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.     

Indirect approach to invariant point determination for SLR and VLBI systems: an assessment

We assess the accuracy of some indirect approaches to invariant point (IVP), or system reference point, determination of satellite laser ranging (SLR) and very long baseline interferometry (VLBI) systems using both observed and simulated survey data sets. Indirect IVP determination involves the observation of targets located on these systems during specific rotational sequences and by application of geometrical models that describe the target motion during these sequences. Of concern is that most SLR and VLBI systems have limited rotational freedom thereby placing constraint on the reliability of parameter estimation, including the IVP position. We assess two current approaches to IVP analysis using survey data observed at the Yarragadee (Australia) SLR and the Medicina (Italy) VLBI sites and also simulated data of a large rotationally constrained (azimuth-elevation) VLBI system. To improve reliability we introduce and assess some new geometric conditions, including inter-axis, inter-circle and inter-target conditions, to existing IVP analysis strategies. The error component of a local tie specifically associated with the indirect determination of SLR and VLBI IVP is less than 0.5 mm. For systems with significant rotational limits we find that the inter-axis and inter-circle conditions are critical to the computation of unbiased IVP coordinates at the sub-millimetre level. When the inter-axis and inter-circle geometric conditions are not imposed, we retrieve biased vertical coordinates of the IVP (in our simulated VLBI system) in the range of 1.2–3.4 mm. Using the new geometric conditions we also find that the axis-offset estimates can be recovered at the sub- millimetre accuracy (0.5 mm).     

相对论框架中的VLBI观测模型

本文以太阳系质心参考系为基础推导了VLBI时延和引力延迟的后牛顿表达式;讨论了各天体对VLBI时延的影响量级及其作用范围;并根据地心参考系与太阳系质心参考系的坐标转换关系,给出了地心参考系中的VLBI观测模型。建议采用(25)式和(16)式作为VLBI时延和引力延迟改正的计算公式。     

利用VLBI、SLR技术建立我国地球参考框架

本文首先概述了VLBI、SLR数据的特点,给出了建立地球参考框架的模型;通过对模型中参数的协方差分析,得出了利用10～15个良好分布且具有高精度站坐标的VLBI站就可建立和维持精度为苦干厘米的我国最佳地球参考框架的结论;最后,提出了利用VLBI站和国内现有SLR固定站的并置观测建立我国VLBI/SLR地球参考框架的这一途径,并对此框架的作用进行了探讨。     

VLBI,SVLBI技术用于月球探测器定位的理论模型

"嫦娥一号"为我国的深空探测拉开了序幕,高端的VLBI以及SVLBI技术在我国探测器定位领域中的地位是其他技术无可取代的.以VLBI技术为基础,分别列出利用地而VLBI和空间VLBI观测量两种观测确定月球探测器位置的理论模型,并整理得到间接平差的误差方程.     

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.     

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.     

利用2008～2009年VLBI数据进行日长变化的研究

处理了2008-01～2009-03的VLBI观测数据,提取了日长变化信息,并与IVS网站的结果进行了对比;计算了日长变化的月周期长度和半月周期长度;利用近几年VLBI数据中的日长变化信息绘制日长变化曲线,分析了日长的季节性变化及引起日长变化的因素。     

Evaluation of co-location ties relating the VLBI and GPS reference frames

We have compared the VLBI and GPS terrestrial reference frames, realized using 5 years of time-series observations of station positions and polar motion, with surveyed co-location tie vectors for 25 sites. The goal was to assess the overall quality of the ties and to determine whether a subset of co-location sites might be found with VLBI–GPS ties that are self-consistent within a few millimeters. Our procedure was designed to guard against internal distortion of the two space-geodetic networks and takes advantage of the reduction in tie information needed with the time-series combination method by using the very strong contribution due to co-location of the daily pole of rotation. The general quality of the available ties is somewhat discouraging in that most have residuals, compared to the space-geodetic frames, at the level of 1–2 cm. However, by a careful selection process, we have identified a subset of nine local VLBI–GPS ties that are consistent with each other and with space geodesy to better than 4 mm (RMS) in each component. While certainly promising, it is not possible to confidently assess the reliability of this particular subset without new information to verify the absolute accuracy of at least a few of the highest-quality ties. Particular care must be taken to demonstrate that possible systematic errors within the VLBI and GPS systems have been properly accounted for. A minimum of two (preferably three or four) ties must be measured with accuracies of 1 mm or better in each component, including any potential systematic effects. If this can be done, then the VLBI and GPS frames can be globally aligned to less than 1 mm in each Helmert component using our subset of nine ties. In any case, the X and Y rotations are better determined, to about 0.5 mm, due to the contribution of co-located polar motion.     

