IGS Earth Rotation Parameters

Since its official start in January 1994, the International GPS Service (IGS) has been distributing, as part of its product combination, two distinct Earth rotation parameter (ERP) series: the IGS Rapid series and the IGS Final series. Initially, the IGS Rapid ERP values were interpolations of the International Earth Rotation Service (IERS) Bulletin A, whereas the IGS Final ERP series was based on the IERS Bulletin B. Since June 1996, the IGS has been generating its own Final ERP series consistent with the IGS combined orbit products and based on weighted means of individual IGS analysis center (AC) solutions. At first, only the polar motion (PM) coordinates and their rates were combined. Length of Day (LOD) and Universal Time (UT) solutions, also based on separate weighted mean combinations, followed in March 1997. Currently, the IGS Rapid and Final combinations are produced and made available within 17 hours and 11 days, respectively, after the last observation. Both IGS and the best AC series are consistent and precise at the 0.1-milliarcsecond (mas) level for PM and at about 30 μs for LOD. Biases in some AC solutions may exceed these consistency levels. Comparisons of both IGS ERP series with external standards, such as the IERS multitechnique Bulletins and atmospheric angular momentum series, confirm the estimated precisions. ? 1999 John Wiley & Sons, Inc.     

Prediction of Earth orientation parameters by artificial neural networks

 Earth orientation parameters (EOPs) [polar motion and length of day (LOD), or UT1–UTC] were predicted by artificial neural networks. EOP series from various sources, e.g. the C04 series from the International Earth Rotation Service and the re-analysis optical astrometry series based on the HIPPARCOS frame, served for training the neural network for both short-term and long-term predictions. At first, all effects which can be described by functional models, e.g. effects of the solid Earth tides and the ocean tides or seasonal atmospheric variations of the EOPs, were removed. Only the differences between the modeled and the observed EOPs, i.e. the quasi-periodic and irregular variations, were used for training and prediction. The Stuttgart neural network simulator, which is a very powerful software tool developed at the University of Stuttgart, was applied to construct and to validate different types of neural networks in order to find the optimal topology of the net, the most economical learning algorithm and the best procedure to feed the net with data patterns. The results of the prediction were analyzed and compared with those obtained by other methods. The accuracy of the prediction is equal to or even better than that by other prediction methods. Received: 6 February 2001 / Accepted: 23 October 2001     

Is there utility in rigorous combinations of VLBI and GPS Earth orientation parameters?

Combinations of station coordinates and velocities from independent space-geodetic techniques have long been the standard method to realize robust global terrestrial reference frames (TRFs). In principle, the particular strengths of one observing method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and accurate co-location ties are available. More recently, the methodology has been extended to combine time-series of results at the normal equation level. This allows Earth orientation parameters (EOPs) to be included and aligned in a fully consistent way with the TRF. While the utility of such multi-technique combinations is generally recognized for the reference frame, the benefits for the EOPs are yet to be quantitatively assessed. In this contribution, which is a sequel to a recent paper on co-location ties (Ray and Altamimi in J Geod 79(4–5): 189–195, 2005), we have studied test combinations of very long baseline interferometry (VLBI) and Global Positioning System (GPS) time-series solutions to evaluate the effects on combined EOP measurements compared with geophysical excitations. One expects any effect to be small, considering that GPS dominates the polar motion estimates due to its relatively dense and uniform global network coverage, high precision, continuous daily sampling, and homogeneity, while VLBI alone observes UT1-UTC. Presently, although clearly desirable, we see no practical method to rigorously include the GPS estimates of length-of-day variations due to significant time-varying biases. Nevertheless, our results, which are the first of this type, indicate that more accurate polar motion from GPS contributes to improved UT1-UTC results from VLBI. The situation with combined polar motion is more complex. The VLBI data contribute directly only very slightly, if at all, with an impact that is probably affected by the weakness of the current VLBI networks (small size and sparseness) and the quality of local ties relating the VLBI and GPS frames. Instead, the VLBI polar motion information is used primarily in rotationally aligning the VLBI and GPS frames, thereby reducing the dependence on co-location tie information. Further research is needed to determine an optimal VLBI-GPS combination strategy that yields the highest quality EOP estimates. Improved local ties (including internal systematic effects within the techniques) will be critically important in such an effort.     

