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Abstract

Analysis centers (ACs) for global navigation satellite systems (GNSSs) cannot accurately obtain real-time Earth rotation parameters (ERPs). Thus, the prediction of ultra-rapid orbits in the international terrestrial reference system (ITRS) has to utilize the predicted ERPs issued by the International Earth Rotation and Reference Systems Service (IERS) or the International GNSS Service (IGS). In this study, the accuracy of ERPs predicted by IERS and IGS is analyzed. The error of the ERPs predicted for one day can reach 0.15. mas and 0.053. ms in polar motion and UT1-UTC direction, respectively. Then, the impact of ERP errors on ultra-rapid orbit prediction by GNSS is studied. The methods for orbit integration and frame transformation in orbit prediction with introduced ERP errors dominate the accuracy of the predicted orbit. Experimental results show that the transformation from the geocentric celestial references system (GCRS) to ITRS exerts the strongest effect on the accuracy of the predicted ultra-rapid orbit. To obtain the most accurate predicted ultra-rapid orbit, a corresponding real-time orbit correction method is developed. First, orbits without ERP-related errors are predicted on the basis of ITRS observed part of ultra-rapid orbit for use as reference. Then, the corresponding predicted orbit is transformed from GCRS to ITRS to adjust for the predicted ERPs. Finally, the corrected ERPs with error slopes are re-introduced to correct the predicted orbit in ITRS. To validate the proposed method, three experimental schemes are designed: function extrapolation, simulation experiments, and experiments with predicted ultra-rapid orbits and international GNSS Monitoring and Assessment System (iGMAS) products. Experimental results show that using the proposed correction method with IERS products considerably improved the accuracy of ultra-rapid orbit prediction (except the geosynchronous BeiDou orbits). The accuracy of orbit prediction is enhanced by at least 50% (error related to ERP) when a highly accurate observed orbit is used with the correction method. For iGMAS-predicted orbits, the accuracy improvement ranges from 8.5% for the inclined BeiDou orbits to 17.99% for the GPS orbits. This demonstrates that the correction method proposed by this study can optimize the ultra-rapid orbit prediction.

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... However, the three-dimensional root-mean-square errors (3D RMS) of GPS ultra-rapid predicted orbits within the 6-and 24-h periods may be up to 41.7 mm and 80.2 mm, respectively (IGS mail 6053), which lags behind the final precise orbit of the International GNSS Service (IGS) and does not meet with the high-precision requirements of GNSS users. Because the accuracy of ultra-rapid orbits is low, orbit prediction strategies [4], optimal Sensors 2018, 18, 3900 2 of 17 prediction arcs [5], prediction time intervals [6], and the impact of Earth rotation parameters [7] were investigated by scholars to refine the orbit models and strategies. However, the research on ultra-rapid orbits is concerned mainly with the predicted values, whereas for the observed values, little has been done in detail. ...
... Because the results are similar to the 409 stations, the scheme with 200 stations was ignored in Figure 3. Moreover, to develop the relationship between the station numbers, DOP values, and orbit accuracy, the correlation factors between the DOP values and the orbit accuracy are given in Table 4 based on the method proposed in [7,11]. However, note that there is an exponential dependence between the number of stations and the DOP values in the orbit determination [10], which is not discussed in this study. ...
... 200 stations was ignored in Figure 3. Moreover, to develop the relationship between the station numbers, DOP values, and orbit accuracy, the correlation factors between the DOP values and the orbit accuracy are given in Table 4 based on the method proposed in [7,11]. However, note that there is an exponential dependence between the number of stations and the DOP values in the orbit determination [10], which is not discussed in this study. ...
Article
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For ultra-rapid orbits provided by the Global Navigation Satellite System (GNSS), the key parameters, accuracy and timeliness, must be taken into consideration in real-time and near real-time applications. However, insufficient observations in later epochs appear to generate low accuracy in observed orbits, for which a correlation between the Dilution of Precision (DOP) of the orbit parameters and their accuracy is found. To correct the observed GNSS ultra-rapid orbit, a correction method based on the DOP values is proposed by building the function models between DOP values and the orbit accuracy. With 10-day orbit determination experiments, the results show that the observed ultra-rapid-orbit errors, generated by insufficient observations, can be corrected by 12–22% for the last three hours of the observed orbits. Moreover, considering the timeliness constraints in ultra-rapid-orbit determination, a DOP amplification factor is defined to weight the contribution of each tracking station and optimize the station distribution in the orbit determination procedure. Finally, six schemes are designed to verify the method and strategy in determining the ultra-rapid orbit based on one-month observations. The orbit accuracy is found to decrease by 1.27–6.34 cm with increasing amplification factor from 5–20%. Thus, the observed ultra-orbit correction method proposed is ideal when considering accuracy and timeliness in ultra-rapid orbit determination.