流动VLBI天线系统噪声温度及天线效率测量

我国自行研制的第一套流动VLBI系统——DCW—01型流动VLBI测量仪，目前已在国家重大科学工程“中国地壳运动观测网络”中投入使用。在流动VLBI的观测试验中，天线系统噪声温度和天线效率是观测前系统调试和检测的两项重要内容。天线系统噪声温度是衡量流动VLBI观测系统内部噪声程度的特性指标；天线效率反映了天线系统对到达天线能量的刊用率，在很多计算公式中是一个很重要的参数。因此，精确地测量它们的值是进行相关处理和计算的前提。文中结合我国流动VLBI观测站的研制与建设，介绍了流动VLBI测量仪的天线及接收机系统，并详细阐述了其天线系统噪声温度和天线效率的测量。     

利用1985～2010年VLBI数据进行日长变化分析

处理了1985～2010年的VLBI观测数据,提取了日长变化信息,分析了其内符合精度和外符合精度;通过傅立叶分析以及小波分析得出了日长变化的半月周期、月周期、半年周期、周年周期以及更长周期;利用解算出的日长变化信息绘制日长变化积分曲线,分析日长的季节性变化和长期变化,并分析了日长变化因素。     

近三年VLBI观测的数据处理及分析

介绍了标准NGS数据格式与IVS(international VLBI service for geodesy and astrometry)网站公布的新格式之间的差异,将2005~2007年的VLBI数据进行了格式转换,利用由挪威大地测量研究所和澳大利亚地球科学研究所共同开发的OCCAM 6.2软件解算出大地测量参数(Xp,Yp,UT1-UTC、dψ,dε),并在解算过程中,将两种不同的UT1内插模型进行了对比,同时还将解算结果与IERS网站公布的数据进行了对比。     

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.     

空间VLBI观测量估计大地测量参数的模拟计算

介绍了研究空间VLBI在大地测量等领域应用的意义，探讨了空间VLBI的观测量类型、观测模型及其涉及的大地测量所关心的参数；并采用1980～2004年的VLBI观测数据进行了计算，对大地测量所关心的几种参数的计算结果进行了分析。     

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.     

Estimating very high resolution urban surface temperature using a spectral unmixing and thermal mixing approach

Land surface temperature (LST) plays a critical role in characterizing energy exchanges of the Earth's surface and atmosphere. Recent advances in thermal infrared (TIR) remote sensing technology enable the emergence of airborne very-high-resolution (VHR) TIR sensors to identify detailed LST distribution for environmental, geological and urban applications. However, the usage of airborne VHR TIR data may be limited by its high cost, long acquisition period, extensive data processing, etc. A cost-effective alternative could be VHR LST estimation. We proposed a physically based method, referred to as the VHR spectral unmixing and thermal mixing (VHR-SUTM) approach, to estimate LST at the meter level. Particularly, considering both spectral and thermal properties, spectral unmixing was employed to estimate fractional urban compositions for a comprehensive representation of heterogeneous urban surfaces. Further, VHR LST was modeled as a summation of the thermal features of representative urban compositions weighted by their respective abundances. Results suggest a high agreement between the resampled VHR LST estimates and the retrieved LSTs. With relatively high estimation accuracy (RMSE of 2.02 K and MAE of 1.51 K), the VHR-SUTM technique could serve as a promising and practical method for various applications in urban and environment studies.     

Estimation of Geodetic Parameters with VLBI Data of Last 5 Years

The meaning to research the potential of VLBI for geodetic applications is summarized. And the observation models and their related parameters of geodetic interest are investigated. Then, the principle and method of using the random model in VLBI data processing are investigated. With the world wide VLBI data from 2000-2004, the conditions to compute the parameters of geodetic interest are introduced, and so are the computing methods and processes. And the computed results of the parameters of geodetic interest are analyzed.     

A comparison of GPS, VLBI and model estimates of ocean tide loading displacements

In recent years, ocean tide loading displacements (OTLD) have been measured using the Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI). This study assesses the accuracy of GPS measurements of OTLD by comparison with VLBI measurements and estimates derived from numerical ocean tide models. A daily precise point positioning (PPP) analysis was carried out on ∼11 years of GPS data for each of 25 sites that have previous OTLD estimates based on data from co-located VLBI sites. Ambiguities were fixed to integer values where possible. The resulting daily estimates of OTLD, at eight principal diurnal and semi-diurnal tidal frequencies, were combined to give GPS measurements of OTLD at each site. The 3D GPS and VLBI measurements of OTLD were compared with estimates computed (by convolution with Green’s functions) from five modern ocean tide models (CSR4.0, FES2004, GOT00.2, NAO99b and TPXO6.2). The GPS/model agreement is shown to be similar to the VLBI/model agreement. In the important radial direction, the GPS/model misfit is shown to be smaller than the VLBI/model misfit for seven of the eight tidal constituents; the exception being the K2 constituent. Fixing of GPS carrier-phase ambiguities to integer values resulted in a marginal improvement to the GPS/model agreement. Statistically, it is shown there is no significance to the difference between the fit of the GPS and VLBI measurements of OTLD to modelled values. Equally, differences in fit of either the complete set of GPS or VLBI estimates to the five sets of model-derived values cannot be identified with statistical significance. It is thus concluded that, overall, we cannot distinguish between GPS and VLBI measurements of OTLD, and that at the global scale, present ocean tide models are accurate to within the current measurement noise of these techniques.     

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.     

VLBI、卫星网和地面网联合平差的数学模型

本文同时顾及地面网尺度系统误差和卫星网尺度系统误差对各自网点坐标的影响,对联合平差中常用的两种7参数转换模型:Bursa模型和Molodensky模型进行了分析比较,在此基础上,提出了一种新的7参数转换模型;建立了甚长基线(VLBI)、卫星网和地面网联合平差的数学模型,并用模拟数据进行了数值分析,得到了一些有益结论。