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Over the years, prediction techniques for the highly variable angular velocity of the Earth represented by Earth's rotation (UT1-UTC) and length-of-day (LOD) have been continuously improved. This is because many applications like navigation, astronomy, space exploration, climate studies, timekeeping, disaster monitoring, and geodynamic studies, all rely on predictions of these Earth rotation parameters. They provide early warning of changes in the Earth's rotation, allowing various industries and scientific fields to operate more precisely and efficiently. Thus, in our study, we focused on short-term prediction for UT1-UTC (dUT1) and LOD. Our prediction approach is to combine machine learning (ML) technique with efficient evolutionary computation (EC) algorithms to achieve reliable and improved predictions. Gaussian process regression (GPR) is used as the ML technique with genetic algorithm (GA) as the EC algorithm. GA is used for hyperparameter optimization of GPR model as selecting appropriate values for hyperparameter are essential to ensure that the prediction model can accurately capture the underlying patterns in the data. We conducted some experiments with our prediction approach to thoroughly test its capabilities. Moreover, two forecasting strategies were used to assess the performance in both hindcast and operational settings. In most of the experiments, the data used are the multi-technique combinations (C04) generated by International Earth Rotation and Reference Systems Service (IERS). In one of the experiments, we also investigated the performance of our prediction model on dUT1 and LOD from four different products obtained from IERS EOP 20 C04, DTRF20, JTRF20 and USNO. The prediction products are evaluated with real estimates of the EOP product with which the model is trained. The combined excitations of the atmosphere, oceans, hydrology, and sea level (AAM + OAM + HAM + SLAM) are used as predictors because they are highly correlated to the input data. The results depict the highest performance of 0.412 ms in dUT1 and 0.092 ms/day in LOD, on day 10 of predictions. It is worth noting that the later predictions were obtained by incorporating the uncertainty of the input data as weights in the prediction model, which was a novel approach tested in this study. Graphical Abstract
Over the years, prediction techniques for the highly variable angular velocity of the Earth represented by Earth's rotation (UT1-UTC) and length-of-day (LOD) have been continuously improved. This is because many applications like navigation, astronomy, space exploration, climate studies, timekeeping, disaster monitoring, and geodynamic studies, all rely on predictions of these Earth rotation parameters. They provide early warning of changes in the Earth's rotation, allowing various industries and scientific fields to operate more precisely and efficiently. Thus, in our study, we focused on short-term prediction for UT1-UTC (dUT1) and LOD. Our prediction approach is to combine machine learning (ML) technique with efficient evolutionary computation (EC) algorithms to achieve reliable and improved predictions. Gaussian process regression (GPR) is used as the ML technique with genetic algorithm (GA) as the EC algorithm. GA is used for hyperparameter optimization of GPR model as selecting appropriate values for hyperparameter are essential to ensure that the prediction model can accurately capture the underlying patterns in the data. We conducted some experiments with our prediction approach to thoroughly test its capabilities. Moreover, two forecasting strategies were used to assess the performance in both hindcast and operational settings. In most of the experiments, the data used are the multi-technique combinations (C04) generated by International Earth Rotation and Reference Systems Service (IERS). In one of the experiments, we also investigated the performance of our prediction model on dUT1 and LOD from four different products obtained from IERS EOP 20 C04, DTRF20, JTRF20 and USNO. The prediction products are evaluated with real estimates of the EOP product with which the model is trained. The combined excitations of the atmosphere, oceans, hydrology, and sea level (AAM + OAM + HAM + SLAM) are used as predictors because they are highly correlated to the input data. The results depict the highest performance of 0.412 ms in dUT1 and 0.092 ms/day in LOD, on day 10 of predictions. It is worth noting that the later predictions were obtained by incorporating the uncertainty of the input data as weights in the prediction model, which was a novel approach tested in this study. Graphical Abstract
The Length of Day (LOD) and the Universal Time (UT1) play crucial roles in satellite positioning, deep space exploration, and related fields. The primary method for predicting LOD and UT1 is least squares fitting combined with autoregressive (AR) models. Polynomial Curve Fitting (PCF) has greater accuracy in capturing long-term trends compared to standard least squares fitting. In this study, PCF combined with Weighted Least Squares (WLS) is employed to fit and extrapolate the periodic and trend components of the LOD series after removing tidal influences. Additionally, considering the time-varying characteristics of the LOD series, a Long Short-Term Memory (LSTM) network is utilized to predict the residuals derived from the fitting process. The 14 C04 LOD series released by the International Earth Rotation and Reference System Service (IERS) is used as the base series, with 70 LOD and UT1-UTC prediction experiments conducted during the period from 1 September 2021–31 December 2022. The results indicate that the PCF+WLS+LSTM method is well-suited for medium- and long-term (90–360 days) prediction of the LOD and UT1-UTC. Significant improvements in prediction accuracy were obtained for periods ranging from 90–360 days, particularly beyond 150 days, where the average accuracy improved by over 20% compared to IERS Bulletin A. Specifically, the largest prediction accuracy increase for LOD and UT1-UTC was 49.5% and 59.2%, respectively.
The polar motion (PM, including two parameters PMx and PMy) ultra-short-term prediction (1–10 days) is demanded in the real-time navigation of satellites and spacecrafts. Improving the PMx and PMy ultra-short-term predictions accuracies are a key to optimize the performance of these related applications. Currently, the least squares (LS)+autoregressive (AR) hybrid method is regarded as one of the most capable approaches for ultra-short-term predictions of PMx and PMy. The Kalman filter has proven to be effective in improving the ultra-short-term prediction performance of the LS+AR hybrid method, but the PMx and PMy ultra-short-term predictions accuracies are still not able to satisfy some related applications. In order to improve the performance of PM ultra-short-term prediction, it is worth exploring the combinations of existing methods. Throughout the existing predicted methods, the LS+multivariate autoregressive (MAR) hybrid method by using the Kalman filter has the potential to improve the accuracy of PM ultra-short-term prediction. In addition, a PM prediction performance analysis of the LS+MAR hybrid method by using the Kalman filter, namely the LS+MAR+Kalman hybrid method, is still missing. In this contribution, we proposed the LS+MAR+Kalman hybrid method for PM ultra-short-term prediction. The data sets for PM predictions, which range from 1 to 10 days, have been tested based on the International Earth Rotation and Reference Systems Service Earth Orientation Parameter (IERS EOP) 14 C04 series to assess the performance of the LS+MAR+Kalman hybrid model. The experimental results illustrated that the LS+MAR+Kalman hybrid method can effectively execute PMy ultra-short-term predictions. The improvement of PMy prediction accuracy can rise up to 12.69% for 10-day predictions, and the improvement of ultra-short-term predictions is 7.64% on average.
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