人造地球卫星VLBI观测的相对论时延模型

理论研究表明，VLBI观测技术将为空间目标的监测提供一种先进的、有效的技术手段，能够对高空和深空目标进行全天时、全天候的高精度监测定位。以太阳系质心参考系和非旋转地球质心参考系的坐标转换关系为基础，推导了人造地球卫星地面VLBI观测的相对论时间延迟模型，给出了一个通用的解析表达式式(14)，这一公式严格解析又无误差，建议采用本公式。同时详细地讨论了公式的适用范围和各种舍掉项的量级估计，并详细给出了时间延迟理论模型的计算步骤。     

广义相对论框架中有关时间的定义与应用

在完整后牛顿近似下的太阳系质心参考系和地球质心参考系的定义及其转换关系的基础上,研究了在广义相对论框架下各种时间系统(太阳系质心坐标时、地球质心坐标时、太阳系动力学时和地球时)的定义、以及它们的具体实现和相互之间的转换关系,为空间大地测量学的研究提供了明确的时间概念和理论依据.     

广义相对论框架中有关时间的定义与应用

在完整后牛顿近似下的太阳系质心参考系和地球质心参考系的定义及其转换关系的基础上，研究了在广义相对论框架下各种时间系统(太阳系质心坐标时、地球质心坐标时、太阳系动力学时和地球时)的定义、以及它们的具体实现和相互之间的转换关系，为空间大地测量学的研究提供了明确的时间概念和理论依据。     

完整后牛顿近似下原时与坐标时的转换

IAU2000通过了新的时空参考系和时间尺度决议,建议时空坐标理论必须在完整的后牛顿近似下来考虑.基于IAU2000决议,文中研究了在完整后牛顿近似下相对论参考系的基本概念、太阳系质心天球参考系(BCRS)和地球质心天球参考系(GCRS)的定义及其转换公式;推导了原时与坐标时之间的理论关系和严格转换公式.得到的理论公式可为进一步确定或定义相对论框架下的其它时间尺度(例如地球时和太阳系动力学时)提供了严格的理论基础和依据.     

完整后牛顿近似下原时与坐标时的转换

IAU2000通过了新的时空参考系和时间尺度决议，建议时空坐标理论必须在完整的后牛顿近似下来考虑。基于IAU2000决议，文中研究了在完整后牛顿近似下相对论参考系的基本概念、太阳系质心天球参考系(BCRS)和地球质心天球参考系(GCRS)的定义及其转换公式；推导了原时与坐标时之间的理论关系和严格转换公式。得到的理论公式可为进一步确定或定义相对论框架下的其它时间尺度(例如地球时和太阳系动力学时)提供了严格的理论基础和依据。     

两种地心参考系的惯性性质及比较

本文讨论了地心恒星参考系和地心本征参考系的惯性性质,指出在距离地心160公里范围之外的空间,地心恒星参考系的惯性性质优于地心本征参考系。然而,为了研究人造卫星系统内部的某些效应,则以建立原点位于人造卫星质心的卫星本征参考系为佳。     

太阳系质心参考系与地心参考系中的激光测距问题

给出了太阳系质心参考系（BRS）和地心参考系（GRS）中的相对论激光测距理论模型,并且利用现有的坐标变换关系证明两种模型在毫米级的精度上是完全等价的。最后指出,由IERS推荐的坐标变换公式与激光测距模型之间存在不自洽性,这种不自恰性对激光测月（LLR）的影响可达约10cm。     

脉冲星导航的相对论定位法(Ⅱ):4维时空的观测方程

现行X射线脉冲星导航方法中存在两种固有误差,源于推算太阳系质心在当前时刻接收脉冲的相位以及将航天器固有时转换成太阳系质心坐标时。针对这一情况,文章根据相对论定位系统的基本思想和后牛顿引力理论,导出了X射线脉冲星导航的4维观测方程。相对于现行的3维观测方程,新方法只需根据航天器测量脉冲轮廓的相位即可完成航天器定位,不必考虑太阳系质心处的光子到达时间因而不必推算该处观测者在当前时刻的脉冲轮廓相位;也不必进行航天器固有时与质心坐标时的转换因而不必预先估计航天器的运动状态。新方法简单易行,能够有效地减小测量误差,建议在X射线脉冲星导航中取代现行观测方程。     