Prediction of Earth orientation

Summary 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.     

Assessment of periodic sub-diurnal Earth rotation variations at tidal frequencies through transformation of VLBI normal equation systems

We present an empirical model for periodic variations of diurnal and sub-diurnal Earth rotation parameters (ERPs) that was derived based on the transformation of normal equation (NEQ) systems of Very Long Baseline Interferometry (VLBI) observing sessions. NEQ systems that contain highly resolved polar motion and UT1-TAI with a temporal resolution of 15 min were generated and then transformed to the coefficients of the tidal ERP model to be solved for. To investigate the quality of this model, comparisons with empirical models from the Global Positioning System (GPS), another VLBI model and the model adopted by the conventions of the International Earth Rotation and Reference Systems Service (IERS) were performed. The absolute coefficients of these models agree almost completely within 7.5 μ as in polar motion and 0.5 μs in UT1-TAI. Several bigger differences exist, which are discussed in this paper. To be able to compare the model estimates with results of the continuous VLBI campaigns, where signals with periods of 8 and 6 h were detected, terms in the ter- and quarter-diurnal band were included in the tidal ERP model. Unfortunately, almost no common features with the results of continuous VLBI campaigns or ERP predictions in these tidal bands can be seen.     

Possible improvement of Earth orientation forecast using autocovariance prediction procedures

 Autocovariance prediction has been applied to attempt to improve polar motion and UT1-UTC predictions. The predicted polar motion is the sum of the least-squares extrapolation model based on the Chandler circle, annual and semiannual ellipses, and a bias fit to the past 3 years of observations and the autocovariance prediction of these extrapolation residuals computed after subtraction of this model from pole coordinate data. This prediction method has been applied also to the UT1-UTC data, from which all known predictable effects were removed, but the prediction error has not been reduced with respect to the error of the current prediction model. However, the results show the possibility of decreasing polar motion prediction errors by about 50 for different prediction lengths from 50 to 200 days with respect to the errors of the current prediction model. Because of irregular variations in polar motion and UT1-UTC, the accuracy of the autocovariance prediction does depend on the epoch of the prediction. To explain irregular variations in x, y pole coordinate data, time-variable spectra of the equatorial components of the effective atmospheric angular momentum, determined by the National Center for Environmental Prediction, were computed. These time-variable spectra maxima for oscillations with periods of 100–140 days, which occurred in 1985, 1988, and 1990 could be responsible for excitation of the irregular short-period variations in pole coordinate data. Additionally, time-variable coherence between geodetic and atmospheric excitation function was computed, and the coherence maxima coincide also with the greatest irregular variations in polar motion extrapolation residuals. Received: 22 October 1996 / Accepted: 16 September 1997     

Improved UT1 predictions through low-latency VLBI observations

The quality of predictions of Earth orientation parameters (EOPs) in general, and of Universal Time (UT1) in particular, depends strongly on the time delay between the last observation available and the first prediction. Since 30 September 2007 (MJD 54373), the latency of UT1 results from a subset of single baseline VLBI observations running once per week (Mondays) has been decreased from 2 to 3 days to about 8 h. This was achieved by transmitting the raw VLBI data of 1-h duration from the observing sites in Tsukuba (Japan), Wettzell (Germany) and Ny-Ålesund (Norway) to the correlator of the Max-Planck-Institute for Radio Astronomy and the German Federal Agency of Cartography and Geodesy at Bonn, Germany, by high-speed Internet connections (e-Transfer). The reduced latency of the observations has improved the accuracy of the combined International Earth Rotation and Reference Systems Service (IERS) Rapid Service/Prediction Center (RS/PC) UT1-UTC solution by roughly 50% on the days when the data are available. Because this combination is an input to the UT1-UTC prediction process, the improved latency is also responsible for a roughly 21% improvement in the accuracy of short-term IERS RS/PC UT1-UTC predictions on the days where the data are available.     

