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.     

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.     

Monte Carlo simulations of the impact of troposphere,clock and measurement errors on the repeatability of VLBI positions

Within the International VLBI Service for Geodesy and Astrometry (IVS) Monte Carlo simulations have been carried out to design the next generation VLBI system (“VLBI2010”). Simulated VLBI observables were generated taking into account the three most important stochastic error sources in VLBI, i.e. wet troposphere delay, station clock, and measurement error. Based on realistic physical properties of the troposphere and clocks we ran simulations to investigate the influence of the troposphere on VLBI analyses, and to gain information about the role of clock performance and measurement errors of the receiving system in the process of reaching VLBI2010’s goal of mm position accuracy on a global scale. Our simulations confirm that the wet troposphere delay is the most important of these three error sources. We did not observe significant improvement of geodetic parameters if the clocks were simulated with an Allan standard deviation better than 1 × 10⁻¹⁴ at 50 min and found the impact of measurement errors to be relatively small compared with the impact of the troposphere. Along with simulations to test different network sizes, scheduling strategies, and antenna slew rates these studies were used as a basis for the definition and specification of VLBI2010 antennas and recording system and might also be an example for other space geodetic techniques.     

Atmospheric loading corrections at the observation level in VLBI analysis

This paper investigates whether in very long baseline interferometry (VLBI) analysis atmospheric loading corrections should be applied a priori at the observation level or whether it is sufficient to correct for atmospheric loading effects a posteriori by adding constant values per session to the estimated station coordinates. Simulated observations at single stations corresponding to the precise point positioning approach of global navigation satellite systems show that the atmospheric loading effect can be fully recovered by a posteriori corrections, i.e., the height differences between both approaches stay well below 1 mm. However, real global VLBI network solutions with sessions from 1984 to 2008 reveal that the effect of neglected atmospheric loading corrections at the stations is distributed to the other stations in the network, thus resulting in station height differences between solutions with observation level and with a posteriori corrections which can be as large as 10 mm and a ‘damping’ effect of the corrections. As soon as the terrestrial reference frame and the corresponding coordinate time series are determined, it would be conceptually wrong to apply atmospheric loading corrections at the VLBI stations. We recommend the rigorous application of atmospheric loading corrections at the observation level to all stations of a VLBI network because the seven parameters for translation, rotation, and in particular the network-scale of VLBI networks are significantly affected.     

Earth orientation determinations by short duration VLBI observations

Summary In May 1989 and April 1990 the radio telescopes of the Wettzell Geodetic Fundamental Station in Germany and of the Shanghai Observatory near Seshan in China observed two series of daily VLBI experiments of short duration for precise determination of UT1. In 1990 a few experiments were complemented by the Hartebeesthoek Radio Astronomy Observatory in South Africa and the Medicina telescope of the Bologna Istituto di Radioastronomia in Italy. Employing the South African station together with the east-west baseline formed by the observatories of Seshan and Medicina permitted simultaneous determinations of UT1 and polar motion. Here we report on the results of these observations. Comparing the UT1 results with those of the IRIS Intensive series gives a clear indication of the absolute accuracy of such short duration VLBI measurements which is estimated to be of the order of ±60µs.     

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。     

Multiple transit times and least squares for gyroscopic azimuth

Principles of North determination using suspended gyrocompasses are reviewed. Accuracy is evaluated and a procedure with two series of measurements symmetrical with respect to the zero torsion tape position is mathematically proven to be the “best” (minimum variance). Our purpose is to prove that a 20″ accuracy (1 σ) instrument was brought to a level of accuracy four times better by using multiple transit times and least squares fit. Over a total of 15 North determinations based on more than a thousand transit times, an external standard error of 4″.4 was obtained using a WildGAK-1.     

