Strength of long lines in terrestrial geodetic control networks

a knowledge of the à posteriori accuracy of long lines in classical triangulation networks is important not only for establishing the quality of existing primary national control networks, but also for assessing the likely contribution of satellite derived observations. Extensive tests carried out with various networks, ranging from a basic triangulation chain to Block VI of the European Triangulation Network, show definite trends. The à posteriori standard errors of both the scale and the orientation of an adjusted line diminish considerably as the length of the line increases. In the case of medium sized countries, the results compare favourably with those predicted for satellite derived data. The conclusions emphasize the need for great care in the reduction of terrestrial observations and the elimination of all possible systematic errors before proceeding with a least squares adjustment.     

Error model for geodetic positions derived from Doppler satellite observations

Doppler observations of Navy Navigation Satellites have been used to strengthen and extend many terrestrial geodetic networks. The main sources of errors in positions determined from these observations are random error of observations, random and systematic errors in satellite positions due to uncertainties in the gravity field, and biases in the coordinate system in which the satellite ephemeris is given. Effects of uncertainties in the gravity field on station coordinates computed with respect to a precise satellite ephemeris are reduced to about 70 cm after 20 satellite passes are observed, but systematic effects prevent assurance that additional observations will improve the accuracy further. A one part per million reduction in scale must be applied to positions computed with the ephemeris to obtain agreement with terrestrial and other precise determinations of scale. The origin of the system is coincident with the center of mass of the earth to 1 m accuracy but the polar axis may be tilted three to five meters at the earth's surface with respect to coordinate systems upon which star catalogues are based.     

联合平差中大地网定向和尺度系统误差的影响和分离

本文从地面大地网的定向、尺度系统误差的定义及对坐标的影响关系出发,分析了这些系统误差与地面网、卫星网之问转换参数的关系,推导了系统误差对转换参数的影响公式。在此基础上,提出了转换参数的区域性问题,并提出了分离区域性定向误差与尺度比参数的联合平差模型。     

分离系统差的地面网与卫星网之间转换的数学模型及其解算方法

本文分析了地面网所含系统差之后,指出只需要两个参数就可描述地面网的定向系统差。若分别考虑地面水平网的尺度参数K_L和高程网的尺度参数K_H,则地面网与卫星网间转换的数学模型中参数的个数为10个。若假定K_L=K_H,则参数需要9个。导出了含有9个和10个未知参数的模型。提出采用部分参数带权的相关平差法解决九参数和十参数模型的法方程式系数阵秩亏问题。最后,利用我国实际数据检核了这些模型。计算表明,这种方法能有效地将坐标系的定向参数和地面网的定向系统差参数分开。揭示了我国地面水平网的尺度参数与高程网的尺度参数不一致,并给出了它们的参考值。     

The accuracy of astronomic azimuth determinations

Astronomic azimuths are used in classical geodesy, through the Laplace equation, to control the orientation of geodetic networks. The method most commonly used by the United States National Geodetic Survey for the determination of astronomic azimuth is often referred to as the “direction method”, and is based on observations of Polaris at any hour angle. We have analyzed repeat determinations, by analysis of variance (ANOVA) techniques, to derive realistic estimates of the expected accuracy of typical astronomic azimuths to be used in the readjustment of the North American Datum. We found that the dominant errors are systematic in nature, with a very important source being observer bias, or “personal equation”. We were unable to decompose the remaining systematic error, which presumably consists primarily of instrument biases, anomalous refraction, and setup errors. We found, from an analysis of determinations that were first corrected for observer bias, an increase in the variance of repeat azimuth determinations as a function of latitude that agrees reasonably well with theoretical expectations.     

VLBI、卫星网和地面网联合平差的数学模型

本文同时顾及地面网尺度系统误差和卫星网尺度系统误差对各自网点坐标的影响,对联合平差中常用的两种7参数转换模型:Bursa模型和Molodensky模型进行了分析比较,在此基础上,提出了一种新的7参数转换模型;建立了甚长基线(VLBI)、卫星网和地面网联合平差的数学模型,并用模拟数据进行了数值分析,得到了一些有益结论。     

The impact of errors in polar motion and nutation on UT1 determinations from VLBI Intensive observations

The earth’s phase of rotation, expressed as Universal Time UT1, is the most variable component of the earth’s rotation. Continuous monitoring of this quantity is realised through daily single-baseline VLBI observations which are interleaved with VLBI network observations. The accuracy of these single-baseline observations is established mainly through statistically determined standard deviations of the adjustment process although the results of these measurements are prone to systematic errors. The two major effects are caused by inaccuracies in the polar motion and nutation angles introduced as a priori values which propagate into the UT1 results. In this paper, we analyse the transfer of these components into UT1 depending on the two VLBI baselines being used for short duration UT1 monitoring. We develop transfer functions of the errors in polar motion and nutation into the UT1 estimates. Maximum values reach 30 [μs per milliarcsecond] which is quite large considering that observations of nutation offsets w.r.t. the state-of-the-art nutation model show deviations of as much as one milliarcsecond.     