EOP预报误差对导航卫星轨道预报的影响分析

导航卫星轨道预报是利用精密定轨结果在惯性系下进行轨道外推,再将外推得到的惯性系轨道转换为地固系轨道,然后生成卫星星历数据。由于坐标系转换时使用的是带有误差的地球定向参数（EOP：Earth Orientation Parameters）预报值,转换结果会产生误差,进而影响轨道预报结果的精度。分析了EOP快速预报产品公报A的预报精度,研究了参数预报误差对轨道预报精度的影响。结果表明,对于利用GPS精密星历外推模拟得到的卫星轨道而言,EOP预报1天引起的轨道预报误差大致分布在0．232±0．183m,参数预报7天引起的轨道预报误差大致分布在0．438±0．356m。     

Combined Earth orientation parameters based on homogeneous and continuous VLBI and GPS data

The CONT02 campaign is of great interest for studies combining very long baseline interferometry (VLBI) with other space-geodetic techniques, because of the continuously available VLBI observations over 2 weeks in October 2002 from a homogeneous network. Especially, the combination with the Global Positioning System (GPS) offers a broad spectrum of common parameters. We combined station coordinates, Earth orientation parameters (EOPs) and troposphere parameters consistently in one solution using technique- specific datum-free normal equation systems. In this paper, we focus on the analyses concerning the EOPs, whereas the comparison and combination of the troposphere parameters and station coordinates are covered in a companion paper in Journal of Geodesy. In order to demonstrate the potential of the VLBI and GPS space-geodetic techniques, we chose a sub-daily resolution for polar motion (PM) and universal time (UT). A consequence of this solution set-up is the presence of a one-to-one correlation between the nutation angles and a retrograde diurnal signal in PM. The Bernese GPS Software used for the combination provides a constraining approach to handle this singularity. Simulation studies involving both nutation offsets and rates helped to get a deeper understanding of this singularity. With a rigorous combination of UT1–UTC and length of day (LOD) from VLBI and GPS, we showed that such a combination works very well and does not suffer from the systematic effects present in the GPS-derived LOD values. By means of wavelet analyses and the formal errors of the estimates, we explain this important result. The same holds for the combination of nutation offsets and rates. The local geodetic ties between GPS and VLBI antennas play an essential role within the inter-technique combination. Several studies already revealed non-negligible discrepancies between the terrestrial measurements and the space-geodetic solutions. We demonstrate to what extent these discrepancies propagate into the combined EOP solution.     

Achievements of the Earth orientation parameters prediction comparison campaign

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 10 days into the future), short-term (30 days), and medium-term (500 days) 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.     

DORIS and the Determination of the Earth’s Polar Motion

DORIS (Détermination d’Orbite et Radiopositionnement Intégrés par Satellite) is a system used for precise orbit determination (POD) and ground-station positioning. It has been implemented on-board various satellites: the SPOT (Système pour l’Observation de la Terre) remote sensing satellites SPOT-2, SPOT-3, SPOT-4, SPOT-5, TOPEX/Poseidon and more recently on its successors Jason-1 and ENVISAT. DORIS is also a terrestrial positioning system that has found many applications in geophysics and geodesy; in particular, it contributes to the realization of the International Terrestrial Reference Frame, ITRF2000 and the forthcoming ITRF2005. Although not its primary objective, DORIS can bring information on Earth orientation monitoring, mainly polar motion and length of day (LOD) variations that complement other astrogeodetic techniques. In this paper, we have analyzed various recent polar motion solutions derived from independent analysis centers using different software packages and applying various analysis strategies. Comparisons of these solutions to the International Earth Rotation and Reference Systems Service (IERS) C04 solution are performed. Depending on the solutions, the accuracy of DORIS polar components are in the range of 0.5–1 mas corresponding to a few centimeters on the Earth’s surface. This is approximately ten times larger than results derived from GPS, which are typically 0.06 mas in both components. This does not allow DORIS results to be taken into account in the IERS–EOP combinations. A gain in the precision could come from technical improvements to the DORIS system, in addition to improvement of the orbit, tropospheric, ionospheric and Earth gravity field modeling.     

