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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. ...

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]. ...

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). ...

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. ...

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. ...

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. ...

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). ...

The accuracy of ultra-rapid orbits is a key parameter for the performance of GNSS (Global Navigation Satellite System) real-time or near real-time precise positioning applications. The quality of the current BeiDou demonstration system (BDS) ultra-rapid orbits is lower than that of GPS, especially for the new generational BDS-3 satellites due to the fact that the availability of the number of ground tracking stations is limited, the geographic distribution of these stations is poor, and the data processing strategies adopted are not optimal. In this study, improved data processing strategies for the generation of ultra-rapid orbits of BDS-2/BDS-3 satellites are investigated. This includes both observed and predicted parts of the orbit. First, the predicted clock offsets are taken as constraints in the estimation process to reduce the number of the unknown parameters and improve the accuracy of the parameter estimates of the orbit. To obtain more accurate predicted clock offsets for the BDS’ orbit determination, a denoising method (also called the Tikhonov regularization algorithm), inter-satellite correlation, and the partial least squares method are all incorporated into the clock offsets prediction model. Then, the Akaike information criterion (AIC) is used to determine the arc length in the estimation models by taking the optimal arc length in the estimation of the initial orbit states into consideration. Finally, a number of experiments were conducted to evaluate the performance of the ultra-rapid orbits resulting from the proposed methods. Results showed that: (1) Compared with traditional models, the accuracy improvement of the predicted clock offsets from the proposed methods were 40.5% and 26.1% for BDS-2 and BDS-3, respectively; (2) the observed part of the orbits can be improved 9.2% and 5.0% for BDS-2 and BDS-3, respectively, by using the predicted clock offsets as constraints; (3) the accuracy of the predicted part of the orbits showed a high correlation with the AIC value, and the accuracy of the predicted orbits could be improved up to 82.2%. These results suggest that the approaches proposed in this study can significantly enhance the accuracy of the ultra-rapid orbits of BDS-2/BDS-3 satellites.

Passive resonant gyroscopes (PRG) utilizing the Pound-Drever-Hall (PDH) method are expected to have a lower shot-noise limit in rotational rate measurement. However, there are also many technical obstacles in the way to touch the intrinsic noise ﬂoor. In this article, we ﬁnd that the residual amplitude modulation (RAM) eﬀect accrued in the phase locking process deteriorates the accuracy and stability of the output signal of PRGs, and becomes a dominant limiting factor, especially in the low-frequency range. Since the suppression is not good enough in the PRGs due to the strict requirements, we propose to use the Pearson correlation coeﬃcient (PCC) to evaluate the correlation between the RAM signal and the PDH signal to achieve a suﬃcient correlation before active servo control. With the implementation of this improvement, the RAM-induced relative frequency stability for the 12-m optical ring cavity is reduced down to 1.2 × 10^-18. The contribution of the RAM eﬀect to the rotational sensitivity of our 3 m × 3 m PRG is lowered to 8.0 × 10^-9 rad/s/√Hz at 1 mHz, which is one order of magnitude better than the unconstrained situation. With this upgrade, a rotational resolution of 5.2 × 10^-10 rad/s of the PRG is achieved, which is the best performance among all PRGs so far.

This paper proposes a one-step forecasting method based on the LS+AR prediction model that calculates LS and AR model parameters simultaneously. The EOPs products released by the IERS were used as primary data to predict changes in LOD parameters over spans of 1–500 days for 1230 experiments. The experimental results showed that the proposed method has an obvious improvement in long-term LOD parameters prediction accuracy compared with the LS+AR mode. However, limited by the large matrix in the calculation process, the computational efficiency of the proposed method needs to be further improved.

Large-scale high sensitivity laser gyroscopes have important applications for ground-based and space-based gravitational wave detection. We report on the development of a 3 m × 3 m heterolithic passive resonant gyroscope (HUST-1) which is installed on the ground of a cave laboratory. We operate the HUST-1 on different longitudinal cavity modes and the rotation sensitivity reaches 1.6 × 10⁻⁹ rad s⁻¹ Hz−1/2 above 1 Hz. The drift of the cavity length is one of the major sensitivity limits for our gyroscope in the low frequency regime. By locking cavity length to an ultra-stable reference laser, we achieve a cavity length stability of 5.6 × 10⁻⁹ m Hz−1/2 at 0.1 mHz, a four orders of magnitude improvement over the unconstrained cavity in the low frequency regime. We stabilize the cavity length of a large-scale heterolithic passive resonant gyroscope through active feedback and realize long-term operation. The rotation sensitivity reaches 1.7 × 10⁻⁷ rad s⁻¹ Hz−1/2 at 0.1 mHz, a three orders of magnitude improvement over the unconstrained cavity, which is no longer limited by the cavity length drift in this frequency range.