... Ultra-rapid UT1-UTC is currently one of the main factors affecting the performance of GNSS satellite ultra-rapid orbit determination [10]. Compared with the present performance, the existing error in ultra-rapid UT1-UTC has a significant impact on ultrarapid orbit determination [6,[11][12][13]. Therefore, further improvement in the processing strategy of ultra-rapid UT1-UTC determination will significantly improve the performance of spatial datum expressed by GNSS satellite ultra-rapid orbit. ...
... At present, in ultra-rapid orbit determination, a piecewise linear function is generally used to process the consecutive single types of UT1-UTC observation data, e.g., Bulletin A, for several days provided by IERS to obtain the ultra-rapid UT1-UTC. However, Wang et al. [13] has shown that the correlation coefficients for the interpolated UT1-UTC of true values and fitting values are gradually reduced when the time resolution of UT1-UTC is increased, and using only the consecutive single type of UT1-UTC observation data over several days to determine ultra-rapid UT1-UTC may also need to be further analyzed and discussed. On the other hand, there is systematic bias in GNSS-based length-of-day (LOD) with respect to the values of EOP (Earth orientation parameter) 14 CO4 of IERS, and it is possible to improve the effect of this systematic bias and provide a more reliable initial value for ultra-rapid LOD derived from ultra-rapid UT1-UTC [26]. ...
Article
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Errors in ultra-rapid UT1-UTC primarily affect the overall rotation of spatial datum expressed by GNSS (Global Navigation Satellite System) satellite ultra-rapid orbit. In terms of existing errors of traditional strategy, e.g., piecewise linear functions, for ultra-rapid UT1-UTC determination, and the requirement to improve the accuracy and consistency of ultra-rapid UT1-UTC, the potential to improve the performance of ultra-rapid UT1-UTC determination based on an LS (Least Square) + AR (Autoregressive) combination model is explored. In this contribution, based on the LS+AR combination model and by making joint post-processing/rapid UT1-UTC observation data, we propose a new strategy for ultra-rapid UT1-UTC determination. The performance of the new strategy is subsequently evaluated using data provided by IGS (International GNSS Services), iGMAS (international GNSS Monitoring and Assessment System), and IERS (International Earth Rotation and Reference Systems Service). Compared to the traditional strategy, the numerical results over more than 1 month show that the new strategy improved ultra-rapid UT1-UTC determination by 29-43%. The new strategy can provide a reference for GNSS data processing to improve the performance of ultra-rapid products.
... The rotational variations of the solid Earth, relative to the international celestial reference frame (ICRF) and the international terrestrial reference frame (ITRF), are defined by five Earth Orientation Parameters (EOPs), namely nutation, polar motion (PM) and changes in universal time ΔUT1, which can be accurately measured by advanced geodetic observation (e.g., Petit and Luzum 2010;Ratcliff and Gross 2010;Gross 2015;Ray 2016;Ray et al. 2017) and routinely released by the International Earth Rotation and Reference System Service (IERS) (Bizouard et al. 2019). While real-time EOPs are not available mainly due to delays in collecting and processing global data sets, they are of great significance for a number of practical applications, such as precise positioning, satellite navigation and satellite orbit determination (e.g., Ray et al. 2017;Wang et al. 2017). Therefore, accurate and efficient forecast of EOPs is urgently needed but a challenging task since PM, part of EOPs, contains not only the components excited by quasi-periodic mass redistributions and relative motions within the Earth system (Lambeck 1980;Jochmann 2009;Chen et al. 2013a, b;Gross 2015;Bizouard, 2020;Harker et al. 2021) but also the freely damping Chandler Wobble (CW) (Gross 2000(Gross , 2015Schuh et al. 2001;Wang et al. 2016). ...
Article
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By taking into account the variable free polar motion (PM) known as the Chandler wobble (CW) and irregular forced PM excited by quasi-periodic changes in atmosphere, oceans and land water (described by the data of effective angular momenta EAM), we propose a short-term PM forecast method based on the Holt-Winters (HW) additive algorithm (termed as the HW-VCW method, with VCW denoting variable CW). In this method, the variable CW period is determined by minimizing the differences between PM observations and EAM-derived PM for every 8-year sliding timespan. Compared to the X- and Y-pole forecast errors (ΔPMX and ΔPMY) of the International Earth Rotation and Reference Systems Service (IERS) Bulletin A, our results derived from operational EAM can reduce ΔPMX by up to 38.4% and ΔPMY by up to 34.3% for forecasts ranging from 1 to 30 days. Further, we prove that using EAM forecast instead of operational EAM in the HW-VCW method can achieve similar accuracies.