GPS、VLBI和SLR确定地心坐标的精度分析

为评价GPS、VLBI和SLR这3种空间技术确定地心坐标的真正实现精度,我们把3种技术在并置站上的地心坐标进行了相互比较。经过偏心改正和7个参数的转换后,可获得任意2种技术地心坐标不符值的加权中误差,以此作为外符精度。可以看出,VLBI与GPS地心坐标三分量的外符精度在1cm之内,SLR与VLBI和GPS地心坐标三分量的外符精度在1～3cm之间。表明VLBI和CPS实现的地心坐标精度比SLR高一些,已达毫米级。     

利用VLBI数据进行天顶湿延迟的分析研究

利用VLBI观测数据处理得到的天顶湿延迟数据,分析4个VLBI测站2008年全年的天顶湿延迟的变化规律,给出结果。其次,采用Continuous VLBI 2008国际会议(CONT08)的原始VLBI数据算出天顶湿延迟数据,并与International VLBI Service(IVS)网站上公布的数据以及解算精度进行比较,给出比较结果。     

Geodesy and relativity

Relativity, or gravitational physics, has widely entered geodetic modelling and parameter determination. This concerns, first of all, the fundamental reference systems used. The Barycentric Celestial Reference System (BCRS) has to be distinguished carefully from the Geocentric Celestial Reference System (GCRS), which is the basic theoretical system for geodetic modelling with a direct link to the International Terrestrial Reference System (ITRS), simply given by a rotation matrix. The relation to the International Celestial Reference System (ICRS) is discussed, as well as various properties and relevance of these systems. Then the representation of the gravitational field is discussed when relativity comes into play. Presently, the so-called post-Newtonian approximation to GRT (general relativity theory) including relativistic effects to lowest order is sufficient for practically all geodetic applications. At the present level of accuracy, space-geodetic techniques like VLBI (Very Long Baseline Interferometry), GPS (Global Positioning System) and SLR/LLR (Satellite/Lunar Laser Ranging) have to be modelled and analysed in the context of a post-Newtonian formalism. In fact, all reference and time frames involved, satellite and planetary orbits, signal propagation and the various observables (frequencies, pulse travel times, phase and travel-time differences) are treated within relativity. This paper reviews to what extent the space-geodetic techniques are affected by such a relativistic treatment and where—vice versa—relativistic parameters can be determined by the analysis of geodetic measurements. At the end, we give a brief outlook on how new or improved measurement techniques (e.g., optical clocks, Galileo) may further push relativistic parameter determination and allow for refined geodetic measurements.     

A VLBI Delay Model for Radio Sources at a Finite Distance

A relativistic delay model for Earth-based very long baseline interferometry (VLBI) observation of sources at finite distances is derived. The model directly provides the VLBI delay in the scale of terrestrial time. The effect of the curved wave front is represented by using a pseudo source vector K = (R ₁ + R ₂)/(R ₁ + R ₂), and the variation of the baseline vector due to the difference of arrival time is taken into account up to the second-order by using Halley’s method. The precision of the new VLBI delay model is 1 ps for all radio sources above 100 km altitude from the Earth’s surface in Earth-based VLBI observation. Simple correction terms (parallax effect) are obtained, which can also adopt the consensus model (e.g. International Earth Rotation and Reference Frames Service conventions) to finite-distance radio source at R > 10 pc with the same precision. The new model may enable estimation of distance to the radio source directly with VLBI delay data.     

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.     

ΔVLBI用于“嫦娥一号”地月转移轨道段定轨及EOP解算

推导了基于相对论时空理论的"嫦娥一号"地月转移轨道段差分VLBI(ΔVLBI)的数学模型,在此基础上利用"嫦娥一号"实测的VLBI时延观测量和模拟的河外射电源时延观测量组成了ΔVLBI时延观测量,在参数最优先验精度下解算了不同弧段长度的"嫦娥一号"轨道及地球定向参数(EOP)等未知参数,并根据各参数的解算精度及外符合程度确定了最优观测弧段长度,并分析了该条件下的参数解算精度。     

On a relativistic geodesy

Theoretical formulas for relativistic estimation of geopotential differences are given. The relativistic geoid is defined. A technique for measuring potential differences with high precision clocks (masers or equivalent) is described. The method can operate over arbitrary terrestrial distances. Two clocks are used. The drift between the clocks is estimated by using closed loops. The clocks are used in an operational mode during the whole measuring interval. No satellite links are necessary but VLBI, GPS and ANIK-links can be used in combination with the method.     