February 1, 2017, EOP 14C04 aligned to the ITRF2014 was adopted by IERS. To assess the improvement of EOP 14C04, the differences between EOP 14C04 and EOP 08C04 are firstly analyzed. Then, the causes of the differences between the two solutions are examined. Finally, the differences are further assessed for their prediction performance using the LS+AR model. The results demonstrate that (1) there is a trend in the difference between the two solutions; (2) the cause of the above-mentioned difference should be attributed to the different reference frames; (3) the new EOP 14C04 shows better performance for high-frequency signals.

Earth Rotation Parameter (ERP) is one of the most important parameters in the area of positioning and navigation, autonomous orbit determination and Earth reference framework. However, due to the restriction of timeliness of data processing, the predicted ERPs are taken into the relevant applications to meet the requirements of real-time or near real-time users. Therefore, given the disadvantages of short-term prediction models for ERPs, such as model mismatch, over parametrization and divergence with time, this study proposed a method for improving the short-term prediction model for ERP based on long-term observations. Firstly, the optimal length of observations was analyzed for the Least Square (LS) prediction model based on the Akaike Information Criterion (AIC). It is found that one year of ERP observations is the optimal data sets to establish the prediction model. Then, two constraints models based on LS, called (Constraint LS) CLS and (Enhanced CLS) ECLS, were discussed to decrease the errors in prediction models, which takes the correlation factors and residuals of prediction model into consideration. The results indicated that the prediction errors of ERP can be significantly decreased for short-term prediction, which improved the accuracy of ERP prediction with 50% for polar motions (PM), and 20% for UT1-UTC. Moreover, considering the divergence of predicted ERP along with the increasing of time and separate prediction of each parameters in ERP of Auto Regressive model (AR), a Multivariable Regression model (MAR) was introduced to correct the residuals of predicted ERP, which combined the PM, and UT1-UTC with LOD into prediction models. And the accuracy of predicted ERP can be improved at least 20% compared with AR model. Finally, according to data experiments, the improved short-term prediction model was analyzed based on different observations. It is suggested that our method can improve the short-term prediction in cases that long-term ERP observations are available.

Between 2015 and 2016, the BeiDou satellite navigation system (BDS) successfully launched 5 BeiDou global navigation satellite system experimental (BDS-3e) satellites. The number of available BDS satellites has increased. In this study, in order to analyze the impact of BDS-3e satellites on the current BDS, which is the BeiDou regional navigation satellite system (BDS-2), the number of visible satellites globally was used to analyze the influence of BDS-3e satellites on the service area of BDS. Then, based on the observations from May 3 to 11, 2017, the strategy of combined data processing of BDS-2 satellites and BDS-3e satellites is presented. Simultaneously, the orbits and clocks of BDS-2 satellites and BDS-3e satellites are calculated and their accuracy is analyzed. At last, based on the obtained orbits and clocks, the influence of BDS-3e satellites on the BDS precise positioning is initially analyzed. The results show that BDS-3e satellites can increase the number of visible satellites of BDS by 1 to 3 globally, thus increasing the service area of BDS. The accuracy of orbits and clocks of BDS-2 satellites and BDS-3e satellites determined by B1I and B3I signals satisfy the requirement of precise positioning. Furthermore, the participation of BDS-3e satellites improve the position dilution of precision (PDOP) value of positioning. The accuracy of precise point positioning (PPP) in the vertical component is significantly improved for tracking station in the low latitudes of the eastern hemisphere. According to multi-day statistics of a single tracking station, the accuracy of the static solution and the kinematic solution is improved by 64.7% and 25.6%, respectively. Moreover, the BDS-3e satellites significantly improve the accuracy of real-time kinematic (RTK) positioning for a medium baseline of 10 km. The E, N, and U components are improved by 5.6%, 14.3% and 7.7%, respectively.