Methodology for the combination of sub-daily Earth rotation from GPS and VLBI observations

A combination procedure of Earth orientation parameters from Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) observations was developed on the basis of homogeneous normal equation systems. The emphasis and purpose of the combination was the determination of sub-daily polar motion (PM) and universal time (UT1) for a long time-span of 13 years. Time series with an hourly resolution and a model for tidal variations of PM and UT1-TAI (dUT1) were estimated. In both cases, 14-day nutation corrections were estimated simultaneously with the ERPs. Due to the combination procedure, it was warranted that the strengths of both techniques were preserved. At the same time, only a minimum of de-correlating or stabilizing constraints were necessary. Hereby, a PM time series was determined, whose precision is mainly dominated by GPS observations. However, this setup benefits from the fact that VLBI delivered nutation and dUT1 estimates at the same time. An even bigger enhancement can be seen for the dUT1 estimation, where the high-frequency variations are provided by GPS, while the long term trend is defined by VLBI. The estimated combined tidal PM and dUT1 model was predominantly determined from the GPS observations. Overall, the combined tidal model for the first time completely comprises the geometrical benefits of VLBI and GPS observations. In terms of root mean squared (RMS) differences, the tidal amplitudes agree with other empirical single-technique tidal models below 4 μas in PM and 0.25 μs in dUT1. The noise floor of the tidal ERP model was investigated in three ways resulting in about 1 μas for diurnal PM and 0.07 μs for diurnal dUT1 while the semi-diurnal components have a slightly better accuracy.     

Precision real-time navigation of LEO satellites using global positioning system measurements

Continued advancements in remote sensing technology along with a trend towards highly autonomous spacecraft provide a strong motivation for accurate real-time navigation of satellites in low Earth orbit (LEO). Global Navigation Satellite System (GNSS) sensors nowadays enable a continuous tracking and provide low-noise radiometric measurements onboard a user spacecraft. Following the deactivation of Selective Availability a representative real-time positioning accuracy of 10 m is presently achieved by spaceborne global positioning system (GPS) receivers on LEO satellites. This accuracy can notably be improved by use of dynamic orbit determination techniques. Besides a filtering of measurement noise and other short-term errors, these techniques enable the processing of ambiguous measurements such as carrier phase or code-carrier combinations. In this paper a reference algorithm for real-time onboard orbit determination is described and tested with GPS measurements from various ongoing space missions covering an altitude range of 400–800 km. A trade-off between modeling effort and achievable accuracy is performed, which takes into account the limitations of available onboard processors and the restricted upload capabilities. Furthermore, the benefits of different measurements types and the available real-time ephemeris products are assessed. Using GPS broadcast ephemerides a real-time position accuracy of about 0.5 m (3D rms) is feasible with dual-frequency carrier phase measurements. Slightly inferior results (0.6–1 m) are achieved with single-frequency code-carrier combinations or dual-frequency code. For further performance improvements the use of more accurate real-time GPS ephemeris products is mandatory. By way of example, it is shown that the TDRSS Augmentation Service for Satellites (TASS) offers the potential for 0.1–0.2 m real-time navigation accuracies onboard LEO satellites.     