... In the study by Goh et al. (2016), a preprocessed orbit parameter method has been proposed to minimize the orbit propagation and attitude determination errors. In the study by Wang et al. (2017), a corresponding realtime orbit correction method has been used to reduce the impact of earth rotation parameters on GNSS ultrarapid orbit prediction, which can improve the accuracy of ultra-rapid orbit prediction at least by 50%. Sang et al. (2017) have presented a two-step TLE-based method in which the numerical orbits are first fitted into a TLE set, and then correction functions are applied to improve the position accuracy considering the accuracy, computing efficiency, and memory. ...
Article
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High-accuracy orbit prediction plays a crucial role in several aerospace applications, such as satellite navigation, orbital maneuver, space situational awareness , etc. The conventional methods of orbit prediction are usually based on dynamic models with clear mathematical expressions. However, coefficients of perturbation forces and relevant features of satellites are approximate values, which induces errors during the process of orbit prediction. In this study, a new orbit prediction model based on principal component analysis (PCA) and extreme gradient boosting (XGBoost) model is proposed to improve the accuracy of orbit prediction by learning from the historical data in a simulated environment. First, a series of experiments are conducted to determine the approximate numbers of features, which are used in the following machine learning (ML) process. Then, PCA and XGBoost models are used to find incremental corrections to orbit prediction with dynamic models. The results reveal that the designed framework based on PCA and XGBoost models can effectively improve the orbit prediction accuracy in most cases. More importantly, the proposed model has excellent generalization capability for different satellites, which means that a model learned from one satellite can be used on another new satellite without learning from the historical data of the target satellite. Overall, it has been proved that the proposed ML model can be a supplement to dynamic models for improving the orbit prediction accuracy.
... In addition, due to the uneven variation of the Earth's rotation, the prediction errors associated with the EOPs that will indirectly affect certain practical applications. (Gambis and Luzum 2011;Wang et al. 2017). Therefore, research on the prediction of EOPs has significant theoretical and practical value. ...
Article
Conventional polar motion (PM) parameter modelling and forecasting research is directly based on observation data for PM parameters. For any given PM, its periodic characteristics are basically the same since it is affected by the same excitation source. However, the time-varying patterns of PM in different coordinates or with different parameterizations are generally different. Therefore, it is possible for one parameterization to show better regularity than another. Notably, for the first time, daily polar displacement and the angle of polar displacement with respect to the X axis of the terrestrial frame display better regularity than the observed polar motion value. Therefore, improved accuracy could be expected in modelling and forecasting using the above two parameters. Different approach was tested to verify the effectiveness and the superiority of the proposed method based on multiple sets of PM prediction experiments with the data of IERS 14 C04 series which spanned from 1 January 2018 to 26 September 2020. Compared with typical conventional approach, the maximum prediction accuracy of the proposed method in the PMX direction and the PMY direction is increased by 59.9% and 63.2%, respectively, and the corresponding 1-500-day forecasting accuracies are improved by 25.1% and 36.4%, respectively, on average.
... Thus, the parameters are usually provided after a delay of hours to days and cannot meet the real-time demands of satellite navigation and positioning and spacecraft tracking (Jayles et al. 2016). The level of precision of EOP forecasting directly affects the analytical accuracy of scientific applications, such as space tracking measurements and precision orbit determination (Gambis and Luzum 2011;Wang et al. 2017). Therefore, it is necessary to obtain high-precision polar motion parameters prediction products. ...
Article
The Least-squares extrapolation of harmonic models and autoregressive (LS + AR) prediction is currently considered to be one of the best prediction model for polar motion parameters. In this method, LS fitting residuals are treated as data to train an AR model. But it is readily known that using too many data will result in learning a badly relevant AR model, implying increasing the model bias. It can also be possible that using too few data will result in a lower estimation accuracy of the AR model, implying increasing the model variance. So selecting data is a critical issue to compromise between bias and variance, and hence to obtain a model with optimized prediction performance. In this paper, an experimental study is conducted to check the effect of different data volume on the final prediction performance and hence to select an optimal data portion for AR model. The earth orientation parameters products released by the International Earth Rotation and Reference Systems Service were used as primary data to predict changes in polar motion parameters over spans of 1–500 days for 800 experiments. The experimental results showed that although the short term prediction were not ameliorated, but the method that the AR model parameters calculated by appropriate data volume can effectively improve the accuracy of long-term prediction of polar motion.
... Orbit prediction strategies [33], optimal arcs prediction [34], predicted time intervals [35], and the impact of Earth rotation parameters [36] have been investigated by scholars for the refinement of the orbit models and strategies due to the low accuracy of the predicted ultra-rapid orbits. The accuracy of the BDS-2/BDS-3 ultra-rapid orbit for both the observed and predicted components cannot meet the requirements of a BDS third phase system specification (observed orbit/clock offset <5 cm/0.2 ns; predicted orbit/clock offsets <10 cm/5 ns). ...
