Geodetic VLBI with an artificial radio source on the Moon: a simulation study

We perform extensive simulations in order to assess the accuracy with which the position of a radio transmitter on the surface of the Moon can be determined by geodetic VLBI. We study how the quality and quantity of geodetic VLBI observations influence these position estimates and investigate how observations of such near-field objects affect classical geodetic parameters like VLBI station coordinates and Earth rotation parameters. Our studies are based on today’s global geodetic VLBI schedules as well as on those designed for the next-generation geodetic VLBI system. We use Monte Carlo simulations including realistic stochastic models of troposphere, station clocks, and observational noise. Our results indicate that it is possible to position a radio transmitter on the Moon using today’s geodetic VLBI with a two-dimensional horizontal accuracy of better than one meter. Moreover, we show that the next-generation geodetic VLBI has the potential to improve the two-dimensional accuracy to better than 5 cm. Thus, our results lay the base for novel observing concepts to improve both lunar research and geodetic VLBI.     

Effect of the selection of reference radio sources on geodetic estimates from VLBI observations

This paper evaluates the effect of the accuracy of reference radio sources on the daily estimates of station positions, nutation angle offsets, and the estimated site coordinates determined by very long baseline interferometry (VLBI), which are used for the realization of the international terrestrial reference frame (ITRF). Five global VLBI solutions, based on VLBI data collected between 1979 and 2006, are compared. The reference solution comprises all observed radio sources, which are treated as global parameters. Four other solutions, comprising different sub-sets of radio sources, were computed. The daily station positions for all VLBI sites and the corrections to the nutation offset angles were estimated for these five solutions. The solution statistics are mainly affected by the positional instabilities of reference radio sources, whereas the instabilities of geodetic and astrometric time-series are caused by an insufficient number of observed reference radio sources. A mean offset of the three positional components (Up, North, East) between any two solutions was calculated for each VLBI site. From a comparison of the geodetic results, no significant discrepancies between the respective geodetic solutions for all VLBI sites in the Northern Hemisphere were found. In contrast, the Southern Hemisphere sites were more sensitive to the selected set of reference radio sources. The largest estimated mean offset of the vertical component between two solutions for the Australian VLBI site at Hobart was 4 mm. In the worst case (if a weak VLBI network observed a limited number of reference radio sources) the daily offsets of the estimated height component at Hobart exceeded 100 mm. The exclusion of the extended radio sources from the list of reference sources improved the solution statistics and made the geodetic and astrometric time-series more consistent. The problem with the large Hobart height component offset is magnified by a comparatively small number of observations due to the low slewing rate of the VLBI dish (1°/ s). Unless a minimum of 200 scans are performed per 24-h VLBI experiment, the daily vertical positions at Hobart do not achieve 10 mm accuracy. Improving the slew rate at Hobart and/or having an increased number of new sites in the Southern Hemisphere is essential for further improvement of geodetic VLBI results for Southern Hemisphere sites.     

The impact of radio source structure on European geodetic VLBI measurements

European geodetic very long baseline interferometry (VLBI) sessions (also known as EUROPE sessions) have been carried out on a regular basis for the past 15 years to study relative crustal motions within Europe. These sessions are based on observations of extragalactic radio sources, which serve as distant fiducial marks to establish an accurate and stable celestial reference frame for long-term geodetic measurements. The radio sources, however, are not always point-like on milliarcsecond scales, as VLBI imaging has revealed. In this work, we quantify the magnitude of the expected effect of intrinsic source structure on geodetic bandwidth synthesis delay VLBI measurements for a subset of 14 sources regularly observed during the EUROPE sessions. These sources have been imaged at both X-band (8.4 GHz) and S-band (2.3 GHz) based on dedicated observations acquired with the European VLBI Network (EVN) in November 1996. The results of this calculation indicate that the reference source 0457+024 causes significant structural effects in measurements obtained on European VLBI baselines (about 10 picoseconds on average), whereas most of the other sources produce effects that are only occasionally larger than a few picoseconds. Applying the derived source structure models to the data of the EUROPE5-96 session carried out at the same epoch as the EVN experiment shows no noticeable changes in the estimated VLBI station locations.     