Affine distortion of small GPS networks with large height differences

GPS is a promising tool for real-time monitoring of deformations of slopes or large structures. However, remaining systematic effects in GPS phase observations after double differencing and application of a priori models affect the resulting coordinates. They complicate the proper separation of the actual deformations from pseudo-deformations induced by the systematic effects. This paper shows that for small monitoring networks (baseline lengths <5 km) only affine distortions of the network geometry are generated by the remaining distance dependent systematic effects, e.g. unmodelled tropospheric and ionospheric propagation effects, or satellite orbit errors. Hence, a generic correction model is given by a three-dimensional affine transformation involving a maximum of 12 transformation parameters. For the determination of these parameters, four high quality GPS stations are necessary which are not affected by the actual deformations to be monitored. Based on the analysis of network geometries of synthetic GPS networks with large height differences and considering the physics of the GPS observations it is shown, however, that less than 12 parameters are sufficient for the computation of the corrections. The proposed 8 parameter model was applied to the GPS monitoring network of the Gradenbach landslide. For this small network with large height differences, it was shown that the distortions can be reduced by about 75%.     

GPS空间基线向量网与地面控制网的联合平差模型

利用全球定位系统(GPS)所建立的空间基线向量网,对于改善已有地面网,分析网的系统误差和进行地球动力学的监测等具有广泛的意义。本文着重讨论了上述空间基线向量网和地面控制网的三维联合平差和二维联合平差的方法和模型。指出,为了避免地面网高程误差以及引入地面网尺度因子的模型误差对三维联合平差结果的影响,在二维大地坐标系统中进行上述两网联合平差的方法具有重要的现实意义。     

Improved GRACE science results after adjustment of geometric biases in the Level-1B K-band ranging data

The GRACE (Gravity Recovery and Climate Experiment) satellite mission relies on the inter-satellite K-band microwave ranging (KBR) observations. We investigate systematic errors that are present in the Level-1B KBR data, namely in the geometric correction. This correction converts the original ranging observation (between the two KBR antennas phase centers) into an observation between the two satellites’ centers of mass. It is computed from data on the precise alignment between both satellites, that is, between the lines joining the center of mass and the antenna phase center of either satellite. The Level-1B data used to determine this alignment exhibit constant biases as large as 1–2 mrad in terms of pitch and yaw alignment angles. These biases induce non-constant errors in the Level-1B geometric correction. While the precise origin of the biases remains to be identified, we are able to estimate and reduce them in a re-calibration approach. This significantly improves time-variable gravity field solutions based on the CNES/GRGS processing strategy. Empirical assessments indicate that the systematic KBR data errors have previously induced gravity field errors on the level of 6–11 times the so-called GRACE baseline error level. The zonal coefficients (from degree 14) are particularly affected. The re-calibration reduces their rms errors by about 50%. As examples for geophysical inferences, the improvement enhances agreement between mass variations observed by GRACE and in-situ ocean bottom pressure observations. The improvement also importantly affects estimates of inter-annual mass variations of the Antarctic ice sheet.     

An evaluation of some systematic error sources affecting terrestrial gravity anomalies

Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination. Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system. These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data. In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air gravity anomalies of about −0.10 mgal which value is nearly constant over the continent     

Performance of three types of Stokes's kernel in the combined solution for the geoid

When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best source of this information. Received: 11 August 1997 / Accepted: 18 August 1998     

The impact of celestial pole offset modelling on VLBI UT1 intensive results

Very Long Baseline Interferometry (VLBI) Intensive sessions are scheduled to provide operational Universal Time (UT1) determinations with low latency. UT1 estimates obtained from these observations heavily depend on the model of the celestial pole motion used during data processing. However, even the most accurate precession- nutation model, IAU 2000/2006, is not accurate enough to realize the full potential of VLBI observations. To achieve the highest possible accuracy in UT1 estimates, a celestial pole offset (CPO), which is the difference between the actual and modelled precession-nutation angles, should be applied. Three CPO models are currently available for users. In this paper, these models have been tested and the differences between UT1 estimates obtained with those models are investigated. It has been shown that neglecting CPO modelling during VLBI UT1 Intensive processing causes systematic errors in UT1 series of up to 20 μas. It has been also found that using different CPO models causes the differences in UT1 estimates reaching 10 μas. Obtained results are applicable to the satellite data processing as well.     