With the rapid increase in the numbers of new generation Global Navigation Satellite Systems (GNSS) satellites, signal frequencies and ground tracking stations, the burden on data processing increases significantly, especially for those real-time or near real-time applications, e.g. generating ultra-rapid satellite orbit and Earth rotation parameters (ERP) products. In order to reduce the number of observations used to estimate the orbit and ERP unknown parameters for better computational efficiency, this study first introduced a parameter called orbit and ERP dilution of precision (OEDOP) factor and a method in "optimally" selecting multi-GNSS tracking stations based on the OEDOP factor is investigated to minimize the data processing burden without significantly sacrificing the accuracy and precision of the satellite orbit and ERP determination. The trade-off between computational efficiency and quality of results is primary focus of this research. The contribution of each tracking station to the precision of the parameter estimates is investigated first, according to the location and multi-GNSS data measurement capacity of the station as well as the length of observations, then those stations that contribute least will be identified and excluded in the estimation system. It aims to use as a fewer number of tracking stations as possible but the degradation in the precision of the solution is still under a desired level. The method was tested using GNSS observations from 409 International GNSS service (IGS) stations over a one-month period. Results showed that when the "degradation" factor of the precision of satellite orbit and ERPs solutions is 5%, 10%, 15% and 20% the accuracy of the satellites orbit and polar motion parameters estimated from an optimal minimum number of stations (in comparison with the results from all stations) reduced about 0.33-9.92 cm and 5.77-41.53 μas respectively, and the accuracy of UT1-UTC reduced 10.63-15.50 μs; while their computational speed was improved by 196%, 332%, 527% and 617% respectively. This suggests that our method is a good trade-off method and an ideal option in cases that rapid solutions are required, e.g. ultra-rapid determination of orbit and ERP using multi-GNSS measurements from global ground tracking stations.

Earth rotation parameters (ERP) play a key role in connecting the International Celestial Reference Frame (ICRF) and the International Terrestrial Reference Frame (ITRF). Furthermore, high precision orbit determination and positioning need the precise ERPs, while ERPs are closely related the geophysical fliud mass redistribution and geodynamics. In this paper, global uniformly distributed 75 IGS stations with more than 60 sites tracking GPS+GLONASS simultaneously are selected to estimate Earth Rotation Parameters. Accuracy and method to improve ERP from only IGS stations in and neighboring China are also analyzed in order to provide the reference for BeiDou ERP estimation. The results show that the precision of Polar motion (PM) estimated from daily GPS and GLONASS observations can be achieve at the precision of 0.066 and 0.157 mas, respectively and the precision of length of day (LOD) can achieve at 0.0283 and 0.0289 ms when compared to IERS C04 solutions, respectively. The precision of PM and LOD from regional stations with daily GPS (GLONASS) observations are better than 0.178 mas (0.365 mas) and 0.0291 ms (0.0360 ms), respectively. The precision of PM and LOD from combined GPS+GLONASS are better than 0.153 mas and 0.0292 ms. In addition, the impact of ERP error on aircraft orbit is furthermore discussed. The impact on the LOD is greater than the PM. The orbital error can respectively reach 1, 1 and 0.1 m in X, Y and Z direction with 0.5 mas error in PM and 0.5 ms error in LOD.

The Earth's rotation undergoes changes with the influence of geophysical factors, such as Earth's surface fluid mass redistribution of the atmosphere, ocean and hydrology. However, variations of Earth Rotation Parameters (ERP) are still not well understood, particularly the short-period variations (e.g., diurnal and semi-diurnal variations) and their causes. In this paper, the hourly time series of Earth Rotation Parameters are estimated using Global Positioning System (GPS), Global Navigation Satellite System (GLONASS), and combining GPS and GLONASS data collected from nearly 80 sites from 1 November 2012 to 10 April 2014. These new observations with combining different satellite systems can help to decorrelate orbit biases and ERP, which improve estimation of ERP. The high frequency variations of ERP are analyzed using a de-trending method. The maximum of total diurnal and semidiurnal variations are within one milli-arcseconds (mas) in Polar Motion (PM) and 0.5 milli-seconds (ms) in UT1-UTC. The semidiurnal and diurnal variations are mainly related to the ocean tides. Furthermore, the impacts of satellite orbit and time interval used to determinate ERP on the amplitudes of tidal terms are analyzed. We obtain some small terms that are not described in the ocean tide model of the IERS Conventions 2010, which may be caused by the strategies and models we used or the signal noises as well as artifacts. In addition, there are also small differences on the amplitudes between our results and IERS convention. This might be a result of other geophysical excitations, such as the high-frequency variations in atmospheric angular momentum (AAM) and hydrological angular momentum (HAM), which needs more detailed analysis with more geophysical data in the future.

