The impact of celestial pole offset modelling on VLBI UT1 intensive results

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

The impact of errors in polar motion and nutation on UT1 determinations from VLBI Intensive observations

The earth’s phase of rotation, expressed as Universal Time UT1, is the most variable component of the earth’s rotation. Continuous monitoring of this quantity is realised through daily single-baseline VLBI observations which are interleaved with VLBI network observations. The accuracy of these single-baseline observations is established mainly through statistically determined standard deviations of the adjustment process although the results of these measurements are prone to systematic errors. The two major effects are caused by inaccuracies in the polar motion and nutation angles introduced as a priori values which propagate into the UT1 results. In this paper, we analyse the transfer of these components into UT1 depending on the two VLBI baselines being used for short duration UT1 monitoring. We develop transfer functions of the errors in polar motion and nutation into the UT1 estimates. Maximum values reach 30 [μs per milliarcsecond] which is quite large considering that observations of nutation offsets w.r.t. the state-of-the-art nutation model show deviations of as much as one milliarcsecond.     

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.     

Impact of seasonal station motions on VLBI UT1 intensives results

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

Results of the VLBI experiments conducted with Syowa Station, Antarctica

The first successful geodetic Very Long Baseline Interferometry (VLBI) observations to Antarctica were made on baselines from Syowa Station (Antarctica) to Tidbinbilla (Australia) and to Kashima (Japan) in January 1990. Regular geodetic experiments started in 1998 with the installation of a permanent VLBI terminal at Syowa Station. These observations are conducted at the standard geodetic VLBI frequencies of 2.3 and 8.4 GHz, S- and X-Bands. In the first year, the 11-m multipurpose antenna at Syowa Station observed together with the 26-m radio telescope of the University of Tasmania in Australia and the 26-m radio telescope of the Hartebeesthoek Radio Astronomy Observatory in South Africa. From 1999, the experiments were expanded to also include the O’Higgins Station in Antarctica, Fortaleza in Brazil and Kokee on Hawaii. From 1999 until the end of 2003, 25 observing sessions have been reduced and analyzed using the CALC/SOLVE geodetic VLBI data reduction package. The results show that the horizontal baseline of Syowa-Hobart is increasing at the rate of 57.0±1.9 mm/year. The baseline Syowa-Hartebeesthoek is also increasing, but at the lower rate of 9.8±1.9 mm/year. The VLBI result of 2.0±3.1 mm/year and the GPS result of −1.9±0.7 mm/year for the Syowa-O’Higgins horizontal baseline support the hypothesis of one rigid Antarctic plate without intra-plate deformation, which is consistent with the NNR-NUVEL-1A global plate motion model. The location of the Euler pole of the Antarctic plate by VLBI is estimated as 59.7°S and 62.6°E with a rotation rate of 0.190 deg/Myr, while that by GPS in our study is estimated as 60.6°S and 42.2°E with a rotation rate of 0.221 deg/Myr. These pole positions are slightly different to that implied by the NNR-NUVEL-1A model of 63.0°S and 64.2°E with a rotation rate of 0.238 deg/Myr. VLBI observations over a longer time span may resolve small discrepancy of current plate motion from the NNR-NUVEL-1A model. The consistency of the VLBI coordinates with the GPS coordinates at Syowa Station, after correction for the local tie vector components between the two reference markers, is also discussed.     

Multi-reference evaluation of uncertainty in earth orientation parameter measurements

Uncertainties in polar motion and length-of-day measurements are evaluated empirically using several data series from the space-geodetic techniques of the global positioning system (GPS), satellite laser ranging (SLR), and very long baseline interferometry (VLBI) during 1997–2002. In the evaluation procedure employed here, known as the three-corner hat (TCH) technique, the signal common to each series is eliminated by forming pair-wise differences between the series, thus requiring no assumed values for the “truth” signal. From the variances of the differenced series, the uncertainty of each series can be recovered when reasonable assumptions are made about the correlations between the series. In order to form the pair-wise differences, the series data must be given at the same epoch. All measurement data sets studied here were sampled at noon (UTC); except for the VLBI series, whose data are interpolated to noon and whose UT1 values are also numerically differentiated to obtain LOD. The numerical error introduced to the VLBI values by the interpolation and differentiation is shown to be comparable in magnitude to the values determined by the TCH method for the uncertainties of the VLBI series. The TCH estimates for the VLBI series are corrupted by such numerical errors mostly as a result of the relatively large data intervals. Of the remaining data sets studied here, it is found that the IGS Final combined series has the smallest polar motion and length-of-day uncertainties.     

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.     

Measuring rapid variations in Earth orientation,geocenter and crust with satellite laser ranging

This analysis was performed with the GEOSAT software developed at NDRE for high-precision analysis of satellite tracking and VLBI data for geodetic and geodynamic applications. To determine the amplitudes of the tidally coherent daily and sub-daily variations in the Earth's orientation, geocenter, and crust, we have analyzed twelve months of SLR tracking data from the LAGEOS I & II and ETALON I & II satellites, obtained between October 1992 and September 1993. Station coordinates and mean geocenter are determined with an accuracy of 1 to 2 cm. Amplitudes of diurnal and semidiurnal variations in UT1, polar motion, and geocenter are determined with a precision of ~2µts, ~20µas, and 1–3 mm in each component. It is demonstrated that it is possible to determine a one-year continuous high-precision series in UT1 using multi-satellite laser ranging.     