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Chapter
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Based on the theory of variation equation, precise low satellite orbit and Earth gravity field model can be determined by using numerical integration technology. Feasibilities and requirements of the algorithm are analyzed by numerical evaluation. Using CHAMP real orbit data, some calculations were performed for studying the influence of initial orbit vectors precise, the force model, and force model parameters errors. The results show that the error of initial orbit vectors and force model parameters are the critical factors and have a great influence on satellite orbit shapes, especially numerical integration is highly sensitivity to initial orbit vector errors.
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A Kalman filter has been developed at JPL to smooth and predict Earth orientation changes for application to spacecraft navigation by the NASA Deep Space Network. The filter, which provides estimates of the Earth orientation changes (and of the excitation of these changes) based on whatever measurements are available, has been used for a number of research applications, both in the reduction of geodetic and astrometric data, and in research into the geophysical causes of Earth orientation changes. The derivation of the stochastic models used by the filter, the implementation of the models into the filter, a statistical description of what the filter does, and the results of filtering specific data sets are discussed.
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The hydrological contribution to polar motion is a major challenge in explaining the observed geodetic residual of non-atmospheric and non-oceanic excitations since hydrological models have limited input of comprehensive global direct observations. Although global terrestrial water storage (TWS) estimated from the Gravity Recovery and Climate Experiment (GRACE) provides a new opportunity to study the hydrological excitation of polar motion, the GRACE gridded data are subject to the post-processing de-striping algorithm, spatial gridded mapping and filter smoothing effects as well as aliasing errors. In this paper, the hydrological contributions to polar motion are investigated and evaluated at seasonal and intra-seasonal time scales using the recovered degree-2 harmonic coefficients from all GRACE spherical harmonic coefficients and hydrological models data with the same filter smoothing and recovering methods, including the Global Land Data Assimilation Systems (GLDAS) model, Climate Prediction Center (CPC) model, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis products and European Center for Medium-Range Weather Forecasts (ECMWF) operational model (opECMWF). It is shown that GRACE is better in explaining the geodetic residual of non-atmospheric and non-oceanic polar motion excitations at the annual period, while the models give worse estimates with a larger phase shift or amplitude bias. At the semi-annual period, the GRACE estimates are also generally closer to the geodetic residual, but with some biases in phase or amplitude due mainly to some aliasing errors at near semi-annual period from geophysical models. For periods less than 1-year, the hydrological models and GRACE are generally worse in explaining the intraseasonal polar motion excitations.
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The method for predicting x, y, and UT1-UTC as conceived and implemented by the Subbureau for Rapid Service and Prediction of the International Earth Rotation Service (IERS) is shown. For polar motion, the method is an extrapolation of an annual ellipse and Chandler circle. The method for UT1-UTC involves a simple differencing technique.
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Refined analytical expressions for the frequencies corresponding to the Chandler motion of the pole and the diurnal rotation of the deformable Earth are derived. Numerical estimates of the period and amplitude of the polar oscillations are presented. The trajectory of the Chandler polar motion derived via numerical modeling is in qualitative and quantitative agreement with experimental data from the International Earth Rotation Service (IERS). An evolutionary model describing slow variations in the Earth’s rotation parameters under the action of the dissipative moments of the tidal gravitational forces on time scales considerably longer than the precession period of the Earth’s axis is constructed. The axis of the Earth’s figure tends to approach the angular momentum vector of the proper rotation.
Impact of Extrapolating Orbit and Reference Frame Transformation on Precision Orbit Determination of Navigation Satellite Master Thesis
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Liu, W., 2009. Impact of Extrapolating Orbit and Reference Frame Transformation on Precision Orbit Determination of Navigation Satellite Master Thesis. Nation University of defense technology, Changsha, China.
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Earth rotation parameter estimation from GNSS and its impact on aircraft orbit determination
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Wan, L., Wei, E., Jin, S., 2014. Earth rotation parameter estimation from GNSS and its impact on aircraft orbit determination. Astron. Geodyn. Res. Center 303, 105-114.
Analysis of influence of EOP prediction error on autonomous orbit determination
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Zhang W., Liu W., Gong X., 2011. Analysis of influence of EOP prediction error on autonomous orbit determination [J]. Journal of Geodesy and Geodynamics, 31(6): 17-22.
Impact of extrapolating orbit and reference frame transformation on precision orbit determination of navigation satellite
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Liu W., 2009. Impact of extrapolating orbit and reference frame transformation on precision orbit determination of navigation satellite [M]. Master Thesis, Nation University of defense technology, Changsha, China.