Regularization of geopotential determination from satellite data by variance components

 Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large linear systems. The posterior density function for the variance components, weighting factors and regularization parameters are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach. Received: 5 June 2001 / Accepted: 28 November 2001     

GPS坐标时间序列噪声估计及相关性分析

比较分析了极大似然估计法、最小二乘方差分量估计法以及最小范数二次无偏估计法对GPS站坐标时间序列噪声的估计效果,确定最小范数二次无偏估计法为最优的噪声方差估计方法。在此基础上对中国及其周边区域20个IGS站坐标时间序列中各方向噪声方差进行一元线性回归分析。结果表明,中国及其周边区域IGS站不同方向的噪声间具有中等强度以上的相关性,其中N方向闪烁噪声与其他方向闪烁噪声的相关性要强于白噪声。水平方向的噪声振幅能够解释垂直方向噪声振幅变化的40%~60%,而N方向噪声振幅能够解释E方向噪声振幅变化的60%~80%,获得的线性回归方程具有使用价值。     

GPS、SLR、VLBI联合处理站坐标

采用了GPS、VLBI、SLR三种技术的并置站坐标,计算了三种技术实现的参考框架的转换参数,联合处理得到并置站的坐标并与IERS公布的坐标进行了比较。     

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.     

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).     

VLBI observations of GNSS-satellites: from scheduling to analysis

The possibility of observing satellites with the very long baseline interferometry (VLBI) technique has been discussed for several years in the geodetic community, with observations of either existing satellites of the global navigation satellite systems or of satellites dedicated to realise a space tie. Such observations were carried out using the Australian telescopes in Hobart and Ceduna which, for the first time, integrated all the necessary steps: planning the observations (automated scheduling), correlation of the data and the generation of a series of time delay observables suitable for a subsequent geodetic analysis. We report on the development of new and the adaptation of existing routines for observing and data processing, focusing on technology development. The aim was to use methods that are routinely used in geodetic VLBI. A series of test experiments of up to six hours duration was performed, allowing to improve the observations from session to session and revealing new problems still to be solved. The newly developed procedures and programs now enable more observations. Further development assumed, this bears the prospect of being directly applied to the observation of dedicated space-tie satellites.     

An investigation into the correlations among GNSS observations and their impact on height and zenith wet delay estimation for medium and long baselines

Most stochastic modelling techniques neglect the correlations among the raw un-differenced observations when forming the variance–covariance matrix of the Global Navigation Satellite System (GNSS) observations. Some methods were developed to model these correlations. One such method is the Minimum Norm Quadratic Unbiased Estimator (MINQUE). Studies have shown that MINQUE improves ambiguity resolution, and ultimately, the positioning solution in short baselines. However, its effect in cases of processing with longer baselines and on the estimation of zenith wet delay (ZWD) is somewhat unknown. In this paper, a comparison between the impact of neglecting the correlations among the observations using an elevation-angle-dependent model (EADM) and modelling the correlations using MINQUE on height determination and ZWD for medium and long baselines is carried out. The initial testing was carried out across two Australian GNSS stations with a medium-length baseline throughout a three-week campaign. The results showed that using MINQUE did not resolve the coordinate, height and wet delay components as accurately as the EADM. The results were further verified with two long-baseline campaigns whereby EADM was also able to provide better wet delay estimates. The coordinate results were, however, mixed. Overall, the study concluded that the inclusion of the correlations among the observations, in general, do not improve the resolution of the coordinate and wet delay estimates.     