On the meaning of geodetic orientation

After deriving models for changes of coordinates and azimuths due to rotations, the investigation considers methods for modeling terrestrial orientation in adjustments of geodetic networks. If a misorientation of a geodetic network exists, this can be due to systematic errors in astronomic longitude or in astronomic azimuth, or in both. A separation of these two effects is not possible in practice. The initial azimuth at the datum origin contributes to the orientation only as much as any other azimuth of the same weight.     

绝对重力与相对重力混合平差的基准及质量控制

绝对重力与相对重力测量混合平差是综合利用各种重力测量资料确定重力网基准，提高重力网综合质量的有效途径，文中首先从重力观测的系统误差入手，讨论重力网平差的函数模型；进而根据两类重力观测信息对重力基准的贡献，分析了不同平差方法所对应的各类基准及基统计意义与可靠性；最后对重力网平差的质量控制方法进行了讨论。     

An improved and extended GPS-derived 3D velocity field of the glacial isostatic adjustment (GIA) in Fennoscandia

We present a new GPS-derived 3D velocity field for the Fennoscandia glacial isostatic adjustment (GIA) area. This new solution is based upon ∼3,000 days of continuous GPS observations obtained from the permanent networks in Fennoscandia. The period encompasses a prolongated phase of stable observation conditions after the northern autumn of 1996. Several significant improvements have led to smaller uncertainties and lower systematic errors in the new solutions compared to our previous results. The GPS satellite elevation cut-off angle was lowered to 10°, we fixed ambiguities to integers where possible, and only a few hardware changes occurred over the entire network. The GAMIT/GLOBK software package was used for the GPS analysis and reference frame realization. Our new results confirmed earlier findings of maximum discrepancies between GIA models and observations in northern Finland. The reason may be related to overestimated ice-sheet thickness and glaciation period in the north. In general, the new solutions are more coherent in the velocity field, as some of the perturbations are now avoided. We compared GPS-derived GIA rates with sea-level rates from tide-gauge observations, repeated precise leveling, and with GIA model computations, which showed consistency.     

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     

On the adjustment of combined GPS/levelling/geoid networks

A detailed treatment of adjustment problems in combined global positioning system (GPS)/levelling/geoid networks is given. The two main types of `unknowns' in this kind of multi-data 1D networks are usually the gravimetric geoid accuracy and a 2D spatial field that describes all the datum/systematic distortions among the available height data sets. An accurate knowledge of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to a local vertical datum. Two modelling alternatives for the correction field are presented, namely a pure deterministic parametric model, and a hybrid deterministic and stochastic model. The concept of variance component estimation is also proposed as an important statistical tool for assessing the actual gravimetric geoid noise level and/or testing a priori determined geoid error models. Finally, conclusions are drawn and recommendations for further study are suggested. Received: 9 September 1998 / Accepted: 8 June 1999     

Deterministic and stochastic parameters in inertial survey adjustment

In the adjustment of inertial position surveys the additional parameters describing the systematic errors of individual traverses can be considered as deterministic or stochastic. The paper deals with various aspects of the deterministic or stochastic approach by way of a standard functional model. If purely deterministic parameters are set up, the solvability of the least squares problem depends on redundant observations like coordinate discrepancies of forward and backward runs or coordinate differences at cross-over points of traverse networks. Inequalities are presented to handle the configuration problem for any net and for several ways of introducing parameter sets. Also condition equations being geometrically explainable are developed solving the datum problem in free adjustment applications. Based on the Ebersberger Forst campaigns with a large amount of Ferranti, Honeywell and Litton data, numerical investigations into the stochastic properties of the additional parameters and the observations follow. It turns out that additional parameters for Honeywell and Litton data can be considered as stochastic parameters while for Ferranti data significant azimuth and time dependent effects can be found. The investigations of true errors show that in case of the deterministic adjustment approach a diagonal covariance matrix can be introduced and in case of stochastic additional parameters a first order Gauss-Markov process serves as a good approximation for the stochastic behaviour of the observations.