Radiointerferometric polar motion observations with high temporal resolution

Summary For several years polar motion has been routinely monitored with the technique of geodetic Very Long Baseline Interferometry (VLBI) at five-day intervals. Here we present the results of the first two series of VLBI measurements for polar motion monitoring observed on a quasi daily basis employing only a single baseline. The high sensitivity of the long north-south baseline between radio telescopes at Wettzell in Germany and Hartebeesthock in South Africa for both components of polar motion permitted relatively short and inexpensive measurements of only two hours duration per session. The results of this series agree very well with the pole path determined with the IRIS network using 4 observatories in each observing session of 24 hour duration. With the polar motion results of the two series spanning about 35 days each, spectral analyses were performed which have shown a fortnightly period with a high degree of probability. These measurements demonstrate the potential of long north-south VLBI baselines for monitoring polar motion with very high temporal resolution for studies of short period fluctuations.     

VGOS超宽带观测的首次UT1测量数据处理及分析

在国际甚长基线干涉测量（very long baseline interferometry, VLBI）大地测量与天体测量服务组织协调下,首次利用隶属于VLBI全球观测系统（VLBI global observing system, VGOS）的美国Kokee和德国Wettzell观测站及并置的传统VLBI观测站开展了世界时（universal time, UT1）联合测量试验,观测数据在上海VLBI中心进行了干涉处理。结果表明,VGOS超宽带观测系统的UT1测量精度约为7 μs,并置基线的传统S/X双频系统测量精度约为14 μs,VGOS系统的UT1解算结果优于S/X系统。通过试验建立了从相关处理、相关后处理到UT1参数解算的完整数据处理流程,验证了上海VLBI相关处理机的VGOS数据处理能力,为承担国内和国际VGOS观测数据的相关处理任务奠定了基础。     

Gravity-dependent signal path variation in a large VLBI telescope modelled with a combination of surveying methods

The very long baseline interferometry (VLBI) antenna in Medicina (Italy) is a 32-m AZ-EL mount that was surveyed several times, adopting an indirect method, for the purpose of estimating the eccentricity vector between the co-located VLBI and Global Positioning System instruments. In order to fulfill this task, targets were located in different parts of the telescope’s structure. Triangulation and trilateration on the targets highlight a consistent amount of deformation that biases the estimate of the instrument’s reference point up to 1 cm, depending on the targets’ locations. Therefore, whenever the estimation of accurate local ties is needed, it is critical to take into consideration the action of gravity on the structure. Furthermore, deformations induced by gravity on VLBI telescopes may modify the length of the path travelled by the incoming radio signal to a non-negligible extent. As a consequence, differently from what it is usually assumed, the relative distance of the feed horn’s phase centre with respect to the elevation axis may vary, depending on the telescope’s pointing elevation. The Medicina telescope’s signal path variation ΔL increases by a magnitude of approximately 2 cm, as the pointing elevation changes from horizon to zenith; it is described by an elevation-dependent second-order polynomial function computed as, according to Clark and Thomsen (Techical report, 100696, NASA, Greenbelt, 1988), a linear combination of three terms: receiver displacement ΔR, primary reflector’s vertex displacement ΔV and focal length variations ΔF. ΔL was investigated with a combination of terrestrial triangulation and trilateration, laser scanning and a finite element model of the antenna. The antenna gain (or auto-focus curve) ΔG is routinely determined through astronomical observations. A surprisingly accurate reproduction of ΔG can be obtained with a combination of ΔV, ΔF and ΔR.     

Height bias and scale effect induced by antenna gravitational deformations in geodetic VLBI data analysis

The impact of signal path variations (SPVs) caused by antenna gravitational deformations on geodetic very long baseline interferometry (VLBI) results is evaluated for the first time. Elevation-dependent models of SPV for Medicina and Noto (Italy) telescopes were derived from a combination of terrestrial surveying methods to account for gravitational deformations. After applying these models in geodetic VLBI data analysis, estimates of the antenna reference point positions are shifted upward by 8.9 and 6.7 mm, respectively. The impact on other parameters is negligible. To simulate the impact of antenna gravitational deformations on the entire VLBI network, lacking measurements for other telescopes, we rescaled the SPV models of Medicina and Noto for other antennas according to their size. The effects of the simulations are changes in VLBI heights in the range [−3, 73] mm and a net scale increase of 0.3–0.8 ppb. The height bias is larger than random errors of VLBI position estimates, implying the possibility of significant scale distortions related to antenna gravitational deformations. This demonstrates the need to precisely measure gravitational deformations of other VLBI telescopes, to derive their precise SPV models and to apply them in routine geodetic data analysis.     

