地球参考框架联合解算方法

地球参考框架是地球坐标系统的实现,本文系统介绍了地球参考框架的确定方法,结合ITRF2005参考框架,详细介绍了地球参考框架联合解算的方法,并对地球参考框架的质量分析方法进行了探讨。     

顾及时变的参考框架转换研究

在传统的大地坐标参考框架转换中,参考点都被固定在同一个历元。由于各种地球动力学现象的存在,以大地测量为目的的静态参考系统已不存在,同时随着高精度参考框架的连续观测和测定,参考框架的转化必须顾及时变性。本文讨论了时变参考框架转换中2个互逆的过程,采纳了相似转换中参考点之间的内在约束来克服转换中人为的公式简化和秩亏问题。通过数值计算分析,该方法成功实现了坐标框架之间的转换,并保持了尺度、旋转和平移参数及其变化率精度的独立性。     

坐标参考框架长期解内约束模型

地球参考框架是一切测绘活动、地球科学研究的物理基础。目前,地球参考框架常采用长期解的形式,即利用一组全球分布的基准站在某一参考历元的坐标和速度来表示。由于观测有误差,且各基准站又具有非线性变化,故需要对不同历元的瞬时地球参考框架进行累积,形成稳定的长期参考框架。以不同历元观测数据得到的瞬时参考框架成果为输入,构建了一种基于多历元观测数据建立参考框架长期累积解的融合模型。从坐标转换模型和测站坐标的时变模型出发,详细推导了建立长期解的函数模型,依据该函数模型的秩亏数设计了转换参数的内约束基准。采用2010-08—2014-12的国际全球导航卫星系统服务第2次处理结果进行试算,并与国际地球参考框架2014成果进行了对比。结果表明,X、Y、Z方向标准偏差分别为3.45 ?mm、4.04 mm、2.84 mm,速度精度分别为1.53 mm/a、1.46 mm/a、1.21 mm/a,X、Y、Z方向的加权均方根误差优于3 ?mm。     

The reference frames of Mercury after the MESSENGER mission

We report on recent refinements and the current status for the rotational state models and the reference frames of the planet Mercury. We summarize the performed measurements of Mercury rotation based on terrestrial radar observations as well as data from the Mariner 10 and the MESSENGER missions. Further, we describe the different available definitions of reference systems for Mercury and obtain the corresponding reference frame using data provided by instruments on board MESSENGER. In particular, we discuss the dynamical frame, the principal-axes frame, the ellipsoid frame, as well as the cartographic frame. We also describe the reference frame adopted by the MESSENGER science team for the release of their cartographic products, and we provide expressions for transformations from this frame to the other reference frames.     

Assessment of the possible contribution of space ties on-board GNSS satellites to the terrestrial reference frame

The realization of the international terrestrial reference frame (ITRF) is currently based on the data provided by four space geodetic techniques. The accuracy of the different technique-dependent materializations of the frame physical parameters (origin and scale) varies according to the nature of the relevant observables and to the impact of technique-specific errors. A reliable computation of the ITRF requires combining the different inputs, so that the strengths of each technique can compensate for the weaknesses of the others. This combination, however, can only be performed providing some additional information which allows tying together the independent technique networks. At present, the links used for that purpose are topometric surveys (local/terrestrial ties) available at ITRF sites hosting instruments of different techniques. In principle, a possible alternative could be offered by spacecrafts accommodating the positioning payloads of multiple geodetic techniques realizing their co-location in orbit (space ties). In this paper, the GNSS–SLR space ties on-board GPS and GLONASS satellites are thoroughly examined in the framework of global reference frame computations. The investigation focuses on the quality of the realized physical frame parameters. According to the achieved results, the space ties on-board GNSS satellites cannot, at present, substitute terrestrial ties in the computation of the ITRF. The study is completed by a series of synthetic simulations investigating the impact that substantial improvements in the volume and quality of SLR observations to GNSS satellites would have on the precision of the GNSS frame parameters.     

