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     

Multi-technique comparisons of 10?years of wet delay estimates on the west coast of Sweden

We present comparisons of 10-year-long time series of the atmospheric zenith wet delay (ZWD), estimated using the global positioning system (GPS), geodetic very long baseline interferometry (VLBI), a water vapour radiometer (WVR), radiosonde (RS) observations, and the reanalysis product of the European Centre for Medium-Range Weather Forecasts (ECMWF). To compare the data sets with each other, a Gaussian filter is applied. The results from 10 GPS–RS comparisons using sites in Sweden and Finland show that the full width at half maximum at which the standard deviation (SD) is a minimum increases with the distance between each pair. Comparisons between three co-located techniques (GPS, VLBI, and WVR) result in mean values of the ZWD differences at a level of a few millimetres and SD of less than 7?mm. The best agreement is seen in the GPS–VLBI comparison with a mean difference of ?3.4?mm and an SD of 5.1?mm over the 10-year period. With respect to the ZWD derived from other techniques, a positive bias of up to ~7?mm is obtained for the ECMWF reanalysis product. Performing the comparisons on a monthly basis, we find that the SD including RS or ECMWF varies with the season, between 3 and 15?mm. The monthly SD between GPS and WVR does not have a seasonal signature and varies from 3 to 7?mm.     

Atmospheric modelling in GPS analysis and its effect on the estimated geodetic parameters

Permanently operating Global Positioning System (GPS) receivers are used today, for example, in precise positioning and determination of atmospheric water vapour content. The GPS signals are delayed by various gases when traversing the atmosphere. The delay due to water vapour, the wet delay, is difficult to model using ground surface data and is thus often estimated from the GPS data. In order to obtain the most accurate results from the GPS processing, a modelling of the horizontal distribution of the wet delay may be necessary. Through simulations, three such models are evaluated, one of which is developed in this paper. In the first model the water vapour is assumed to be horizontally stratified, thus the wet delay can be described by only one zenith parameter. The second model gives the wet delay with one zenith and two horizontal gradient parameters. The third model uses the correlation between the wet-delay values in different directions. It is found that for large gradients and strong turbulence the two latter models yield lower errors in the estimated vertical coordinate and wet-delay parameters. For large gradients this improvement is up to 7 mm in the zenith wet-delay parameter, from 9 mm down to 2 and 4 mm for the second and third models, respectively. Received: 7 May 1998 / Accepted: 1 March 1999     

利用一维变分同化方法从地基GPS相位延迟中获取大气折射率

GPS信号相位延迟中包含很多大气信息,通过一定的方法可以从中获取有价值的大气参数。基于地基GPS相位延迟数据,提出了一种结合经验模式的一维变分同化获取大气折射率的方法。利用GPS相位延迟模拟数据进行同化试验,讨论了背景误差的设置对同化结果的影响,采用实测个例对该方法进行了验证。结果表明,该一维变分同化方法可行,并可获取高精度的0~60 km大气折射率。低层大气背景误差设置的准确程度会对整个高度范围内的同化效果产生影响。首次将同化获取的大气折射率应用于无线电波折射修正,取得了很好的修正效果,修正精度可达1 mm量级。     

Strategies for spatial and temporal extrapolation and interpolation of wet delay

. The excess radio-path delay due to the atmospheric water vapor, the wet delay, can be derived from water vapor radiometer (WVR) measurements. WVR data used for external calibration of space geodetic measurements are not always acquired in the directions of the space geodetic signal sources, thus extrapolation and interpolation methods for the wet delay are needed. We evaluate three different methods using approximately 10 days of WVR measurements. Two methods, the gradient method and turbulence method, use the directional information in the data, while the third method used is linear regression in time regardless of the direction of the observations. The turbulence method yielded at least 10% less RMS estimation error than the errors from the other two methods. Received: 20 May 1997 / Accepted: 15 December 1997     

Improvement in PWV estimation from GPS due to the absolute calibration of antenna phase center variations

Climatology of column-integrated atmospheric water vapor over Spain has been carried out by means of three techniques: soundings, sun photometers and GPS receivers. Comparing data from stations equipped with more than one of these instruments, we found that a large discontinuity occurred on November 6, 2006, in the differences between the data series from GPS receivers and those from the other two techniques. Prior to that date, the GPS data indicate a wet bias of 2–3 mm for all stations when compared with sounding or photometer data, whereas after that date this bias practically reduces to zero. The root mean square error also decreases about half of its value. On November 6, 2006, the International GNSS Service adopted an absolute calibration model for the antennas of the GPS satellites and receivers instead of the relative one. This change is expected to be an improvement, increasing the accuracy of station position determination and consequently benefiting post-processing products such as zenith total delay from which the atmospheric water vapor content is calculated.     