基于VLBI与BDS联合解算ERP的算法研究

利用PANDA软件解算2016年第61~91天的MGEX(Multi-GNSS Experiment)服务站的北斗数据,获得地球自转参数(ERP)。利用VieVS2.2软件处理了同时段的甚长基线干涉测量(VLBI)数据。采用基于IERS 08C04序列的定权方法对BDS和VLBI的解算结果进行加权平均,得到综合的ERP值。结果表明,与IERS比较,极移在X方向差值的RMS为0.249 mas,Y方向差值的RMS为0.296 mas,UT1-UTC差值的RMS为0.053 ms.利用BDS与VLBI数据对ERP参数进行联合解算,弥补了BDS解算结果不稳定和VLBI观测不连续的缺陷,使解算结果的稳定性和可靠性均有所提高。      

Improving the modeling of the atmospheric delay in the data analysis of the Intensive VLBI sessions and the impact on the UT1 estimates

The very long baseline interferometry (VLBI) Intensive sessions are typically 1-h and single-baseline VLBI sessions, specifically designed to yield low-latency estimates of UT1-UTC. In this work, we investigate what accuracy is obtained from these sessions and how it can be improved. In particular, we study the modeling of the troposphere in the data analysis. The impact of including external information on the zenith wet delays (ZWD) and tropospheric gradients from GPS or numerical weather prediction models is studied. Additionally, we test estimating tropospheric gradients in the data analysis, which is normally not done. To evaluate the results, we compared the UT1-UTC values from the Intensives to those from simultaneous 24-h VLBI session. Furthermore, we calculated length of day (LOD) estimates using the UT1-UTC values from consecutive Intensives and compared these to the LOD estimated by GPS. We find that there is not much benefit in using external ZWD; however, including external information on the gradients improves the agreement with the reference data. If gradients are estimated in the data analysis, and appropriate constraints are applied, the WRMS difference w.r.t. UT1-UTC from 24-h sessions is reduced by 5% and the WRMS difference w.r.t. the LOD from GPS by up to 12%. The best agreement between Intensives and the reference time series is obtained when using both external gradients from GPS and additionally estimating gradients in the data analysis.     

昆明站流动ⅥBI站坐标的首次确定

我国第一台流动甚长基线干涉测量（VLBI）设备经近十年的研制目前在昆明进行了试观测，本文介绍了实验观测及数据的获取情况。并对数据文件进行了处理。结果显示，在上海佘山25米天线至昆明流动站近2千公里的基线上，昆明流动站坐标精度优于5cm。基线相对精度优于10^-8。     

Effects of illumination functions on the computation of gravity-dependent signal path variation models in primary focus and Cassegrainian VLBI telescopes

This paper sets the rules for an optimal definition of precise signal path variation (SPV) models, revising and highlighting the deficiencies in the calculations adopted in previous studies and improving the computational approach. Hence, the linear coefficients that define the SPV model are rigorously determined. The equations that are presented depend on the dimensions and the focal lengths of the telescopes as well as on the feed illumination taper. They hold for any primary focus or Cassegrainian very long baseline interferometry (VLBI) telescope. Earlier investigations usually determined the SPV models assuming a uniform illumination of the telescope mirrors. We prove this hypothesis to be over-simplistic by comparing results derived adopting (a) uniform, (b) Gaussian and (c) binomial illumination functions. Numerical computations are developed for AZ-EL mount, 32 m Medicina and Noto (Italy) VLBI telescopes, these latter being the only telescopes which possess thorough information on gravity-dependent deformation patterns. Particularly, assuming a Gaussian illumination function, the SPV in primary focus over the elevation range [0°, 90°] is 10.1 and 7.2 mm, for Medicina and Noto, respectively. With uniform illumination function the maximal path variation for Medicina is 17.6 and 12.7 mm for Noto, thus highlighting the strong dependency on the choice of the illumination function. According to our findings, a revised SPV model is released for Medicina and a model for Noto is presented here for the first time. Currently, no other VLBI telescope possesses SPV models capable of correcting gravity-dependent observation biases.     

Asymmetric tropospheric delays from numerical weather models for UT1 determination from VLBI Intensive sessions on the baseline Wettzell–Tsukuba

One-baseline 1-h Very Long Baseline Interferometry (VLBI) Intensive sessions are carried out every day to determine Universal Time (UT1). Azimuthal asymmetry of tropospheric delays around the stations is usually ignored and not estimated because of the small number of observations. In this study we use external information about the asymmetry for the Intensive sessions between Tsukuba (Japan) and Wettzell (Germany), which are carried out on Saturdays and Sundays (1) from direct ray-tracing for each observation at Tsukuba and (2) in the form of linear horizontal north and east gradients every 6 h at both stations. The change of the UT1 estimates is at the 10 μs level with maximum differences of up to 50 μs, which is clearly above the formal uncertainties of the UT1 estimates (between 5 and 20 μs). Spectral analysis reveals that delays from direct ray-tracing for the station Tsukuba add significant power at short periods (1–2 weeks) w.r.t. the state-of-the-art approach, and comparisons with length-of-day (LOD) estimates from Global Positioning System (GPS) indicate that these ray-traced delays slightly improve the UT1 estimates from Intensive sessions.     

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.     

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.     

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.