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%.     

Influence of subdaily polar motion model on nutation offsets estimated by very long baseline interferometry

This paper studies the connection between the subdaily model for polar motion used in the processing of very long baseline interferometry (VLBI) observations and the estimated nutation offsets. By convention accepted by the International Earth Rotation Service, the subdaily model for polar motion recommended for routine processing of geodetic observations does not contain any daily retrograde terms due to their one-to-one correlation with the nutation. Nevertheless, for a 24-h VLBI solution a part of the signal contained in the polar motion given by the used subdaily model is numerically mistaken for a retrograde daily sidereal signal. This fictitious retrograde daily signal contributes to the estimated nutation, leading to systematic differences between the nutation offsets from VLBI solutions computed with different subdaily polar motion models. We demonstrate this effect using solutions for all suitable 24-h VLBI sessions over a time span of 11 years (2000–2011). By changing the amplitudes of one tidal term in the underlying subdaily model for polar motion and comparing the estimated parameters to the solutions computed with the unchanged subdaily model, the paper shows and explains theoretically the effects produced by the individual subdaily terms on the VLBI nutation estimates.     

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。     

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.     

GPS长基线数据处理的软件实现

GPS长基线数据处理在大地测量和大型精密工程中有广泛的应用,GAMIT等国际高精度GPS数据处理软件虽能满足GPS长基线数据处理的解算精度要求,但操作复杂,且对用户的GPS理论有较高的要求。本文在分析长基线GPS数据处理中各类因素影响及误差消除方法基础上,结合图形用户界面程序设计思想,设计并实现了GPS长基线数据处理软件。经不同长度的基线数据解算结果表明,该软件可实现上千公里基线的解算,基线解算精度高,与GAMIT的解算精度相当,且解算过程自动化程度高,用户操作简单,为大范围高精度GPS数据处理提供了一种简便可行的平台。     

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。     

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     

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.     

数据格式转换中空间参考的变异性分析

不同GIS软件对空间参考的定义在语义上并不完全相同,这就会在数据交换过程中出现空间坐标系前后不一致的情况,从而导致转换结果发生整体偏移。作者以MapInfo通用转换器为平台,针对常用的DXF、SHP、TAB格式进行了多视角的转换实验,对结果进行了详细分析。本文分析认为产生偏移的主要原因是空间参考中的大地基准不匹配,为此提出了两种不同的解决方案:转换过程中由用户指定正确的坐标系避免偏移的产生;对已经完成转换的结果则修改文件头中的坐标参数以修正偏移。     

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.     

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.     

基于自回归法的滑坡监测数据Kalman滤波的应用

介绍了卡尔曼滤波的基本模型,针对运动学方法以监测点位置参数、速率参数为状态向量,以加速度为噪声向量建立观测方程和状态方程的过程比较复杂。把自回归法引入状态方程和观测方程的建立中,并结合某露天矿滑坡动态监测数据分析了模型的应用。结果表明,滤波值和观测值之间差值保持在1～3cm之间,滤波后图像较原观测值图像更为光滑,表明所建模型是合适的,能够反映滑坡动态变化过程,从而为矿滑坡监测预报提供数学工具。     

利用单北斗卫星导航系统建立高精度区域坐标框架的研究与实践

当前区域高精度坐标框架建立严重依赖GPS,利用我国自主研发的北斗卫星导航定位系统(BDS)建立高精度地球参考框架具有重要的战略和现实意义。本文采用基于非差观测值的非差处理模式,单独利用常州基准站(CZCORS)的BDS数据,建立了高精度常州市域坐标框架。将基于单北斗获得的CGCS2000坐标成果与GPS结果进行了比较,两者差异较小,平面和高程方向的平均RMS值分别为3.1和4.2 mm。结果表明,单独使用北斗建立区域参考框架可以满足工程建设的需求,这为北斗系统的推广应用提供了重要的参考依据。     

测站坐标时间序列跳变探测研究及对TRF的影响

针对地球参考架测站坐标残差数据中仍存在一些较大的未被标注的跳变,这会引起该测站坐标和速度因未标注的跳变而估计有误的问题,该文利用广义离群检测(GESD)算法的粗差和野值探测及基于t-检验序贯格局转换分析(STARS)法的跳变探测,更好地剔除了野值、标志出了未被标注的跳变.由于测站坐标时间序列的复杂性,跳变检测的误报率和漏检时有发生,故该文采用了与STARS方法相结合的差值法和人眼观察法综合检测跳变;然后基于上海天文台建立的中国地球自转与地球参考系服务地球参考架和地球定向参数确定软件包,重新进行地球参考框架建立和维持,消除未标注跳变对地球参考框架的不利影响.结果 表明,重新解算的测站坐标残差明显减小,对测站非连续性也有了很好修复,不仅提高了地球参考架精度和稳定性,而且有助于后续周期性信号的拟合和提取.     

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     

Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission.     

Estimating regional deformation from a combination of space and terrestrial geodetic data

We discuss an approach for efficiently combining different types of geodetic data to estimate time-dependent motions of stations in a region of active deformation. The primary observations are analyzed separately to produce loosely constrained estimates of station positions and coordinate system parameters which are then combined with appropriate constraints to estimate velocities and coseismic displacements. We define noninteger degrees of freedom to handle the case of finite constraints and stochastic perturbation of parameters and develop statistical tests for determining compatibility between different data sets. With these developments, we show an example of combining space and terrestrial geodetic data to obtain the deformation field in southern California. Received: 23 January 1997 / Accepted: 30 September 1997