Real-time precise orbit and clock products are crucial for real-time high-precision precise point positioning (PPP). The key for precise orbit prediction is to precisely determine the initial conditions (satellite position, velocity at the initial epoch) and the solar radiation pressure (SRP) parameters using an arc of known precise orbits. The optimal arc length will be investigated for precise orbit prediction, with which the high-accuracy satellite clocks can be estimated. The orbit prediction accuracies with different arc lengths and conditions over time are also investigated. The results indicate that the predicted orbit accuracy is governed by the SRP parameters. In addition, the predicted orbits and estimated clocks are evaluated quantitatively with respect to PPP solutions during in and out of eclipses seasons, based on which the optimal arc length is identified. The numerical results show that high-accuracy orbital prediction can be achieved using an arc length between 36 and 48 h and generally an arc length of 42 h is considered to be optimal. With this optimal arc length, the estimated clock accuracy is 0.048 and 0.122 ns for a prediction interval of 6 and 24 h, respectively. The average PPP ambiguity fix-rates with a prediction interval of 6 h are 80.2 and 84.7 % over an observation period of 30 min and 1 h, respectively.

The International Earth Rotation and Reference Systems Service (IERS) was established by the IAU and the IUGG in 1987. A short outline of its history, its services to the astronomical, geodetic and geophysical communities and of its future prospects is given. Special emphasis is made on IERS' relation to astronomy.

Terrestrial water storage (TWS) and ocean bottom pressure (OBP) are major contributors to the observed polar motion excitations, second only to atmospheric mass movement. However, quantitative assessment of the hydrological and oceanic effects on polar motion remains unclear because of the lack of global observations. In this paper, hydrological and oceanic mass excitations to polar motion are investigated using monthly TWS and OBP derived from the Gravity Recovery and Climate Experiment (GRACE) for January 2003 until December 2008. The results from this analysis are compared with hydrological model excitations from the European Center for Medium-Range Weather Forecasts (ECMWF) and oceanic model excitations obtained from the Jet Propulsion Laboratory (JPL) using Estimating the Circulation and Climate of the Ocean (ECCO). Results show that the GRACE-derived OBP and TWS better explain the geodetic residual polar motion excitations for the Px component at the annual period, while the GRACE OBP and ECMWF hydrological angular momentum agree better with the geodetic residuals for the annual Py excitation. GRACE ocean and hydrology excitations better explain the geodetic residuals for the semiannual Py excitation. However, the JPL ECCO and ECMWF models better explain the intraseasonal geodetic residual of polar motion excitation in the Px and Py components. The GRACE data demonstrate much higher intraseasonal variability than either the models or the geodetic observations.

The Earth orientation parameters (EOP) are determined by space geodetic techniques with very high accuracy. However, the accuracy of their prediction, even for a few days in the future, is several times lower and still unsatisfactory for practical use. The main problem of each prediction technique is to predict simultaneously long and short period oscillations of the EOP. It has been shown that the combination of the prediction methods which are different for deterministic and stochastic components of the EOP can provide the best accuracy of prediction. Several prediction techniques, e.g. combination of the least-squares with autoregressive and autocovariance methods as well as combination of wavelet transform decomposition and autocovariance prediction, were used to predict x, y pole coordinates in polar coordinate system and U T 1 − U T C or length of day (∆) data. Different prediction algorithms were compared considering the difference between the EOP data and their predictions at different starting prediction epochs as well as by comparing the mean EOP prediction errors.

