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Abstract In 2021, the International Earth Rotation and Reference Systems Service (IERS) established a working group tasked with conducting the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) to assess the current accuracy of EOP forecasts. From September 2021 to December 2022, EOP predictions submitted by participants from various institutes worldwide were systematically collected and evaluated. This article summarizes the campaign's outcomes, concentrating on the forecasts of the dX, dY, and dψ, dε components of celestial pole offsets (CPO). After detailing the campaign participants and the methodologies employed, we conduct an in-depth analysis of the collected forecasts. We examine the discrepancies between observed and predicted CPO values and analyze their statistical characteristics such as mean, standard deviation, and range. To evaluate CPO forecasts, we computed the mean absolute error (MAE) using the IERS EOP 14 C04 solution as the reference dataset. We then compared the results obtained with forecasts provided by the IERS. The main goal of this study was to show the influence of different methods used on predictions accuracy. Depending on the evaluated prediction approach, the MAE values computed for day 10 of forecast were between 0.03 and 0.16 mas for dX, between 0.03 and 0.12 mas for dY, between 0.07 and 0.91 mas for dψ, and between 0.04 and 0.41 mas for dε. For day 30 of prediction, the corresponding MAE values ranged between 0.03 and 0.12 for dX, and between 0.03 and 0.14 mas for dY. This research shows that machine learning algorithms are the most promising approach in CPO forecasting and provide the highest prediction accuracy (0.06 mas for dX and 0.08 mas for dY for day 10 of prediction). Graphical abstract

In 2021, the International Earth Rotation and Reference Systems Service (IERS) established a working group tasked with conducting the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) to assess the current accuracy of EOP forecasts. From September 2021 to December 2022, EOP predictions submitted by participants from various institutes worldwide were systematically collected and evaluated. This article summarizes the campaign's outcomes, concentrating on the forecasts of the dX, dY, and dψ, dε components of celestial pole offsets (CPO). After detailing the campaign participants and the methodologies employed, we conduct an in-depth analysis of the collected forecasts. We examine the discrepancies between observed and predicted CPO values and analyze their statistical characteristics such as mean, standard deviation, and range. To evaluate CPO forecasts, we computed the mean absolute error (MAE) using the IERS EOP 14 C04 solution as the reference dataset. We then compared the results obtained with forecasts provided by the IERS. The main goal of this study was to show the influence of different methods used on predictions accuracy. Depending on the evaluated prediction approach, the MAE values computed for day 10 of forecast were between 0.03 and 0.16 mas for dX, between 0.03 and 0.12 mas for dY, between 0.07 and 0.91 mas for dψ, and between 0.04 and 0.41 mas for dε. For day 30 of prediction, the corresponding MAE values ranged between 0.03 and 0.12 for dX, and between 0.03 and 0.14 mas for dY. This research shows that machine learning algorithms are the most promising approach in CPO forecasting and provide the highest prediction accuracy (0.06 mas for dX and 0.08 mas for dY for day 10 of prediction). [ABSTRACT FROM AUTHOR]

Predicting Earth Orientation Parameters (EOP) is crucial for precise positioning and navigation both on the Earth’s surface and in space. In recent years, many approaches have been developed to forecast EOP, incorporating observed EOP as well as information on the effective angular momentum (EAM) derived from numerical models of the atmosphere, oceans, and land-surface dynamics. The Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) aimed to comprehensively evaluate EOP forecasts from many international participants and identify the most promising prediction methodologies. This paper presents the validation results of predictions for universal time and length-of-day variations submitted during the 2nd EOP PCC, providing an assessment of their accuracy and reliability. We conduct a detailed evaluation of all valid forecasts using the IERS 14 C04 solution provided by the International Earth Rotation and Reference Systems Service (IERS) as a reference and mean absolute error as the quality measure. Our analysis demonstrates that approaches based on machine learning or the combination of least squares and autoregression, with the use of EAM information as an additional input, provide the highest prediction accuracy for both investigated parameters. Utilizing precise EAM data and forecasts emerges as a pivotal factor in enhancing forecasting accuracy. Although several methods show some potential to outperform the IERS forecasts, the current standard predictions disseminated by IERS are highly reliable and can be fully recommended for operational purposes. [ABSTRACT FROM AUTHOR]