New VLBI2010 scheduling strategies and implications on the terrestrial reference frames

In connection with the work for the next generation VLBI2010 Global Observing System (VGOS) of the International VLBI Service for Geodesy and Astrometry, a new scheduling package (Vie_Sched) has been developed at the Vienna University of Technology as a part of the Vienna VLBI Software. In addition to the classical station-based approach it is equipped with a new scheduling strategy based on the radio sources to be observed. We introduce different configurations of source-based scheduling options and investigate the implications on present and future VLBI2010 geodetic schedules. By comparison to existing VLBI schedules of the continuous campaign CONT11, we find that the source-based approach with two sources has a performance similar to the station-based approach in terms of number of observations, sky coverage, and geodetic parameters. For an artificial 16 station VLBI2010 network, the source-based approach with four sources provides an improved distribution of source observations on the celestial sphere. Monte Carlo simulations yield slightly better repeatabilities of station coordinates with the source-based approach with two sources or four sources than the classical strategy. The new VLBI scheduling software with its alternative scheduling strategy offers a promising option with respect to applications of the VGOS.     

The effects of frequency-dependent quasar variability on the celestial reference frame

We examine the relationship between source position stability and astrophysical properties of radio-loud quasars making up the International Celestial Reference Frame (ICRF2). Understanding this relationship is important for improving quasar selection and analysis strategies, and therefore reference frame stability. We construct flux density time series, known as light curves, for 95 of the most frequently observed ICRF2 quasars at both the 2.3 and 8.4 GHz geodetic very long baseline interferometry (VLBI) observing bands. Because the appearance of new quasar components corresponds to an increase in quasar flux density, these light curves alert us about potential changes in source structure before they appear in VLBI images. We test how source position stability depends on three astrophysical parameters: (1) flux density variability at X band; (2) time lag between flares in S and X bands; (3) spectral index root-mean-square (rms), defined as the variability in the ratio between S and X band flux densities. We find that the time lag between S and X band light curves provides a good indicator of position stability: sources with time lags $<$ 0.06 years are significantly more stable ( $>$ 20 % improvement in weighted rms) than sources with larger time lags. A similar improvement is obtained by observing sources with low $(<$ 0.12) spectral index variability. On the other hand, there is no strong dependence of source position stability on flux density variability in a single frequency band. These findings can be understood by interpreting the time lag between S and X band light curves as a measure of the size of the source structure. Monitoring of source flux density at multiple frequencies therefore appears to provide a useful probe of quasar structure on scales important to geodesy. The observed astrometric position of the brightest quasar component (the core) is known to depend on observing frequency. We show how multi-frequency flux density monitoring may allow the dependence on frequency of the relative core positions along the jet to be elucidated. Knowledge of the position–frequency relation has important implications for current and future geodetic VLBI programs, as well as the alignment between the radio and optical celestial reference frames.     

我国VLBI观测网备选射电源的扩充

针对我国 VL BI观测网对射电源的特殊要求 ,给出了现有备选射电源的列表和天球分布图 ,提出了扩充备选射电源数量的必要性。结合 2 0 0 0年 1月“上海 -昆明基线”试观测 ,在原有的 12个备选射电源的基础上 ,又增选了 4个。观测及计算结果显示 ,12个备选源中 ,有 11个的信噪比和相关流量都很好 ,1个勉强能用 ;4个增选的源中 ,有 3个达到指标 ,应放入以后的备选源中。     

Precise station positions from VLBI observations to satellites: a simulation study

Very long baseline interferometry (VLBI) tracking of satellites is a topic of increasing interest for the establishment of space ties. This shall strengthen the connection of the various space geodetic techniques that contribute to the International Terrestrial Reference Frame. The concept of observing near-Earth satellites demands research on possible observing strategies. In this paper, we introduce this concept and discuss its possible benefits for improving future realizations of the International Terrestrial Reference System. Using simulated observations, we develop possible observing strategies that allow the determination of radio telescope positions in the satellite system on Earth with accuracies of a few millimeters up to 1–2 cm for weekly station coordinates. This is shown for satellites with orbital heights between 2,000 and 6,000 km, observed by dense regional as well as by global VLBI-networks. The number of observations, as mainly determined by the satellite orbit and the observation interval, is identified as the most critical parameter that affects the expected accuracies. For observations of global positioning system satellites, we propose the combination with classical VLBI to radio sources or a multi-satellite strategy. Both approaches allow station position repeatabilities of a few millimeters for weekly solutions.     