P>The change in the rate of the Earth's rotation, length-of-day (LOD), is principally the result of movement and redistribution of mass in the Earth's atmosphere, oceans and hydrosphere. Numerous studies on the LOD excitations have been made from climatological/hydrological assimilation systems and models of the general circulation of the ocean. However, quantitative assessment and understanding of the contributions to the LOD remain unclear due mainly to the lack of direct global observations. In this paper, the total Earth's surface fluids mass excitations to the LOD at seasonal and intraseasonal timescales are investigated from the Jet Propulsion Laboratory Estimating Circulation and Climate of the Ocean (ECCO) model, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis and the European Center for Medium-Range Weather Forecasts (ECMWF) Re-analysis (ERA)-Interim, GRACE-derived surface fluids mass and the spherical harmonics coefficient C-20 from the satellite laser ranging (SLR) as well as combined GRACE+SLR solutions, respectively. Results show that the GRACE and the combined GRACE and SLR solutions better explain the geodetic residual LOD excitations at annual and semi-annual timescales. For less than 1 yr timescales, GRACE-derived mass is worse to explain the geodetic residuals, whereas SLR agrees better with the geodetic residuals. However, the combined GRACE and SLR results are much improved in explaining the geodetic residual excitations at intraseasonal scales.

Tidally induced sub-daily Earth Rotation Parameters (ERP) variations, when not properly accounted for, can cause apparent orbit and ERP rate errors, which can significantly exceed the IGS solution errors. All International GPS Service (IGS) Analysis Centers currently apply the conventional sub-daily ERP model in their transformations from ITRF (International Terrestrial Reference Frame) to ICRF (International Celestial Reference Frame), both of which are used for IGS global analyses. However, some IGS Analysis Centers did not apply the sub-daily ERP model when transforming ICRF orbit solutions to ITRF, which is used for IGS orbit/clock products. This transformation inconsistency can cause significant orbit RMS differences that could exceed the 5-cm level. Independent ERP rate solutions are sensitive even to small errors in the sub-daily ERP model, and can be used to verify the sub-daily ERP model at, or below 0.1 mas/day precision level.
The Precise Point Positioning (PPP) via precise station position solutions with the IGS orbit/clock combined products, provides an ideal interface to access the IGS realization of ITRF. PPP also yields precise station clock and tropospheric zenith delays (TZD) solutions, all at the sub-cm precision level. However, when using IGS orbit/clock products it is important that the same convention be used with respect to sub-daily ERP. Otherwise, the solutions of station navigation positions, station clocks and TZD's will be affected by significant errors that could exceed the 1-cm level.

GPS ambiguity resolution is the process of resolving the unknown cycle ambiguities of double-difference (DD) carrier-phase
data as integers. It is the key to fast and high-precision relative GPS positioning. Critical in the application of ambiguity
resolution is its reliability. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable
errors in the positioning results. High success rates are required for ambiguity resolution to be reliable. In this contribution
we will introduce and evaluate such diagnostic measures. They complement existing methods of ambiguity resolution and allow
the user and/or analyst to infer their reliability. © 1999 John Wiley & Sons, Inc.

Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced
geodetic and astronomical tasks including positioning and navigation on Earth and in space. To perform this transformation
at the time of observation, that is for real-time applications, accurate predictions of the Earth orientation parameters (EOP)
are needed. The Earth orientation parameters prediction comparison campaign (EOP PCC) that started in October 2005 was organized
for the purpose of assessing the accuracy of EOP predictions. This paper summarizes the results of the EOP PCC after nearly
two and a half years of operational activity. The ultra short-term (predictions to 10days into the future), short-term (30days),
and medium-term (500days) EOP predictions submitted by the participants were evaluated by the same statistical technique
based on the mean absolute prediction error using the IERS EOP 05 C04 series as a reference. A combined series of EOP predictions
computed as a weighted mean of all submissions available at a given prediction epoch was also evaluated. The combined series
is shown to perform very well, as do some of the individual series, especially those using atmospheric angular momentum forecasts.
A main conclusion of the EOP PCC is that no single prediction technique performs the best for all EOP components and all prediction
intervals.
KeywordsEarth orientation parameters-Predictions-Combined solution-Polar motion-UT1-Universal time

According to the real-time positioning of BeiDou navigation satellite. Analysis Center (AC) was necessary to develop Earth Rotation Parameters (ERP) products based on autoregressive integrated moving average (ARIMA) mode, then, it necessary to transform the BeiDou navigation satellite ephemeris of Inertial System to the Earth Solid System according to the ERP prediction products. For MEO, IGSO and GEO, the development of ERP products of AC calculated the BeiDou navigation satellite orbit error was less than 50 cm based on the ERP product of Earth Rotation Service System (IERS) forecast for 30 days in the Earth Solid System orbit as a true value, which indicated that the ERP prediction error impacted the Earth Solid System precise ephemeris calculation accuracy, and indicated AC ERP prediction results with IERS products fairly.