VLBI terrestrial reference frame contributions to ITRF2008

In late 2008, the Product Center for the International Terrestrial Reference Frame (ITRF) of the International Earth Rotation and Reference Systems Service (IERS) issued a call for contributions to the next realization of the International Terrestrial Reference System, ITRF2008. The official contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to ITRF2008 consists of session-wise datum-free normal equations of altogether 4,539 daily Very Long Baseline Interferometry (VLBI) sessions from 1979.7 to 2009.0 including data of 115 different VLBI sites. It is the result of a combination of individual series of session-wise datum-free normal equations provided by seven analysis centers (ACs) of the IVS. All series are completely reprocessed following homogeneous analysis options according to the IERS Conventions 2003 and IVS Analysis Conventions. Altogether, nine IVS ACs analyzed the full history of VLBI observations with four different software packages. Unfortunately, the contributions of two ACs, Institute of Applied Astronomy (IAA) and Geoscience Australia (AUS), had to be excluded from the combination process. This was mostly done because the IAA series exhibits a clear scale offset while the solution computed from normal equations contained in the AUS SINEX files yielded unreliable results. Based on the experience gathered since the combination efforts for ITRF2005, some discrepancies between the individual series were discovered and overcome. Thus, the consistency of the individual VLBI solutions has improved considerably. The agreement in terms of WRMS of the Terrestrial Reference Frame (TRF) horizontal components is 1 mm, of the height component 2 mm. Comparisons between ITRF2005 and the combined TRF solution for ITRF2008 yielded systematic height differences of up to 5 mm with a zonal signature. These differences can be related to a pole tide correction referenced to a zero mean pole used by four of five IVS ACs in the ITRF2005 contribution instead of a linear mean pole path as recommended in the IERS Conventions. Furthermore, these systematics are the reason for an offset in the scale of 0.4 ppb between the IVS’ contribution to ITRF2008 and ITRF2005. The Earth orientation parameters of seven series used as input for the IVS combined series are consistent to a huge amount with about 50 μas WRMS in polar motion and 3 μs in dUT1.     

Simulations of VLBI observations of a geodetic satellite providing co-location in space

We performed Monte Carlo simulations of very-long-baseline interferometry (VLBI) observations of Earth-orbiting satellites incorporating co-located space-geodetic instruments in order to study how well the VLBI frame and the spacecraft frame can be tied using such measurements. We simulated observations of spacecraft by VLBI observations, time-of-flight (TOF) measurements using a time-encoded signal in the spacecraft transmission, similar in concept to precise point positioning, and differential VLBI (D-VLBI) observations using angularly nearby quasar calibrators to compare their relative performance. We used the proposed European Geodetic Reference Antenna in Space (E-GRASP) mission as an initial test case for our software. We found that the standard VLBI technique is limited, in part, by the present lack of knowledge of the absolute offset of VLBI time to Coordinated Universal Time at the level of microseconds. TOF measurements are better able to overcome this problem and provide frame ties with uncertainties in translation and scale nearly a factor of three smaller than those yielded from VLBI measurements. If the absolute time offset issue can be resolved by external means, the VLBI results can be significantly improved and can come close to providing 1 mm accuracy in the frame tie parameters. D-VLBI observations with optimum performance assumptions provide roughly a factor of two higher uncertainties for the E-GRASP orbit. We additionally simulated how station and spacecraft position offsets affect the frame tie performance.     

The International VLBI Service for Geodesy and Astrometry (IVS): current capabilities and future prospects

Very Long Baseline Interferometry (VLBI) plays a unique and fundamental role in the maintenance of the global (terrestrial and celestial) reference frames, which are required for precise positioning in many research areas such as the understanding and monitoring of global changes, and for space missions. The International VLBI Service for Geodesy and Astrometry (IVS) coordinates the global VLBI components and resources on an international basis. The service is tasked by the International Association of Geodesy (IAG) and International Astronomical Union (IAU) to provide products for the realization of the Celestial Reference Frame (CRF) through the positions of quasars, to deliver products for the maintenance of the terrestrial reference frame (TRF), such as station positions and their changes with time, and to generate products describing the rotation and orientation of the Earth. In particular, VLBI uniquely provides direct observations of nutation parameters and of the time difference UT1-UTC. This paper summarizes the evolution and current status of the IVS. It points out the activities to improve further on the product quality to meet future service requirements.     

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.