Earth rotation parameters (ERPs) are essential for transforming between the celestial and terrestrial reference frames, and for high-precision space navigation and positioning. Among the ERPs, polar motion (PM) is a critical parameter for analyzing and understanding the dynamic interaction between the solid Earth, atmosphere, ocean, and other geophysical fluids. Traditional methods for predicting the change in ERPs rely heavily on linear models, such as the least squares (LS) and the autoregressive (AR) model (LS + AR). However, variations in ERP partly reflect non-linear effects in the Earth system, such that the predictive accuracy of linear models is not always optimal. In this paper, long short-term memory (LSTM), a non-linear neural network, is employed to improve the prediction of ERPs. Polar motion prediction experiments in this study are conducted using the LSTM model and a hybrid method LS + LSTM model based on the IERS EOP14C04 time series. Compared with Bulletin A, the PMX and PMY prediction accuracy can reach a maximum of 33.7% and 31.9%, respectively, with the LS + LSTM model. The experimental results show that the proposed hybrid model displays a better performance in mid- and long-term (120–365 days) prediction of polar motion. Graphical Abstract

Earth rotation parameters (ERPs) are fundamental to geodetic and astronomical studies. With its high measurement accuracy and stability, the Very Long Baseline Interferometry (VLBI) plays an irreplaceable role in estimating the ERPs and maintaining the earth reference frame. However, the imperfect global station distribution, observation discontinuity, and vast cost of the VLBI make the GNSS a more attractive technique. In 2020, the third generation of the BeiDou Navigation System (BDS), namely BDS-3, was constructed completely. In this study, we conducted a series of experiments to estimate Earth’s rotation parameters based on the continuous BDS-3 observation data, the discontinuous VLBI observation data, and the combined BDS-3 and discontinuous VLBI observation data. We used two methods, namely the weighted averaging method and the normal equation combination method, to obtain ERP combination solutions. The results are compared with the International Earth Rotation and Reference Systems Service (IERS) EOP 20C04 at 00:00:00 UTC. Final results show that (a) the estimation accuracy becomes stable when the number of BDS-3 tracking stations is more than 40. At the same time, both the number of stations and the volume of polyhedrons formed by the observing stations affect the accuracy of the ERPs estimated by the BDS-3 or VLBI. (b) Results have also shown that the inclusion of the BDS-3 IGSO and GEO satellites contributes little to the ERP estimation. (c) For the BDS-3-only MEO satellites solution, the root mean square (RMS) was 113.2 µas, 102.8 µas, and 13.1 µs/day for X-pole coordinate, Y-pole coordinate, and length of day (LOD), respectively. For the VLBI solution, the RMSs of the X-pole, Y-pole, and LOD were 100.4 µas for the X-pole, 94.2 µas for the Y-pole, and 14.1 µs/day. The RMS was 82.6 µas, 70.3 µas, and 10.5 µs/day for the combined X-pole, Y-pole, and LOD using the weighted averaging method. It was 78.2 µas, 62.6 µas, and 8.6 µs/day when the normal equation combination method was applied. This demonstrates that by taking advantage of the BDS-3 and VLBI technique combinations, accuracy in estimating the ERPs can be improved over that using either of them, in addition to enhanced stability and reliability.