利用2006—2015年VLBI数据进行地球定向参数解算与分析

目前正处在下一代甚长基线干涉测量（very long baseline interferometry,VLBI）系统的建设时期。利用维也纳VLBI与卫星软件（Vienna VLBI and satellite software,VieVS）解算了2006—2015年的VLBI数据,得到了10 a的地球定向参数（Earth orientation parameters,EOP）时间序列,并与国际地球自转服务机构的结果进行了对比。利用解算结果得到了10 a的日长变化时间序列,通过傅里叶分析得出了日长变化的短周期、半月周期、月周期、半年周期和周年周期,同时还分析得到了极移序列中的周年项和张德勒周期项以及章动改正序列中的自由核章动项。此次解算工作可为武汉大学卫星台站日后的VLBI数据解析积累一定的经验。     

The contribution of Very Long Baseline Interferometry to ITRF2005

The contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to the ITRF2005 (International Terrestrial Reference Frame 2005) has been computed by the IVS Analysis Coordinator’s office at the Geodetic Institute of the University of Bonn, Germany. For this purpose the IVS Analysis Centres (ACs) provided datum-free normal equation matrices in Solution INdependent EXchange (SINEX) format for each 24 h observing session to be combined on a session-by-session basis by a stacking procedure. In this process, common sets of parameters, transformed to identical reference epochs and a prioris, and especially representative relative weights have been taken into account for each session. In order to assess the quality of the combined IVS files, Earth orientation parameters (EOPs) and scaling factors have been derived from the combined normal equation matrices. The agreement of the EOPs of the combined normal equation matrices with those of the individual ACs in terms of weighted root mean square (WRMS) is in the range of 50–60 μas for the two polar motion components and about 3 μs for UT1−UTC. External comparisons with International GNSS Serive (IGS) polar motion components is at the level of 130–170 μas and 21 μs/day for length of day (LOD). The scale of the terrestrial reference frame realized through the IVS SINEX files agrees with ITRF2000 at the level of 0.2 ppb.     

International VLBI Service for Geodesy and Astrometry

The International VLBI Service for Geodesy and Astrometry (IVS) regularly produces high-quality Earth orientation parameters from observing sessions employing extensive networks or individual baselines. The master schedule is designed according to the telescope days committed by the stations and by the need for dense sampling of the Earth orientation parameters (EOP). In the pre-2011 era, the network constellations with their number of telescopes participating were limited by the playback and baseline capabilities of the hardware (Mark4) correlators. This limitation was overcome by the advent of software correlators, which can now accommodate many more playback units in a flexible configuration. In this paper, we describe the current operations of the IVS with special emphasis on the quality of the polar motion results since these are the only EOP components which can be validated against independent benchmarks. The polar motion results provided by the IVS have improved continuously over the years, now providing an agreement with IGS results at the level of 20–25 \(\upmu \)as in a WRMS sense. At the end of the paper, an outlook is given for the realization of the VLBI Global Observing System.     

Effect of post-seismic deformation on earth orientation parameter estimates from VLBI observations: a case study at Gilcreek, Alaska

Earth orientation parameters (EOPs) provide a link between the International Celestial Reference Frame (ICRF) and the International Terrestrial Reference Frame (ITRF). Natural geodynamic processes, such as earthquakes, can cause the motion of stations to become discontinuous and/or non-linear, thereby corrupting the EOP estimates if the sites are assumed to move linearly. The VLBI antenna at the Gilcreek Geophysical Observatory has undergone non-linear, post-seismic motion as a result of the M_w=7.9 Denali earthquake in November 2002, yet some VLBI analysts have adopted co-seismic offsets and a linear velocity model to represent the motion of the site after the earthquake. Ignoring the effects of the Denali earthquake leads to error on the order of 300–600 μas for the EOP, while modelling the post-seismic motion of Gilcreek with a linear velocity generates errors of 20–50 μas. Only by modelling the site motion with a non-linear function is the same level of accuracy of EOP estimates maintained. The effect of post-seismic motion on EOP estimates derived from the International VLBI Service IVS-R1 and IVS-R4 networks are not the same, although changes in network geometries and equipment improvements have probably affected the estimates more significantly than the earthquake-induced deformation at Gilcreek.     