Effect of different tropospheric mapping functions on the TRF, CRF and position time-series estimated from VLBI

This paper compares estimated terrestrial reference frames (TRF) and celestial reference frames (CRF) as well as position time-series in terms of systematic differences, scale, annual signals and station position repeatabilities using four different tropospheric mapping functions (MF): The NMF (Niell Mapping Function) and the recently developed GMF (Global Mapping Function) consist of easy-to-handle stand-alone formulae, whereas the IMF (Isobaric Mapping Function) and the VMF1 (Vienna Mapping Function 1) are determined from numerical weather models. All computations were performed at the Deutsches Geodätisches Forschungsinstitut (DGFI) using the OCCAM 6.1 and DOGS-CS software packages for Very Long Baseline Interferometry (VLBI) data from 1984 until 2005. While it turned out that CRF estimates only slightly depend on the MF used, showing small systematic effects up to 0.025 mas, some station heights of the computed TRF change by up to 13 mm. The best agreement was achieved for the VMF1 and GMF results concerning the TRFs, and for the VMF1 and IMF results concerning scale variations and position time-series. The amplitudes of the annual periodical signals in the time-series of estimated heights differ by up to 5 mm. The best precision in terms of station height repeatability is found for the VMF1, which is 5–7% better than for the other MFs.     

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.     

The extension of the parametrization of the radio source coordinates in geodetic VLBI and its impact on the time series analysis

The radio sources within the most recent celestial reference frame (CRF) catalog ICRF2 are represented by a single, time-invariant coordinate pair. The datum sources were chosen mainly according to certain statistical properties of their position time series. Yet, such statistics are not applicable unconditionally, and also ambiguous. However, ignoring systematics in the source positions of the datum sources inevitably leads to a degradation of the quality of the frame and, therefore, also of the derived quantities such as the Earth orientation parameters. One possible approach to overcome these deficiencies is to extend the parametrization of the source positions, similarly to what is done for the station positions. We decided to use the multivariate adaptive regression splines algorithm to parametrize the source coordinates. It allows a great deal of automation, by combining recursive partitioning and spline fitting in an optimal way. The algorithm finds the ideal knot positions for the splines and, thus, the best number of polynomial pieces to fit the data autonomously. With that we can correct the ICRF2 a priori coordinates for our analysis and eliminate the systematics in the position estimates. This allows us to introduce also special handling sources into the datum definition, leading to on average 30 % more sources in the datum. We find that not only the CPO can be improved by more than 10 % due to the improved geometry, but also the station positions, especially in the early years of VLBI, can benefit greatly.     

Monte Carlo simulations of the impact of troposphere,clock and measurement errors on the repeatability of VLBI positions

Within the International VLBI Service for Geodesy and Astrometry (IVS) Monte Carlo simulations have been carried out to design the next generation VLBI system (“VLBI2010”). Simulated VLBI observables were generated taking into account the three most important stochastic error sources in VLBI, i.e. wet troposphere delay, station clock, and measurement error. Based on realistic physical properties of the troposphere and clocks we ran simulations to investigate the influence of the troposphere on VLBI analyses, and to gain information about the role of clock performance and measurement errors of the receiving system in the process of reaching VLBI2010’s goal of mm position accuracy on a global scale. Our simulations confirm that the wet troposphere delay is the most important of these three error sources. We did not observe significant improvement of geodetic parameters if the clocks were simulated with an Allan standard deviation better than 1 × 10⁻¹⁴ at 50 min and found the impact of measurement errors to be relatively small compared with the impact of the troposphere. Along with simulations to test different network sizes, scheduling strategies, and antenna slew rates these studies were used as a basis for the definition and specification of VLBI2010 antennas and recording system and might also be an example for other space geodetic techniques.     

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.     