Geodetic VLBI with an artificial radio source on the Moon: a simulation study

We perform extensive simulations in order to assess the accuracy with which the position of a radio transmitter on the surface of the Moon can be determined by geodetic VLBI. We study how the quality and quantity of geodetic VLBI observations influence these position estimates and investigate how observations of such near-field objects affect classical geodetic parameters like VLBI station coordinates and Earth rotation parameters. Our studies are based on today’s global geodetic VLBI schedules as well as on those designed for the next-generation geodetic VLBI system. We use Monte Carlo simulations including realistic stochastic models of troposphere, station clocks, and observational noise. Our results indicate that it is possible to position a radio transmitter on the Moon using today’s geodetic VLBI with a two-dimensional horizontal accuracy of better than one meter. Moreover, we show that the next-generation geodetic VLBI has the potential to improve the two-dimensional accuracy to better than 5 cm. Thus, our results lay the base for novel observing concepts to improve both lunar research and geodetic VLBI.     

Ultra-rapid earth rotation determination with VLBI during CONT11 and CONT14

We present earth rotation results from the ultra-rapid operations during the continuous VLBI campaigns CONT11 and CONT14. The baseline Onsala–Tsukuba, i.e., using two out of the 13 and 17 stations contributing to CONT11 and CONT14, respectively, was used to derive UT1-UTC in ultra-rapid mode during the ongoing campaigns. The latency between a new observation and a new UT1-UTC result was less than 10 min for more than 95% of the observations. The accuracy of the derived ultra-rapid UT1-UTC results is approximately a factor of three worse than results from optimized one-baseline sessions and/or complete analysis of large VLBI networks. This is, however, due to that the one-baseline picked from the CONT campaigns is not optimized for earth rotation determination. Our results prove that the 24/7 operation mode planned for VGOS, the next-generation VLBI system, is possible already today. However, further improvements in data connectivity of stations and correlators as well in the automated analysis are necessary to realize the ambitious VGOS plans.     

A new estimator for VLBI baseline length repeatability

The goal of this paper is to introduce a more effective technique to approximate for the “repeatability–baseline length” relationship that is used to evaluate the quality of geodetic VLBI results. Traditionally, this relationship is approximated by a quadratic function of baseline length over all baselines. The new model incorporates the mean number of observed group delays of the reference radio sources (i.e. estimated as global parameters) used in the estimation of each baseline. It is shown that the new method provides a better approximation of the “repeatability–baseline length” relationship than the traditional model. Further development of the new approach comes down to modeling the repeatability as a function of two parameters: baseline length and baseline slewing rate. Within the framework of this new approach the station vertical and horizontal uncertainties can be treated as a function of baseline length. While the previous relationship indicated that the station vertical uncertainties are generally 4–5 times larger than the horizontal uncertainties, the vertical uncertainties as determined by the new method are only larger by a factor of 1.44 over all baseline lengths.     

Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz

Range and range rate measurements play an important role in geodetic applications of electromagnetic waves (terrestrial as well as from space, including Very Long Baseline Interferometry (VLBI)) Recent developments of measuring, techniques have led to the situation that the measuring accuracy is no longer the limiting factor in the final accuracies of range and range rate measurements. The main error stems now from the influence of the atmosphere and from assumptions and approximations in context with the derivation of refractive index used to describe the wave propagation properties of the atmosphere. Only in the case that the geometrical optics approximation holds is it possible to calculate or to measure range error for wave propagation in the atmosphere of the earth (troposphereand ionosphere) from knowledge of the refractive index as a function of space (location) and time. Otherwise we have to consides additionally scattering and/or diffraction effects. A discussion of the formulae for the refractive indices in the troposphere and in the ionosphere is followed by a review of the propagation of electromagnetic waves described by the geometrical optics approximation and on the limitations, of geometrical optics. A comprehensive discussion of range errors in the non-ionized atmosphere (troposphere) and in the ionosphere follows. For this purpose we use the elevation of the “ray” at a ground station for division into four domains: a) vertical incidence (as a special case), b) elevation between 90° and 30°, c)elevation between 30° and 5°, d) elevation smaller than 5°.     

VLBI技术测月的数学模型探讨

近年各国已纷纷制定测月计划,采用何种技术对月球进行定位,变得尤为重要。本文通过对VLBI技术特点进行分析,VLBI是目前大地测量中精度最高的技术手段,但只适用于深空探测,因为深空射电信号到达地面时,可看作平行信号。本文针对VLBI技术特点及数学模型,对存在不可忽略视差的VLBI测月模型,通过级数展开,解决月面射电信号到达地球时的视差问题,并顾及地球自转得出最终数学模型,通过站间一次差分消除钟差等影响,得出VLBI对近轨天体(月球)表面射电源定位的数学模型。     

THE THEORY AND APPLICATION OF THE STRUCTURE LIGHT ENGINEERING SURVEYING BASED ON A LASER THEODOLITE WITH THREE FREEDOMS OF ROTATION

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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.     