An Improved Mean-Gravity Model for GPS Hydrostatic Delay Calibration

The determination of global positioning system (GPS) heights with submillimeter accuracy needs proper correction of tropospheric delay. In this letter, the modeling of zenith hydrostatic delay (ZHD) was addressed, considering that wet delay must be treated separately. ZHD is traditionally estimated from Saastamoinen's formula using a mean-gravity model and surface pressure observations. The uncertainty in ZHD associated with the mean-gravity model is about 0.3 mm. An improved parametric model is derived here, which yields an uncertainty in the ZHD less than 0.1 mm when the surface altitude lies in the range of 0-9 km. A second parametric model is derived for higher altitudes (such as above radiosonde observations or atmospheric models). Both parametric models depend on latitude, height, and time variables. This dependence is due to the link between the mean gravity and temperature profiles between the surface and ~80-km altitude. The uncertainty in the parametric models due to short-term temporal variability of the temperature profiles is shown to produce an uncertainty in ZHD smaller than 0.1 mm     

地基GPS遥感大气水汽含量的误差分析

讨论并分析了利用地基ＧＰＳ遥感大气水汽含量时的误差源及其数值评估。其误差来自三个方面：一是计算ＧＰＳ讯号传输时间中湿延迟的误差;二是将该湿延迟转换为大气水汽含量公式中测定转换因子的误差;三是转换模型的误差。     

First comparisons of precipitable water vapor estimation using GPS and water vapor radiometers at the Royal Observatory of Belgium

We compare precipitable water vapor (PWV) time series measured by water vapor radiometers (WVRs) to PWV time series estimated using global positioning system (GPS) observations in a regional network of stations in western Europe. Inside this network, we focus on the baseline Brussels – Wettzell which presents the advantage to have the collocation of a GPS receiver and a WVR at both endpoints. The comparison between our GPS and WVR estimations of precipitable water vapor shows an agreement at the millimeter level. In addition, we show that the zenith total delay (ZTD) estimations computed with our GPS processing strategy agrees with the GPS estimations of ZTD done by the CODE analysis center at the millimeter level. Electronic Publication     

Interferometric Baseline Performance Estimations for Multistatic Synthetic Aperture Radar Configurations Derived from GRACE GPS Observations

Recent studies have demonstrated the usefulness of global positioning system (GPS) receivers for relative positioning of formation-flying satellites using dual-frequency carrier-phase observations. The accurate determination of distances or baselines between satellites flying in formation can provide significant benefits to a wide area of geodetic studies. For spaceborne radar interferometry in particular, such measurements will improve the accuracy of interferometric products such as digital elevation models (DEM) or surface deformation maps. The aim of this study is to analyze the impact of relative position errors on the interferometric baseline performance of multistatic synthetic aperture radar (SAR) satellites flying in such a formation. Based on accuracy results obtained from differential GPS (DGPS) observations between the twin gravity recovery and climate experiment (GRACE) satellites, baseline uncertainties are derived for three interferometric scenarios of a dedicated SAR mission. For cross-track interferometry in a bistatic operational mode, a mean 2D baseline error (1σ) of 1.4 mm is derived, whereas baseline estimates necessary for a monostatic acquisition mode with a 50 km along-track separation reveal a 2D uncertainty of approximately 1.7 mm. Absolute orbit solutions based on reduced dynamic orbit determination techniques using GRACE GPS code and carrier-phase data allows a repeat-pass baseline estimation with an accuracy down to 4 cm (2D 1σ). To assess the accuracy with respect to quality requirements of high-resolution DEMs, topographic height errors are derived from the estimated baseline uncertainties. Taking the monostatic pursuit flight configuration as the worst case for baseline performance, the analysis reveals that the induced low-frequency modulation (height bias) fulfills the relative vertical accuracy requirement (σ<1 m linear point-to-point error) according to the digital terrain elevation data level 3 (DTED-3) specifications for most of the baseline constellations. The use of a GPS-based reduced dynamic orbit determination technique improves the baseline performance for repeat-pass interferometry. The problem of fulfilling the DTED-3 horizontal accuracy requirements is still an issue to be investigated. DGPS can be used as an operational navigation tool for high-precision baseline estimation if a geodetic-grade dual-frequency spaceborne GPS receiver is assumed to be the primary instrument onboard the SAR satellites. The possibility of using only single-frequency receivers, however, requires further research effort.Deutsche Forschungsgemeinschaft (DFG) research fellow until Sept. 2004 at the Microwaves and Radar Institute, Deutsche Zentrum für Luft- und Raumfahrt (DLR) e.V., 82234 Weßling, Germany     