Polar motion modeling,analysis, and prediction with time dependent harmonic coefficients

A time dependent amplitude model was proposed for the analysis and prediction of polar motion time series. The formulation was implemented to analyze part of the new combined solution, EOP (IERS) C 04, daily polar motion time series of 14 years length using a statistical model with first order autoregressive disturbances. A new solution approach, where the serial correlations of the disturbances are eliminated by sequentially differencing the measurements, was used to estimate the model parameters using weighted least squares. The new model parsimoniously represents the 14-year time series with 0.5 mas rms fit, close to the reported 0.1 mas observed pole position precisions for the x and y components. The model can also predict 6 months into the future with less than 4 mas rms prediction error for both polar motion components, and down to sub mas for one-step ahead prediction as validated using a set of daily time series data that are not used in the estimation. This study is dedicated to the memory of Prof. Urho Uotila (1923–2006) whose teaching of “Adjustment Computations” over the years influenced so much, so many of us who had the privilege of being his students.     

Comparison of polar motion with oceanic and atmospheric angular momentum time series for 2-day to Chandler periods

During a 4-year period starting in July 1996 and using intervals ranging from 3 days to 4 years, four precise polar motion (PM) series have been compared to excitation by atmospheric angular momentum (AAM) augmented with oceanic angular momentum (OAM) data. The first three series (C03, C04 and Bulletin A) are multi-technique combinations generated by the International Earth Rotation and Reference Systems Service (IERS) and the fourth combined series (IGS00P02) is produced by the International GPS Service (IGS) using only GPS data. The IGS PM compared the best with the combined excitations of atmosphere and oceans (AAM+OAM) at all intervals, showing high overall correlation of 0.8–0.9. Even for the interval of only three days, the IGS PM gave a significant correlation of about 0.6. Moreover, during the interval of February 1999 – July 2000, which should be representative of the current precision of the IGS PM, a significant correlation (>0.4) extended to periods as short as 2.2 days and 2.5 days for the x_p and y_p PM components, respectively. When using the IERS Bulletin B (C04) PM and an interval of almost 6 years, starting in November 1994, the combined OAM+AAM accounted for practically all the annual, semi-annual and Chandler wobble (CW) PM signals. When only AAM was used, either the US National Centers for Environment Prediction reanalysis data, which were used throughout this study, or the Japanese Meteorological Agency data, two large and well-resolved amplitude peaks of about 0.1 mas/day, remained at the retrograde annual and CW periods.     

Monitoring Earth orientation using space-geodetic techniques: state-of-the-art and prospective

Earth orientation parameters (EOPs) provide the transformation between the International Terrestrial Reference Frame (ITRF) and the International Celestial Reference Frame (ICRF). The different EOP series computed at the Earth Orientation Centre at the Paris Observatory are obtained from the combination of individual EOP series derived from the various space-geodetic techniques. These individual EOP series contain systematic errors, generally limited to biases and drifts, which introduce inconsistencies between EOPs and the terrestrial and celestial frames. The objectives of this paper are first to present the various combined EOP solutions made available at the EOP Centre for the different users, and second to present analyses concerning the long-term consistency of the EOP system with respect to both terrestrial and celestial reference frames. It appears that the present accuracy in the EOP combined IERS C04 series, which is at the level of 200 as for pole components and 20 s for UT1, does not match its internal precision, respectively 100 as and 5 s, because of propagation errors in the realization of the two reference frames. Rigorous combination methods based on a simultaneous estimation of station coordinates and EOPs, which are now being implemented within the International Earth Rotation Service (IERS), are likely to solve this problem in the future.