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。     

基于联邦卡尔曼滤波的月球车联合定位方法

针对月球车定位,设计和推导了一种基于甚长基线干涉测量（very long baseline interferometry,VLBI）和天文导航系统（celestial navigation system,CNS）相结合的月球车联合定位方法,并采用联邦卡尔曼滤波来实现位置信息的最优估计以增强系统的可靠性和容错能力。最后,通过嫦娥-3号（CE-3）实测数据的解算证明了该方法较使用最小二乘法进行联合解算和单独采用VLBI方法定位,可以获得更高的月球车定位精度。同时,也有效地保障了月球车定位的可靠性和稳定性。     

Tropospheric parameters: combination studies based on homogeneous VLBI and GPS data

The combination of tropospheric parameters derived from different space-geodetic techniques has not been of large interest in geodesy so far. However, due to the high correlation between station coordinates and tropospheric parameters, the latter should not be neglected in combinations. This paper deals with the comparison and combination of tropospheric parameters derived from global positioning system (GPS) and very long baseline interferometry (VLBI) observations stemming from a 15-day campaign of continuous VLBI observations in 2002 (CONT02). The observation data of both techniques were processed homogeneously to avoid systematic differences between the solutions. We compared the tropospheric estimates of GPS and VLBI at eight co-location sites and found a very good agreement in the temporal behavior of the tropospheric zenith path delays (ZPD), reflected by correlation factors up to 0.98. Following this, a combination of the tropospheric parameters was performed. We demonstrate that the combination of tropospheric parameters leads to a stabilization of combined station networks. This becomes visible in the improvement of the repeatabilities of the station height components. Furthermore, the potential use of independent data from water vapor radiometers (WVRs) to validate space-technique-derived tropospheric parameters was investigated. Correlation coefficients of 0.95 or better were estimated between the tropospheric parameters of WVR and GPS or VLBI. Additionally, the utility of the tropospheric parameters for validation of local tie vectors was investigated. Both tropospheric zenith delays and tropospheric gradients were found to be very suitable to validate the height component and the horizontal components of the local tie, respectively.     

Centimeter repeatability of the VLBI estimates of European baselines

Summary In the last three years, the European Geodetic Very Long Baseline Interferometry (VLBI) Network has grown to a total of six fixed antennas placed in Germany, Italy, Spain and Sweden, all equipped with the standard geodetic VLBI instrumentation and data recording systems. During this period of time, several experiments have been carried out using this interferometer providing data of very high quality due to the excellent sensitivity and performance of the European stations. The purpose of this paper is to study the consistency of the VLBI geodetic results on the European baselines with respect to the different degrees of freedom in the analysis procedure. In order to complete this study we have made use of both real and simulated data sets, two different software packages (OCCAM 3.0 and CALC 7.4/SOLVE) and a variety of strategies in the data analysis. The results we have obtained show that the repeatability of the VLBI estimates of the baseline lengths in the European network is better than one centimeter, independent of the different analysis methods, and is consistent with the formal error levels expected from the data analysis. This consistency should be enough to produce geophysically significant information in Europe from VLBI data within a relatively short time span.     

THE ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS FOR GPS BASELINE NETWORK BY MINQUE METHOD

This paper studies the estimation of variance and covariance compo-nents for GPS baseline network by MINQUE method.The fundamental rule forselecting variance-covariance model has been presented,and the alternative algo-rithm which simultaneouly estimates fixed variance components and scalled vari-ance components of the distance,azimuth and geodetic height difference for a GPSbaseline vector has been developed.     

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.     

Multi-reference evaluation of uncertainty in earth orientation parameter measurements

Uncertainties in polar motion and length-of-day measurements are evaluated empirically using several data series from the space-geodetic techniques of the global positioning system (GPS), satellite laser ranging (SLR), and very long baseline interferometry (VLBI) during 1997–2002. In the evaluation procedure employed here, known as the three-corner hat (TCH) technique, the signal common to each series is eliminated by forming pair-wise differences between the series, thus requiring no assumed values for the “truth” signal. From the variances of the differenced series, the uncertainty of each series can be recovered when reasonable assumptions are made about the correlations between the series. In order to form the pair-wise differences, the series data must be given at the same epoch. All measurement data sets studied here were sampled at noon (UTC); except for the VLBI series, whose data are interpolated to noon and whose UT1 values are also numerically differentiated to obtain LOD. The numerical error introduced to the VLBI values by the interpolation and differentiation is shown to be comparable in magnitude to the values determined by the TCH method for the uncertainties of the VLBI series. The TCH estimates for the VLBI series are corrupted by such numerical errors mostly as a result of the relatively large data intervals. Of the remaining data sets studied here, it is found that the IGS Final combined series has the smallest polar motion and length-of-day uncertainties.     