差分VLBI测量的一种实现方案

差分VLBI通过交替观测目标天体和参考天体,将共同的误差因素从观测量中扣除,能够实现高精度的相对定位,因而在深空探测中有重要作用.然而,差分VLBI高精度的实现要求目标天体和参考天体的角距很近,这大大限制了其应用.讨论设计了差分VLBI测量的一种实现方案,利用多颗参考源的观测内插出目标源的非几何时延修正,放宽了对目标源和参考源的角距限制.该方案在S波段对目标源非几何时延的修正精度可以达到1 ns水平.     

Short Note: A global model of pressure and temperature for geodetic applications

The empirical model GPT (Global Pressure and Temperature), which is based on spherical harmonics up to degree and order nine, provides pressure and temperature at any site in the vicinity of the Earth’s surface. It can be used for geodetic applications such as the determination of a priori hydrostatic zenith delays, reference pressure values for atmospheric loading, or thermal deformation of Very Long Baseline Interferometry (VLBI) radio telescopes. Input parameters of GPT are the station coordinates and the day of the year, thus also allowing one to model the annual variations of the parameters. As an improvement compared with previous models, it reproduces the large pressure anomaly over Antarctica, which can cause station height errors in the analysis of space-geodetic data of up to 1 cm if not considered properly in troposphere modelling. First tests at selected geodetic observing stations show that the pressure biases considerably decrease when using GPT instead of the very simple approaches applied to various Global Navigation Satellite Systems (GNSS) software packages so far. GPT also provides an appropriate model for the annual variability of global temperature. Electronic supplementary material The online version of this article (doi: contains supplementary material, which is available to authorized users.     

The AUSTRAL VLBI observing program

The AUSTRAL observing program was started in 2011, performing geodetic and astrometric very long baseline interferometry (VLBI) sessions using the new Australian AuScope VLBI antennas at Hobart, Katherine, and Yarragadee, with contribution from the Warkworth (New Zealand) 12 m and Hartebeesthoek (South Africa) 15 m antennas to make a southern hemisphere array of telescopes with similar design and capability. Designed in the style of the next-generation VLBI system, these small and fast antennas allow for a new way of observing, comprising higher data rates and more observations than the standard observing sessions coordinated by the International VLBI Service for Geodesy and Astrometry (IVS). In this contribution, the continuous development of the AUSTRAL sessions is described, leading to an improvement of the results in terms of baseline length repeatabilities by a factor of two since the start of this program. The focus is on the scheduling strategy and increased number of observations, aspects of automated operation, and data logistics, as well as results of the 151 AUSTRAL sessions performed so far. The high number of the AUSTRAL sessions makes them an important contributor to VLBI end-products, such as the terrestrial and celestial reference frames and Earth orientation parameters. We compare AUSTRAL results with other IVS sessions and discuss their suitability for the determination of baselines, station coordinates, source coordinates, and Earth orientation parameters.     

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。     

Advanced relativistic VLBI model for geodesy

Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic purposes. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.     

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.     

Conventions on thermal expansion modelling of radio telescopes for geodetic and astrometric VLBI

Thermal expansion of radio telescopes has long been recognized as an effect which cannot be neglected in geodetic and astrometric VLBI data analysis if millimeter accuracy is desired. In this article, the author documents the conventions which are being set by the International VLBI Service for Geodesy and Astrometry (IVS) for a consistent modelling of this effect in its routine product generation. For the largest telescopes, the annual cycle of thermal expansion may change the height of the VLBI reference point by as much as 20 mm. However, for telescopes which are used in present-day IVS operations, the variations rather range from 4 to 6 mm.     

VLBI观测双线极化条纹拟合方法

提出了一种可用于下一代VLBI观测系统(VGOS)的双线极化条纹拟合方法。现有的VLBI观测模式采用的是右圆极化(RCP),而VGOS系统采用的是双线极化。本文方法包括校正和组合条纹拟合两部分。校正部分选择一颗强源作为参考源,分别得到不同极化方式下的通道时延及相位校正数据,用于目标源的校正。组合条纹拟合部分将4种极化分量的可见度数据组合成伪Stokes分量,通过搜索差分星位角使伪Stokes分量的幅值达到最大,从而获得最终的时延观测量。与单极化条纹拟合相比,组合极化获得的条纹具有更高的信噪比(SNR)及更小的条纹相位弥散度。