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.

The International GNSS Service (IGS) issues four sets of so-called ultra-rapid products per day, which are based on the contributions of the IGS Analysis Centers. The traditional (“old”) ultra-rapid orbit and earth rotation parameters (ERP) solution of the Center for Orbit Determination in Europe (CODE) was based on the output of three consecutive 3-day long-arc rapid solutions. Information from the IERS Bulletin A was required to generate the predicted part of the old CODE ultra-rapid product. The current (“new”) product, activated in November 2013, is based on the output of exactly one multi-day solution. A priori information from the IERS Bulletin A is no longer required for generating and predicting the orbits and ERPs. This article discusses the transition from the old to the new CODE ultra-rapid orbit and ERP products and the associated improvement in reliability and performance. All solutions used in this article were generated with the development version of the Bernese GNSS Software. The package was slightly extended to meet the needs of the new CODE ultra-rapid generation.

GNSS receivers in difficult signal reception areas can find it difficult to acquire the broadcast ephemeris from the satellites and hence determine a position fix. One method to alleviate this is to provide a satellite ephemeris to the receiver to use whilst waiting for the broadcast ephemeris to be received. In this paper a technique to produce extended ephemerides of GPS satellites for mobile devices will be presented. This solution only utilises previously acquired broadcast ephemeris parameters. This is an example of self-assisted GPS, in which an estimated ephemeris can be generated locally on a mobile device rather than provided by an external source. The GPS receiver in the mobile device can then utilise this estimate of the satellite position whilst waiting for the broadcast ephemeris to be acquired, which can take many minutes when performing a warm start in challenging signal reception environments. The time-to-first-fix is therefore reduced. The software takes the form of an orbit prediction algorithm as well as an orbit determination algorithm. Results are shown for these algorithms working on a desktop computer and on a mobile telephone. The orbit prediction algorithm utilises a suite of force models and a numerical integrator to produce an estimated ephemeris. The satellite orbit errors in the geocentric radial direction are 3 m (RMS) after 1 day, 9 m (RMS) after 3 days, and 21 m (RMS) after 7 days. An orbit determination algorithm is also presented that modifies the estimate of the satellite position at the start of the orbit prediction arc; orbit prediction from these modified initial conditions gives a modest improvement in the geocentric radial direction, but large improvements in the along-track direction. The orbit determination algorithm can be used to help the orbit prediction algorithm if the along-track error is seen to be too large.

The International GNSS Service (IGS) provides Ultra-rapid GPS & GLONASS orbits every 6 h. Each product is composed of 24 h of observed orbits with predicted orbits for the next 24 h. We have studied how the orbit prediction performance varies as a function of the arc length of the fitted observed orbits and the parameterization strategy used to estimate the empirical solar radiation pressure (SRP) effects. To focus on the dynamical aspects of the problem, nearly ideal conditions have been adopted by using IGS Rapid orbits and known earth rotation parameters (ERPs) as observations. Performance was gauged by comparison with Rapid orbits as truth by examining WRMS and median orbit differences over the first 6-h and the full 24-h prediction intervals, as well as the stability of the Helmert frame alignment parameters. Two versions of the extended SRP orbit model developed by the Centre for Orbit Determination in Europe (CODE) were tested. Adjusting all nine SRPs (offsets plus once-per-revolution sines and cosines in each satellite-centered frame direction) for each satellite shows smaller mean sub-daily, scale, and origin translation differences. On the other hand, eliminating the four once-per-revolution SRP parameters in the sun-ward and the solar panel axis directions yields orbit predictions that are much more rotationally stable. We found that observed arc lengths of 40–45 h produce the most stable and accurate predictions during 2010. A combined strategy of rotationally aligning the 9 SRP results to the 5 SRP frame should give optimal predictions with about 13 mm mean WRMS residuals over the first 6 h and 50 mm over 24 h. Actual Ultra-rapid performance will be degraded due to the unavoidable rotational errors from ERP predictions.

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.

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.

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.

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

- W Liu

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.

- D D Mccarthy
- G Petit

McCarthy D. D., Petit G., 2004. IERS conventions[J]. Highlights of Astronomy, 13:605-606.

Earth rotation parameter estimation from GNSS and its impact on aircraft orbit determination

- L Wan
- E Wei
- S Jin

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

- W Zhang
- W Liu
- X Gong

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

- W Liu

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.