Local effects of redundant terrestrial and GPS-based tie vectors in ITRF-like combinations

Tie vectors (TVs) between co-located space geodetic instruments are essential for combining terrestrial reference frames (TRFs) realised using different techniques. They provide relative positioning between instrumental reference points (RPs) which are part of a global geodetic network such as the international terrestrial reference frame (ITRF). This paper gathers the set of very long baseline interferometry (VLBI)–global positioning system (GPS) local ties performed at the observatory of Medicina (Northern Italy) during the years 2001–2006 and discusses some important aspects related to the usage of co-location ties in the combinations of TRFs. Two measurement approaches of local survey are considered here: a GPS-based approach and a classical approach based on terrestrial observations (i.e. angles, distances and height differences). The behaviour of terrestrial local ties, which routinely join combinations of space geodetic solutions, is compared to that of GPS-based local ties. In particular, we have performed and analysed different combinations of satellite laser ranging (SLR), VLBI and GPS long term solutions in order to (i) evaluate the local effects of the insertion of the series of TVs computed at Medicina, (ii) investigate the consistency of GPS-based TVs with respect to space geodetic solutions, (iii) discuss the effects of an imprecise alignment of TVs from a local to a global reference frame. Results of ITRF-like combinations show that terrestrial TVs originate the smallest residuals in all the three components. In most cases, GPS-based TVs fit space geodetic solutions very well, especially in the horizontal components (N, E). On the contrary, the estimation of the VLBI RP Up component through GPS technique appears to be awkward, since the corresponding post fit residuals are considerably larger. Besides, combination tests including multi-temporal TVs display local effects of residual redistribution, when compared to those solutions where Medicina TVs are added one at a time. Finally, the combination of TRFs turns out to be sensitive to the orientation of the local tie into the global frame.     

A study on the reference frame consistency in recent Earth gravitational models

All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs, especially when their use is intended for high precision studies. Following the methodology described in an earlier paper by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model, the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae for the assessment of TRF inconsistencies among global geopotential models.     

毫米级地球参考框架动态维持技术研究进展

毫米级地球参考框架的实现需要毫米级的动态维持技术。目前的动态维持技术主要有基于线性速度的线性维持技术、综合考虑基准站非线性运动和地心运动的非线性维持技术以及历元参考框架技术。首先简要总结了线性维持技术的发展现状,从影响机制和坐标时间序列两个角度,围绕坐标非线性变化的建模方法,重点梳理了非线性维持技术的研究进展;然后对历元参考框架的实现过程及其在参考框架维持中的应用进行了介绍;最后基于对现状的分析,提出了实现毫米级地球参考框架动态维持需要解决的几个关键问题。     

On the consistency of the current conventional EOP series and the celestial and terrestrial reference frames

Precise transformation between the celestial reference frames (CRF) and terrestrial reference frames (TRF) is needed for many purposes in Earth and space sciences. According to the Global Geodetic Observing System (GGOS) recommendations, the accuracy of positions and stability of reference frames should reach 1 mm and 0.1 mm year\(^{-1}\), and thus, the Earth Orientation Parameters (EOP) should be estimated with similar accuracy. Different realizations of TRFs, based on the combination of solutions from four different space geodetic techniques, and CRFs, based on a single technique only (VLBI, Very Long Baseline Interferometry), might cause a slow degradation of the consistency among EOP, CRFs, and TRFs (e.g., because of differences in geometry, orientation and scale) and a misalignment of the current conventional EOP series, IERS 08 C04. We empirically assess the consistency among the conventional reference frames and EOP by analyzing the record of VLBI sessions since 1990 with varied settings to reflect the impact of changing frames or other processing strategies on the EOP estimates. Our tests show that the EOP estimates are insensitive to CRF changes, but sensitive to TRF variations and unmodeled geophysical signals at the GGOS level. The differences between the conventional IERS 08 C04 and other EOP series computed with distinct TRF settings exhibit biases and even non-negligible trends in the cases where no differential rotations should appear, e.g., a drift of about 20 \(\upmu \)as year\(^{-1 }\)in \(y_{\mathrm{pol }}\) when the VLBI-only frame VTRF2008 is used. Likewise, different strategies on station position modeling originate scatters larger than 150 \(\upmu \)as in the terrestrial pole coordinates.     