The Earth is subject to complex internal and external forces in space. External forces include the gravitational attraction from the sun, moon, and other planets, and the internal forces include mass loads and frictional forces from the atmosphere, oceans, ice, snow, water, as well as interactions between the crust and mantle. Earth rotation parameters (ERPs) are essential for transforming between the celestial and terrestrial reference frames, and for high-precision space navigation and positioning. Amongst the ERPs, Polar Motion (PM) is a critical parameter for analyzing and understanding the dynamic interaction between the solid Earth, atmosphere, ocean, and other geophysical fluids. To investigate the impact of effective angular momentum (EAM) on long-term ERPs prediction, this thesis conducts research on long-term ERPs prediction considering EAM. Taking into account the influence of EAM, a discrete Liouville equation related to polar motion and UT1-UTC was first established, and the corresponding geodetic angular momentum was obtained. Finally, the residual geodetic angular momentum was obtained and modeled. Taking into account the residual of geodetic angular momentum and the experimental results of EAM, it is shown that, compared with Bulletin A, the LS+LSTM model has improved the accuracy of PMX, PMY, and UT1-UTC in the mid-and long term.Keywords: Earth rotation parameters, Polar Motion, UT1-UTC, Least squares, Long Short-Term Memory model, effective angular momentumFunding: Part of this work is supported by the National Natural Science Foundation of China (NSFC) (Grant No.42174037, No. 42030105, No. 42204006, No. 42274011, No. 42304095) and the State Key Laboratory of Geo-Information Engineering and Key Laboratory of Surveying and Mapping Science and Geospatial Information Technology of MNR, CASM (Grant No. 2024-01-01), the China Postdoctoral Science Foundation under Grant No.2024M752480.

The China Space Station (CSS) is currently in orbit and carries the high-precision optical atomic clock with stability of approximately $2.0 \times 10^{-15} / \sqrtτ$ in its experiment module. We have developed a model to determine the gravity potential (GP) based on the gravity frequency shift equation and have created both one-way and dual-frequency transfer models up to $c^{-4}$. These models consider effects from the troposphere, ionosphere, and solid Earth tides. The proposed model is suitable for measurements at the magnitude of $10^{-19}$. Based on the CSS mission, we conducted the simulation experiments. The results indicate that when processing the simulation frequency signal using the proposed model, we can obtain the GP with the accuracies of $ (1.13\pm0.71)\,\mathrm{m^2/s^2}$, $ (0.09\pm0.89)\,\mathrm{m^2/s^2}$, and $(0.66\pm1.18)\,\mathrm{m^2/s^2}$ for cutoff elevation angles of $5^{\circ}$, $10^{\circ}$ and $15^{\circ}$, respectively. With the high-precision optical atomic clock onboard the CSS, the proposed model enables us to measure the GP differences in the magnitude of centimeter-level accuracy.

Determining the gravity potential (GP) is a major task for geodesy. Advances in atomic clocks enable relativistic geodesy. China Space Station (CSS) carries an optical clock with stability 2×10−15/τ, but no previous frequency comparison model matches its accuracy. Previous tri-frequency models required fixed frequency ratios and ignored higher-order ionospheric effects. In this study, an improved tri-frequency combination model is proposed that extends to the c-4 terms of the GP and accounts for Doppler shifts, tropospheric and higher-order ionospheric effects, tidal effects, and the Shapiro delay. Crucially, it can be applied to any arbitrary combination of three frequencies. To validate the performance of the modified model, we use CSS tri-frequency microwave links for space-to-ground comparison and simulate GP determination at ground stations. With EGM2008 as the truth, the model achieved 0.7 m²/s² accuracy, supporting centimeter-level unification of global height datums. The model provides theoretical support for future real-data processing.

The China Space Station (CSS) is currently in orbit and carries the high-precision optical atomic clock with stability of 2.0×10-15/√τ in its experiment module. We have developed a model to determine the geopotential at the ground based on the gravity frequency shift equation and have created both one-way and dual-frequency transfer models up to c-4. These models consider influence from the troposphere, ionosphere, and solid Earth tides. The proposed model is suitable for measurements at the magnitude of 10-19. Based on the CSS mission, we conducted the simulation experiments. The results indicate that, based on the CSS microwave links, we can obtain the geopotential difference between two sites on the ground with centimeter-level accuracy.This study is supported by the National Natural Science Foundations of China (NSFC) (Grant Nos. 42030105, 42388102, and 42274011) and the China Postdoctoral Science Foundation (Certificate Number: 2024M752480).