Objectives: Very long baseline interferometry (VLBI) is one of the main space geodetic techniques for monitoring Earth orientation parameters (EOP). China is building three VLBI global observing system (VGOS) antennas. In order to improve the EOP measurement accuracies, it is necessary to optimize VGOS observing network by extending the domestic VGOS network to an international network. Methods: We set three Chinese VGOS stations located at Shanghai, Urumqi and Beijing as core stations, by adding two international stations selected from four candidate sites located at Hobart of Australia or Bandung of Indonesia, as well as Johannesburg of South Africa or Hawaii of USA, we could form four different 5-station VGOS networks. The performance of EOP measurement accuracies for each network were analyzed based on generation of bulk observing schedules and subsequent large-scale Monte Carlo simulations. We used the repeatability value defined as standard deviation of EOP estimates as an indicator to evaluate the performance of each schedule and each network. We also compared the EOP formal errors of current VGOS observing sessions to our simulation results. Results: The experiment results show that:(1) The EOP measurement capability of the expanded 5-station networks are all much better than that of the 3-station domestic network. (2) The optimized 5-station network, which consists of 3 domestic antennas, Johannesburg in South Africa and Hobart in Australia, has the best EOP measurement results. Compared to the 3-station domestic network, the repeatability of dUT1, the pole motion XP and YP components are decreased by a factor of 5.7, 2.8 and 18.3, respectively. (3) The optimized 5-station network could reach equal or even better EOP estimates than that of the current IVS VGOS observing networks. We demonstrated that the EOP measurement accuracies can be improved by optimizing the observing network based on Monte Carlo simulations. Conclusions: The simulation results can be served as a start point for the future development of high-precision EOP observing program in China. [ABSTRACT FROM AUTHOR]

We investigated the suitability of the astronomical 15 GHz Very Long Baseline Array (VLBA) observing program MOJAVE-5 for estimation of geodetic parameters, such as station coordinates and Earth orientation parameters. We processed a concurrent dedicated VLBA geodesy program observed at 2.3 GHz and 8.6 GHz starting on September 2016 through July 2020 as reference dataset. We showed that the baseline length repeatability from MOJAVE-5 experiments is only a factor of 1.5 greater than from the dedicated geodetic dataset and still below 1 ppb. The wrms of the difference of estimated Earth orientation parameters with respect to the reference IERS C04 time series are a factor of 1.3 to 1.8 worse. We isolated three major differences between the datasets in terms of their possible impact on the geodetic results, i.e. the scheduling approach, treatment of the ionospheric delay, and selection of target radio sources. We showed that the major factor causing discrepancies in the estimated geodetic parameters is the different scheduling approach of the datasets. We conclude that systematic errors in MOJAVE-5 dataset are low enough for these data to be used as an excellent testbed for further investigations on the radio source structure effects in geodesy and astrometry. [ABSTRACT FROM AUTHOR]

It has been recognized since the early days of interplanetary spaceflight that accurate navigation requires taking into account changes in the Earth's rotation. In the 1960s, tracking anomalies during the Ranger VII and VIII lunar missions were traced to errors in the Earth orientation parameters. As a result, Earth orientation calibration methods were improved to support the Mariner IV and V planetary missions. Today, accurate Earth orientation parameters are used to track and navigate every interplanetary spaceflight mission. The approach taken at JPL (Jet Propulsion Laboratory) to provide the interplanetary spacecraft tracking and navigation teams with the UT1 and polar motion parameters that they need is based upon the use of a Kalman filter to combine past measurements of these parameters and predict their future evolution. A model was then used to provide the nutation/precession components of the Earth's orientation. As a result, variations caused by the free core nutation were not taken into account. But for the highest accuracy, these variations must be considered. So JPL recently developed an approach based upon the use of a Kalman filter and smoother to provide smoothed and predicted celestial pole offsets (CPOs) to the interplanetary spacecraft tracking and navigation teams. The approach used at JPL to do this and an evaluation of the accuracy of the predicted CPOs is given here. For assessing the quality of JPL's nutation predictions, we compare the time series of dX, dY provided by JPL with the predictions obtained from the IERS Rapid Service/Prediction Centre. Our results confirmed that the approach recently developed by JPL can be used for the successful nutation prediction. In particular, we show that after 90 days of prediction, the estimated errors are 43% lower for dX and 33% lower for dY than in the case of the official IERS products, and an average improvement is 19% and 22% for dX and dY, respectively. [ABSTRACT FROM AUTHOR]

Traditional artificial neural networks (ANN) such as back-propagation neural networks (BPNN) provide good predictions of length-of-day (LOD). However, the determination of network topology is difficult and time consuming. Therefore, we propose a new type of neural network, extreme learning machine (ELM), to improve the efficiency of LOD predictions. Earth orientation parameters (EOP) C04 time-series provides daily values from International Earth Rotation and Reference Systems Service (IERS), which serves as our database. First, the known predictable effects that can be described by functional models—such as the effects of solid earth, ocean tides, or seasonal atmospheric variations—are removed a priori from the C04 time-series. Only the residuals after the subtraction of a priori model from the observed LOD data (i.e., the irregular and quasi-periodic variations) are employed for training and predictions. The predicted LOD is the sum of a prior extrapolation model and the ELM predictions of the residuals. Different input patterns are discussed and compared to optimize the network solution. The prediction results are analyzed and compared with those obtained by other machine learning-based prediction methods, including BPNN, generalization regression neural networks (GRNN), and adaptive network-based fuzzy inference systems (ANFIS). It is shown that while achieving similar prediction accuracy, the developed method uses much less training time than other methods. Furthermore, to conduct a direct comparison with the existing prediction techniques, the mean-absolute-error (MAE) from the proposed method is compared with that from the EOP prediction comparison campaign (EOP PCC). The results indicate that the accuracy of the proposed method is comparable with that of the former techniques. The implementation of the proposed method is simple.