A case study of using Raman lidar measurements in high-accuracy GPS applications

This paper investigates the impact of rapid small-scale water vapor fluctuations on GPS height determination. Water vapor measurements from a Raman lidar are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four short observing sessions (6 h) during the VAPIC experiment (15 May–15 June 2004). The retrieval of wet delays from our Raman lidar is shown to agree well with radiosonde retrievals (bias and standard deviation (SD) were smaller than 1 and 2.8 mm, respectively) and microwave radiometers (from two different instruments, bias was 6.0/−6.6 mm and SD 1.3/3.8 mm). A standard GPS data analysis is shown to fail in accurately reproducing fast zenith wet delay (ZWD) variations. The ZWD estimates could be improved when mean post-fit phase residuals were removed. Several methodologies for integrating zenith lidar observations into the GPS data processing are also presented. The final method consists in using lidar wet delays for correcting a priori the GPS phase observations and estimating a scale factor for the lidar wet delays jointly with the GPS station position. The estimation of this scale factor allows correcting for a mis-calibration in the lidar data and provides in the same way an estimate of the Raman lidar instrument constant. The agreement of this constant with an independent determination using radiosonde data is at the level of 1–4%. The lidar wet delays were derived by ray-tracing from zenith pointing measurements: further improvement in GPS positioning is expected from slant path lidar measurements that would properly account for water vapor anisotropy.     

中长距离网络RTK大气延迟的Kriging插值方法研究

利用普通Kriging插值的指数函数模型和高斯函数模型,精密地实时估计网络RTK中用户站每一历元的大气延迟。利用一个含6个参考站的GPS网络(参考站间距为38.8～132.7km)的观测数据进行了实验,结果表明,对于长度为79.1km的基线的双差电离层延迟和双差对流层延迟,相应的Kriging插值(指数模型和高斯模型)的精度一般可达2cm和5cm,这表明普通Kriging插值可用于网络RTK用户站的大气延迟内插。     

利用BDS数据反演大气可降水量及其精度分析

随着GAMIT软件版本的不断更新,对BDS数据基线解算已成为可能。本文提出了一种基于GAMIT软件的BDS大气可降水量反演方法,并对利用探空数据计算得到的大气可降水量与GPS数据反演结果进行精度验证。结果表明,通过BDS反演得到的大气可降水量与探空数据计算结果之间的平均相对误差、均方根误差均小于2 mm,相关系数大于0.98;与GPS反演结果之间的平均相对误差、均方根误差均小于3 mm,相关系数大于0.96。BDS反演结果精度较高,基本能够满足气象需要。     

A proposed GPS method with multi-antennae and single receiver

A method based on multi-antennae linked to a common GPS receiver is proposed. The goal of the technique is to improve height determination for baselines a few kilometres in length. The advantage of this technique resides in the elimination of relative clock parameters in the between-antenna single difference observations. Because single difference observations are free of clock errors more geometrical strength remains to determine the baseline components. This statement is valid as long as intercable biases can be carefully calibrated. For millimetre height determination, the intercable calibration must be done at the same level of accuracy. Under this assumption it is shown that in general the height standard deviation improves by a factor of about three compared to standard GPS data processing. With the proposed method, the effect of relative tropospheric zenith delay errors becomes a bit smaller (in absolute value), compared to standard data processing. To absorb this error, a relative tropospheric zenith delay parameter may be estimated. Even with this additional parameter in the solution the height standard deviation remains two times smaller than the results of standard processing techniques (without tropospheric zenith delay parameter), and at least five times smaller than in the results obtained from standard processing including one tropospheric zenith delay parameter.     