Impact of the VLBA on reference frames and earth orientation studies

The geodetic VLBI community began using VLBA antennas in 1989 for geodesy and astrometry. We examine how usage of the VLBA has improved the celestial reference frame, the terrestrial reference frame, and Earth orientation parameters. Without the VLBA, ICRF2 would have had only 1011 sources instead of 3414. ICRF3 will contain at least 4121 sources, with approximately 70 % or more coming exclusively from VLBA astrometry and geodesy sessions. The terrestrial reference frame is also more stable and precise due to VLBA geodesy sessions. Approximately two dozen geodesy stations that have participated in VLBA sessions show average position formal errors that are \(\sim \)13–14 % better in the horizontal components and \(\sim \)5 % better in the vertical component than would be expected solely from the increased number of observations. Also the Earth orientation parameters obtained from the RDV sessions represent the most accurate EOP series of any of the long-term VLBI session types.     

Transformation between SLR/VLBI and WGS-84 reference frames

In geodetic and geophysical applications of GPS, it is important to realize the ephemerides of the GPS satellites and the coordinates of station positions in a consistent reference system. At present, more than one reference system is being used by various GPS users depending on their specific applications. The WGS-84 and various reference frames based on satellite laser ranging (SLR), very long baseline interferometry (VLBI), or a combination of SLR and VLBI are the most commonly used in high precision geophysical applications. The WGS-84 is widely used in applications which rely on the GPS broadcast ephemeris. Station coordinates estimated in one system may have to be transformed to another for further use or for evaluation/comparison purposes. This paper presents a seven-parameter transformation between the WGS-84 and SLR/VLBI reference frames. The GPS double-differenced phase measurements for two consecutive weeks from a set of five Defense Mapping Agency (DMA) sites (defined in the WGS-84 frame) and from an augmented set of fifteen CIGNET sites (defined in the SLR/VLBI frame) were processed in a least squares estimation scheme to determine station coordinates, from which the transformation parameters were determined. A scale difference of about 0.2 ppm and an orientation difference in longitude of about 31 milliarcseconds were found to be the only parameters of significance between the adopted SLR/VLBI and the WGS-84 frames. Transformation between WGS-84 and the ITRF90 is also included, in which the scale difference is the same as before but the longitude rotation is about 16 mas.     

Comparison of a GPS-defined global reference frame with ITRF2000

The Global Positioning System is a constellation of 24–28 satellites, which can be used to define a global terrestrial reference frame. Daily offsets between a GPS defined frame and ITRF2000 have been estimated using more than a decade of GPS observations from 1990–2001. A linear fit to the full span of data shows agreement between the two frames at the level of –1 ppb and –0.1 ppb/year for scale, 5 mm and 0 mm/year for the X component of center of mass, –2 mm and –3 mm/year for the Y component, and 4 mm and 6 mm/year for the Z component. GPS is a viable tool for defining the global reference frame either alone, or in combination with other geodetic techniques. Electronic Publication     

地球参考标架和动态地球

本文首先对天球参考标架和地球参考标架作了一般叙述。其次较详细地说明地球参考标架究竟是什么,它是如何形成的,直到现在它的发展情况。最后说明了地球参考标架在有关学科中的应用。     

Future global SLR network evolution and its impact on the terrestrial reference frame

Satellite laser ranging (SLR) is an important technique that contributes to the determination of terrestrial geodetic reference frames, especially to the realization of the origin and the scale of global networks. One of the major limiting factors of SLR-derived reference frame realizations is the datum accuracy which significantly suffers from the current global SLR station distribution. In this paper, the impact of a potential future development of the SLR network on the estimated datum parameters is investigated. The current status of the SLR network is compared to a simulated potential future network featuring additional stations improving the global network geometry. In addition, possible technical advancements resulting in a higher amount of observations are taken into account as well. As a result, we find that the network improvement causes a decrease in the scatter of the network translation parameters of up to 24%, and up to 20% for the scale, whereas the technological improvement causes a reduction in the scatter of up to 27% for the translations and up to 49% for the scale. The Earth orientation parameters benefit by up to 15% from both effects.     

