ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16?years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010?ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: ?0.5, ?0.9 and ?4.7?mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3?mm/yr. The estimated formal errors of these parameters are 0.2?mm and 0.2?mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8?mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1?cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2?ppb (8?mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.     

ITRF2008框架下VLBI与GPS确定地心坐标的精度分析

为了解ITRF2008框架下VLBI和GPS两种空间技术确定地心坐标的真正实现精度,在并置站上对VLBI和GPS两种空间技术测定的地心坐标进行了比较,经过偏心改正和七参数转换之后,得到两种空间技术地心坐标不符值的加权中误差,其可以认为是这两种空间技术的真正实现精度,经比较分析这两种地心坐标三个坐标轴方向分量的外符精度都在10mm之内,说明VLBI和GPS确定的地心坐标精度已达到毫米级。     

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。     

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。     

Global sea-level rise and its relation to the terrestrial reference frame

We examined the sensitivity of estimates of global sea-level rise obtained from GPS-corrected long term tide gauge records to uncertainties in the International Terrestrial Reference Frame (ITRF) realization. A useful transfer function was established, linking potential errors in the reference frame datum (origin and scale) to resulting errors in the estimate of global sea level rise. Contrary to scale errors that are propagated by a factor of 100%, the impact of errors in the origin depends on the network geometry. The geometry of the network analyzed here resulted in an error propagation factor of 50% for the Z component of the origin, mainly due to the asymmetry in the distribution of the stations between hemispheres. This factor decreased from 50% to less than 10% as the geometry of the network improved using realistic potential stations that did not yet meet the selection criteria (e.g., record length, data availability). Conversely, we explored new constraints on the reference frame by considering forward calculations involving tide gauge records. A reference frame could be found in which the scatter of the regional sea-level rates was limited. The resulting reference frame drifted by 1.36 ± 0.22? mm/year from the ITRF2000 origin in the Z component and by ?0.44 ± 0.22?mm/year from the ITRF2005 origin. A bound on the rate of global sea level rise of 1.2 to 1.6?mm/year was derived for the past century, depending on the origin of the adopted reference frame. The upper bound is slightly lower than previous estimates of 1.8?mm/year discussed in the IPCC fourth report.     

多普勒系统对历元地球参考框架的影响研究

针对历元地球参考框架在确定站点高频非线性运动和季节性变化方面具有国际地球参考框架不具备的优势问题,该文通过比较两种技术间组合策略建立的多源融合历元地球参考框架的精度,研究DORIS对于多源融合历元地球参考框架的影响。通过基于坐标的法方程叠加方法进行技术内法方程叠加和技术间组合,并利用并置站条件联系不同技术的法方程,从而建立多源融合历元地球参考框架。结果表明,DORIS的引入并不会对多源融合历元地球参考框架的基准定义或其他3种技术站点的点位精度产生较大的影响,同时能够体现4种技术中精度较差的DORIS对于ETRF的精度及稳定性的影响。     

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.     

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 terrestrial and lunar reference frame in lunar laser ranging

The initial value problem and the stability of solution in the determination of the coordinates of three observing stations and four retro-reflectors by lunar laser ranging are discussed. Practical iterative computations show that the station coordinates can be converged to about 1 cm, but there will be a slight discrepancy of the longitudinal components computed by various analysis centers or in different years. There are several factors, one of which is the shift of the right ascension of the Moon, caused by the orientation deviation of the adopted lunar ephemeris, which can make the longitudinal components of all observing stations rotate together along the longitudinal direction with same angle. Additionally, the frame of selenocentric coordinates is stable, but a variation or adjustment of lunar third-degree gravitational coefficients will cause a simultaneous shift along the reflectors' longitudes or rotation around the Y axis. Received: 21 August 1996 / Accepted: 17 November 1998     

利用天测与测地VLBI观测建立天球与地球参考架

本文讨论了利用天测与测地 VLBI观测建立天球与地球参考架过程中所面临的问题及解决的技术途径 ,涉及天球参考架与地球参考架原点与定向的确定、地球参考架时间演变的确定等。并通过实测数据分析与结果比对证明解决途径的有效性。     

ITRF2014参考框架的实现与改进

ITRF2014通过对多种空间大地测量技术解的联合处理,在ITRF2014建立过程中首次对非线性运动建模,包括季节性变化的估计和震后形变(PSD)模型的应用。针对基准定义、输入数据和数据处理策略等方面介绍ITRF2014实现的基本情况,并对之前版本进行优化改进。     

A review of algebraic constraints in terrestrial reference frame datum definition

 Station coordinates are combined with velocities estimated by space geodesy techniques to produce the International Terrestrial Reference System. The input is sets of coordinates and velocities calculated by International Earth Rotation Service analysis centers using space geodesy techniques. The working reference system of individual analysis centers is generally conventionally defined. However, the implications of such processing can have an effect on the resulting combined set. The problem of datum definition as a function of coordinate combinations is reviewed. In particular, the problem of minimum constraints is clearly emphasized and the reference system effect is defined. The goal is to build a process that could be used generally to remove uncertainties in the underlying coordinate system without disturbing the underlying information with additional unnecessary information. Received: 25 January 1999 / Accepted: 20 September 2000     

Sensitivity of UT1 determined by single-baseline VLBI to atmospheric delay model, terrestrial and celestial reference frames

 At the present time, the daily VLBI observations on the Westford-Wettzell baseline is the only continually running VLBI project for studies of high-frequency Earth rotation variations. An analysis of this experiment with regard to the potential errors in the atmospheric delay model and in adopted celestial and terrestrial reference frames is presented in the paper. A new VLBI geometric delay model is applied and an algorithm for global adjustment for this specific single-baseline VLBI developed. The results over three years show discrepancies at the milliarcsecond level between the daily observations and the adopted atmospheric model as well as the combined celestial reference frame. A significant number of these discrepancies are removed by the global adjustment. Received: 19 August 1996; Accepted: 13 September 1996     

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.     

ITRF 2008与ITRF 2014的差异对GNSS数据处理的影响

针对全球导航卫星系统(GNSS)数据处理过程中旧的ITRF 2008参考框架现势性不足及新的ITRF2014框架在数据的数量与质量、参数模型、测站的分布合理性上均有提高等状况,该文以陆态网的最近两年的观测数据为例,对比分析了ITRF2008和ITRF2014框架下各测站的坐标、基线长度、水平速度场的差异,以期为当前高精度GNSS数据处理提供参考。实验表明:两个框架下的成果经基准转换后,测站在X、Y、Z方向的差异均为毫米级;基线差异平均在1 mm以内;水平速度场差值的最大值为5.75(mm·a~(-1)),最小值为-4.88(mm·a~(-1)),平均值为-0.45(mm·a~(-1)),方向上差值的平均值为0.02rad。目前两个框架的差异对一般工程应用基本上可以忽略,但对地震监测的陆态网来说,则必须考虑。     

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.     

On the long-term stability of terrestrial reference frame solutions based on Kalman filtering

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.     

Conventional terrestrial system by VLBI a kinematic approach

The paper examines the potential ofVLBI time delay observables for the establishment and maintenance of a Conventional Terrestrial System (CTS). TheCTS is defined in2-D by the standard epoch positions and velocities of a network of control points located on a spherical reference surface. VLBI time delay observables are sensitive to the rotational motion of theCTS control points with respect to a Conventional Inertial System (CIS) which is represented by a network of radio sources. The motion of a control point with respect to theCIS is partitioned into global and regional components. The global components represent the rotational motion of the sphere with respect to theCIS, while the regional components represent the motion of theCTS points with respect to the sphere.