GPS单点测速的误差分析及精度评价 (英文)

Error sources which decrease the accuracy of GPS in absolute velocity determination have been changed since SA was turned off. Firstly, quantities of all kinds of error sources that influence velocity determination are analyzed. The potential accuracy of GPS absolute velocity determination is derived from both theory and field GPS data simulation. After that, two tests were carried out to evaluate the performance of GPS absolute velocity determination in the case of a static and an airborne GPS receiver and INS （Inertial Navigation System） instrument in kinematic mode. In static mode, the receiver velocity has been estimated to be several mm/s with the carrier-phase derived Doppler measurements, and several cm/s with the receiver generated Doppler measurements. In kinematic mode, GPS absolute velocity estimates are compared with the synchronized measurements from the high accuracy INS. The root mean square statistics of the velocity discrepancies between GPS and INS come up to dm/s. Moreover, it has a strong correlation with the acceleration or jerk of the aircraft.     

顾及双差残差反演GPS信号方向的斜路径水汽含量

给出了顾及GPS双差残差反演斜路径水汽SWV的解算流程;然后详细给出了双差残差到非差残差的转化算法,并对算法进行了改进;最后利用并址的GPS和WVR实测数据对反演SWV算法进行了验证,结果证实改进的反演算法能以优于4 mm精度近实时估算SWV值,与目前国际研究精度在同一量级。     

GPS单点测速的误差分析及精度评价

首先从理论和实测数据模拟两方面分析了SA取消后各类误差源对GPS测速的影响,推导并计算了GPS单点测速可能达到的精度水平。然后用静态数据模拟动态测速试验和实测动态数据测速与同步高精度惯导测速的动态试验进行验证。结果表明,采用载波相位导出的多普勒观测值使用静态数据模拟动态测速,其精度可以达到mm/s级;用接收机输出的多普勒观测值进行测速时,其精度为cm/s级。在动态测速试验中,GPS单点测速方法(即多普勒观测值测速与导出多普勒观测值测速)间的符合精度达到cm/s级,与高精度的惯导测速结果的符合精度为dm/s级,而且和运动载体的动态条件(如加速度和加速度变化率的大小)具有很强的相关性。     

MODIS水汽反演用于InSAR大气校正的理论研究

大气效应尤其是大气水汽的影响是InSAR干涉测量中主要的误差源和限制因素之一,因此高精度的InSAR应用迫切需要及时掌握大气水汽含量及其时空变化。本文深入分析了利用MODIS的水汽反演结果进行InSAR干涉测量大气校正的可行性,对MODIS近红外水汽反演结果与地基GPS水汽探测结果进行了比较和分析。同时根据GPS解算结果,利用实例讨论了基于地面气象参数的水汽延迟模拟的效果。     

GPS/VRS实时网络改正数生成算法研究

为提高厘米级网络GPS/VRS实时动态定位的精度和可靠性,系统地探讨VRS网络实时改正数的生成模型,并提出适用于中长距离参考站网络的电离层、对流层以及卫星轨道改正数计算的改进算法。结合四川GPS参考站网络(SGRSN)以及自主开发的虚拟参考站软件平台VENUS系统,对上述改正数生成算法进行试验验证,结果表明其大气误差改正数精度为2~4 cm,轨道误差的影响可基本消除,满足80 km以上中长距离稀疏参考站网络厘米级实时动态定位服务要求。     

一种提高单历元解算大高差短基线精度的方法

单历元基线解算可以避开传统基线解算中周跳探测等复杂的数据预处理过程。但是当两站高差较大时,即使是短基线,通过双差技术也不能充分消除对流层延迟,且残余对流层误差对单历元基线解算的影响较大,定位精度无法达到毫米级水平。针对以上问题,该文提出了采用半参数广义补偿最小二乘对大高差短基线进行单历元解算,削弱残余对流层误差影响的方法。实际算例表明,与常规的最小二乘法相比,该方法能很好地分离GPS残余对流层误差,各方向定位精度能达到毫米级水平。