Effects of adopting new precession,nutation and equinox corrections on the terrestrial reference frame

First, the paper is devoted to the effects of adopting new definitive precession and equinox corrections on the terrestrial reference frame: The effect on polar motion is a diurnal periodic term with an amplitude increasing linearly in time; on UT1 it is a linear term. Second, general principles are given the use of which can determine the effects of small rotations (such as precession, nutation or equinox corrections) of the frame of a Conventional Inertial Reference System (CIS) on the frame of the Conventional Terrestrial Reference System (CTS). Next, seven CTS options are presented, one of which is necessary to accommodate such rotations (corrections). The last of these options requiring no changes in the origin of terrestrial longitudes and in UT1 is advocated; this option would be maintained by eventually referencing the Greenwich Mean Sidereal Time to a fixed point on the equator, instead of to the mean equinox of date, the current practice. Accommodating possible future changes in the astronomical nutation is discussed in the last section. The Appendix deals with the effects of differences which may exist between the various CTS's and CIS's (inherent in the various observational techniques) on earth rotation parameters (ERP) and how these differences can be determined. It is shown that the CTS differences can be determined from observations made at the same site, while the CIS differences by comparing the ERP's determined by the different techniques during the same time period. Presented at XVIII General Assembly of the International Astronomical Union Patras, Greece, August 17–26, 1982.     

WGS84与ITRF框架间的坐标转换分析

简要介绍了WGS84坐标系和ITRF框架,给出了不同ITRF框架间的坐标转换流程,并利用实例对WGS84与ITRF框架间的转换关系进行了验证分析.结果表明,ITRF2008与WGS84坐标基本一致,但由于ITRF框架的站速度对站坐标的影响与时间成正相关,当需要采用ITRF框架时,应选用最新的国际地球参考框架.     

Rigorous transformation of variance–covariance matrices of GPS-derived coordinates and velocities

With the advances in the field of GPS positioning and the global densification of permanent GPS tracking stations, it is now possible to determine at the highest level of accuracy the transformation parameters connecting various international terrestrial reference frame (ITRF) realizations. As a by-product of these refinements, not only the seven usual parameters of the similarity transformations between frames are available, but also their rates, all given at some epoch t _k . This paper introduces rigorous matrix equations to estimate variance–covariance matrices for transformed coordinates at any epoch t based on a stochastic model that takes into consideration all a priori information of the parameters involved at epoch t _k , and the coordinates and velocities at the reference frame initial epoch t ₀. The results of this investigation suggest that in order to attain maximum accuracy, the agencies determining the 14-parameter transformations between reference frames should also publish their full variance–covariance matrix. Electronic Publication     

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.     

Remarks on Time and Reference Frames

The transformation of the instantaneous terrestrial coordinate system to the mean or average earth-fixed one is parameterized by the polar motion components which are continuously changing in time. Using the non-symmetricity of the connection coefficients connecting the above frames the errors (“misclosures”) are estimated which would be present if the instantaneous frame would be used as the geodetic reference frame.     

基于区域参考框架的GNSS滑坡监测

区域参考框架是实现高精度区域大地形变观测和滑坡灾害长期监测的基础设施。结合活动地块的划分和长期的GNSS观测结果,笔者将我国大陆和海域初步划分为7个“刚性骨架地块”,简称“刚性地块”,拟建立覆盖我国陆海全域的区域参考框架系列:东北、华北、华南、西北、青藏、川滇及南海参考框架。本文介绍了从全球参考框架(IGS14)到区域参考框架的坐标转换方法,并例举了华北参考框架(NChina20)和华南参考框架(SChina20)在滑坡长期监测和滑坡初动自动识别领域的应用。