USB-VLBI综合快速确定环月飞行器短弧轨道

2006-05-29~2006-06-02,有关单位利用欧空局(ESA)的SMART-1环月飞行器进行了USB-VLBI综合测定轨试验,其中一个重要目标就是考察环月飞行器的短弧快速轨道确定能力。这里对综合测轨数据的精度进行了评估,分析了不同类型测轨数据组合和定轨弧长对短弧定轨和预报的影响。利用5 d测量数据进行统计:VLBI时延的RMS约为1 m,时延率的RMS约为0.25 cm/s,USB测速的RMS约为3~6 cm/s,测距的RMS约为1~3 m。30 min定轨及预报一个环月轨道周期(5 h)位置的RMS约为250 m,速度的RMS约为15 cm/s。     

VLBI在GEO卫星精密定轨中的应用

影响GEO轨道确定精度的原因主要有两方面:一是高轨卫星的几何跟踪条件受到局部测轨网的限制;二是卫星相对于地面的动力学约束信息较弱。利用一个针对GEO卫星的简化动力法定轨的协方差分析模型,研究了联合测距跟踪网和甚长基线干涉测量(VLBI)对定轨精度的改善情况。指出测距系统的校正误差是常规测距跟踪网定轨精度的主要误差源;当附加一条东西向VLBI基线时,仅利用不定期的少量VLBI高精度数据就能够显著改善测距偏差对轨道的影响,从而保证了卫星的整体位置解算精度。     

扩展的Helmert型方差分量估计公式

针对实用中某类观测值可能含有多个方差分量的情况,对现有Helmen型方差分量估计公式进行扩展,指出现有公式就是本文所推公式的特例。新公式从另外一个角度推导,理论和计算还表明它们与MINQUE公式和BIQUE公式的等价性,从而为不同方法的互检提供手段。     

On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs

In this paper, a new geometry index of very long baseline interferometry (VLBI) observing networks, the volume of network V, is examined as an indicator of the errors in the Earth orientation parameters (EOP) obtained from VLBI observations. It has been shown that both EOP precision and accuracy can be well described by the power law σ = aV ^c in a wide range of the network size from domestic to global VLBI networks. In other words, as the network volume grows, the EOP errors become smaller following a power law. This should be taken into account for a proper comparison of EOP estimates obtained from different VLBI networks. Thus, performing correct EOP comparison allows us to investigate accurately finer factors affecting the EOP errors. In particular, it was found that the dependence of the EOP precision and accuracy on the recording data rate can also be described by a power law. One important conclusion is that the EOP accuracy depends primarily on the network geometry and to lesser extent on other factors, such as recording mode and data rate and scheduling parameters, whereas these factors have a stronger impact on the EOP precision.     

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

Summary The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10^–9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.     

利用2006—2015年VLBI数据进行地球定向参数解算与分析

目前正处在下一代甚长基线干涉测量（very long baseline interferometry,VLBI）系统的建设时期。利用维也纳VLBI与卫星软件（Vienna VLBI and satellite software,VieVS）解算了2006—2015年的VLBI数据,得到了10 a的地球定向参数（Earth orientation parameters,EOP）时间序列,并与国际地球自转服务机构的结果进行了对比。利用解算结果得到了10 a的日长变化时间序列,通过傅里叶分析得出了日长变化的短周期、半月周期、月周期、半年周期和周年周期,同时还分析得到了极移序列中的周年项和张德勒周期项以及章动改正序列中的自由核章动项。此次解算工作可为武汉大学卫星台站日后的VLBI数据解析积累一定的经验。