Three combined celestial pole offset (CPO) series computed at the Paris Observatory (C04), the United States Naval Observatory (USNO), and the International VLBI Service for Geodesy and Astrometry (IVS), as well as six free core nutation (FCN) models, were compared from different perspectives, such as stochastic and systematic differences, and FCN amplitude and phase variations. The differences between the C04 and IVS CPO series were mostly stochastic, whereas a low-frequency bias at the level of several tens of $$\upmu $$ as was found between the C04 and USNO CPO series. The stochastic differences between the C04 and USNO series became considerably smaller when computed at the IVS epochs, which can indicate possible problems with the interpolation of the IVS data at the midnight epochs during the computation of the C04 and USNO series. The comparison of the FCN series showed that the series computed with similar window widths of 1.1-1.2 years were close to one another at a level of 10-20 $$\upmu $$ as, whereas the differences between these series and the series computed with a larger window width of 4 and 7 years reached 100 $$\upmu $$ as. The dependence of the FCN model on the underlying CPO series was investigated. The RMS differences between the FCN models derived from the C04, USNO, and IVS CPO series were at a level of approximately 15 $$\upmu $$ as, which was considerably smaller than the differences among the CPO series. The analysis of the differences between the IVS, C04, and USNO CPO series suggested that the IVS series would be preferable for both precession-nutation and FCN-related studies. [ABSTRACT FROM AUTHOR]

This work presents short- and medium-term predictions of length of day (LOD) up to 500 days by means of extreme learning machine (ELM). The EOP C04 time-series with daily values from the International Earth Rotation and Reference Systems Service (IERS) serve as the data basis. The influences of the solid Earth and ocean tides and seasonal atmospheric variations are removed from the C04 series. The residuals are used for training of the ELM. The results of the prediction are compared with those from other prediction methods. The accuracy of the prediction is equal to or even better than that by other approaches. The most striking advantages of employing ELM instead of other algorithms are its noticeably reduced complexity and high computational efficiency. [ABSTRACT FROM AUTHOR]

UT1 estimates obtained from the very long baseline interferometry (VLBI) Intensives data depend on the station displacement model used during processing. In particular, because of seasonal variations, the instantaneous station position during the specific intensive session differs from the position predicted by the linear model generally used. This can cause systematic errors in UT1 Intensives results. In this paper, we first investigated the seasonal signal in the station displacements for the 5 VLBI antennas participating in UT1 Intensives observing programs, along with the 8 collocated GPS stations. It was found that a significant annual term is present in the time series for most stations, and its amplitude can reach 8 mm in the height component, and 2 mm in horizontal components. However, the annual signals found in the displacements of the collocated VLBI and GPS stations at some sites differ substantially in amplitude and phase. The semiannual harmonics are relatively small and unstable, and for most stations no prevailing signal was found in the corresponding frequency band. Then two UT1 Intensives series were computed with and without including the seasonal term found in the previous step in the station movement model. Comparison of these series has shown that neglecting the seasonal station position variations can cause a systematic error in UT1 estimates, which can exceed 1 $$\upmu $$s, depending on the observing program. [ABSTRACT FROM AUTHOR]

Very Long Baseline Interferometry (VLBI) Intensive sessions are scheduled to provide operational Universal Time (UT1) determinations with low latency. UT1 estimates obtained from these observations heavily depend on the model of the celestial pole motion used during data processing. However, even the most accurate precession- nutation model, IAU 2000/2006, is not accurate enough to realize the full potential of VLBI observations. To achieve the highest possible accuracy in UT1 estimates, a celestial pole offset (CPO), which is the difference between the actual and modelled precession-nutation angles, should be applied. Three CPO models are currently available for users. In this paper, these models have been tested and the differences between UT1 estimates obtained with those models are investigated. It has been shown that neglecting CPO modelling during VLBI UT1 Intensive processing causes systematic errors in UT1 series of up to 20 μas. It has been also found that using different CPO models causes the differences in UT1 estimates reaching 10 μas. Obtained results are applicable to the satellite data processing as well. [ABSTRACT FROM AUTHOR]