VGOS超宽带观测的首次UT1测量数据处理及分析

在国际甚长基线干涉测量（very long baseline interferometry, VLBI）大地测量与天体测量服务组织协调下,首次利用隶属于VLBI全球观测系统（VLBI global observing system, VGOS）的美国Kokee和德国Wettzell观测站及并置的传统VLBI观测站开展了世界时（universal time, UT1）联合测量试验,观测数据在上海VLBI中心进行了干涉处理。结果表明,VGOS超宽带观测系统的UT1测量精度约为7 μs,并置基线的传统S/X双频系统测量精度约为14 μs,VGOS系统的UT1解算结果优于S/X系统。通过试验建立了从相关处理、相关后处理到UT1参数解算的完整数据处理流程,验证了上海VLBI相关处理机的VGOS数据处理能力,为承担国内和国际VGOS观测数据的相关处理任务奠定了基础。     

Global height datum unification: a new approach in gravity potential space

The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W ₀=62636855.8 m²/s². According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.     

External atmospheric corrections in geodetic very-long-baseline interferometry

Three methods to correct for the atmospheric propagation delay in very-long-baseline interferometry (VLBI) measurements were investigated. In the analysis, the NASA R&D experiments from January 1993 to June 1995 were used. The methods were compared in correcting for the excess propagation delay due to water vapour, the “wet” delay, at one of the sites, the Onsala Space Observatory on the west coast of Sweden. The three methods were: (1) estimating the wet delay using the VLBI data themselves; (2) inferring the wet delay from water vapour radiometer (WVR) data, and (3) using independent estimates based on data from the global positioning system (GPS). Optimum elevation cutoff angles were 22^∘ and 26^∘ when using WVR and GPS data, respectively. The results were found to be similar in terms of reproducibility of the estimated baseline lengths. The shortest baselines tend to benefit from external measurements, whereas the lack of improvement in the longer baselines may be partly due to the large amount of data thrown away when removing observations at low elevation angles. Over a 2 week period of intensive measurements, the two methods using external data showed an overall improvement, for all baseline lengths, compared to the first method. This indicates that there are long-term systematic errors in the wet delay data estimated using WVR and GPS data. Received: 27 October 1998 / Accepted: 20 May 1999     

Single receiver phase ambiguity resolution with GPS data

Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.     

Geodetic constraints from multi-beam laser altimeter crossovers

The round-trip travel time measurements made by spacecraft laser altimeters are primarily used to construct topographic maps of the target body. The accuracy of the calculated bounce point locations of the laser pulses depends on the quality of the spacecraft trajectory reconstruction. The trajectory constraints from Doppler and range radio tracking data can be supplemented by altimetric “crossovers”, to greatly improve the reconstruction of the spacecraft trajectory. Crossovers have been used successfully in the past (e.g., Mars Orbiter Laser Altimeter on Mars Global Surveyor), but only with single-beam altimeters. The same algorithms can be used with a multi-beam laser altimeter, but we present a method using the unique cross-track topographic information present in the multi-beam data. Those crossovers are especially adapted to shallow (small angle) intersections, as the overlapping area is large, reducing the inherent ambiguities of single-beam data in that situation. We call those “swath crossovers”. They prove particularly useful in the case of polar-orbiting spacecraft over slowly rotating bodies, because all the non-polar crossovers have small intersection angles. To demonstrate this method, we perform a simplified simulation based on the Lunar Reconnaissance Orbiter (LRO) and its five-beam Lunar Orbiter Laser Altimeter. We show that swath crossovers over one lunar month can independently, from geometry alone, recover the imposed orbital perturbations with great accuracy (5 m horizontal, < 1 m vertical, about one order of magnitude smaller than the imposed perturbations). We also present new types of constraints that can be derived from the swath crossovers, and designed to be used in a precision orbit determination setup. In future work, we will use such multi-beam altimetric constraints with data from LRO.