year) is compared against Multichannel Singular Spectrum Analysis (MSSA). In this case, the prediction performance is improved on average for xp and yp by 40.9% and 66.4%, respectively. Finally, comparisons against Copula-based methods for long-term prediction are conducted (average improvement 32.3% for xp and 57.8% for yp).

The advantages of this method include (1) exploitation of physical information via Effective Angular Momentum (EAM) functions and by using the concept of ODE fitting, which often corresponds to the laws governing physical phenomena; (2) presence of sensitivity analysis frameworks; and (3) high predictive performance.