VMF3/GPT3: refined discrete and empirical troposphere mapping functions

Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains a new approach intended to refine the currently most important discrete mapping function, the Vienna Mapping Functions 1 (VMF1), which is successively referred to as Vienna Mapping Functions 3 (VMF3). It is designed in such a way as to eliminate shortcomings in the empirical coefficients b and c and in the tuning for the specific elevation angle of \(3^{\circ }\). Ray-traced delays of the ray-tracer RADIATE serve as the basis for the calculation of new mapping function coefficients. Comparisons of modeled slant delays demonstrate the ability of VMF3 to approximate the underlying ray-traced delays more accurately than VMF1 does, in particular at low elevation angles. In other words, when requiring highest precision, VMF3 is to be preferable to VMF1. Aside from revising the discrete form of mapping functions, we also present a new empirical model named Global Pressure and Temperature 3 (GPT3) on a \(5^{\circ }\times 5^{\circ }\) as well as a \(1^{\circ }\times 1^{\circ }\) global grid, which is generally based on the same data. Its main components are hydrostatic and wet empirical mapping function coefficients derived from special averaging techniques of the respective (discrete) VMF3 data. In addition, GPT3 also contains a set of meteorological quantities which are adopted as they stand from their predecessor, Global Pressure and Temperature 2 wet. Thus, GPT3 represents a very comprehensive troposphere model which can be used for a series of geodetic as well as meteorological and climatological purposes and is fully consistent with VMF3.     

Implementation and testing of the gridded Vienna Mapping Function 1 (VMF1)

The new gridded Vienna Mapping Function (VMF1) was implemented and compared to the well-established site-dependent VMF1, directly and by using precise point positioning (PPP) with International GNSS Service (IGS) Final orbits/clocks for a 1.5-year GPS data set of 11 globally distributed IGS stations. The gridded VMF1 data can be interpolated for any location and for any time after 1994, whereas the site-dependent VMF1 data are only available at selected IGS stations and only after 2004. Both gridded and site-dependent VMF1 PPP solutions agree within 1 and 2 mm for the horizontal and vertical position components, respectively, provided that respective VMF1 hydrostatic zenith path delays (ZPD) are used for hydrostatic ZPD mapping to slant delays. The total ZPD of the gridded and site-dependent VMF1 data agree with PPP ZPD solutions with RMS of 1.5 and 1.8 cm, respectively. Such precise total ZPDs could provide useful initial a priori ZPD estimates for kinematic PPP and regional static GPS solutions. The hydrostatic ZPDs of the gridded VMF1 compare with the site-dependent VMF1 ZPDs with RMS of 0.3 cm, subject to some biases and discontinuities of up to 4 cm, which are likely due to different strategies used in the generation of the site-dependent VMF1 data. The precision of gridded hydrostatic ZPD should be sufficient for accurate a priori hydrostatic ZPD mapping in all precise GPS and very long baseline interferometry (VLBI) solutions. Conversely, precise and globally distributed geodetic solutions of total ZPDs, which need to be linked to VLBI to control biases and stability, should also provide a consistent and stable reference frame for long-term and state-of-the-art numerical weather modeling.     

Systematic errors in levelings of mountainous areas

Sources of errors in the precise leveling influencing the results of measurements especially strongly in mountains are considered in this study. Data are given on new error sources, including (1) the difference in temperatures of invar bands of rods and of the air; and (2) displacements of rock bench marks during diurnal variations in temperature of rocks. The ranges of possible total systematic error in leveding are estimated.     

面向地形可视化的多种投影方式研究

为了获得形式多样的地形可视化效果,投影方式的选择至关重要,通过对正投影、透视投影、渐进式投影和平斜投影等多种投影方式的原理与方法进行研究,分析了各种投影方式的适用性及其获得的地形可视化效果,为应用实践提供了有益借鉴。     

Comparison of GMF/GPT with VMF1/ECMWF and implications for atmospheric loading

This paper compares estimates of station coordinates from global GPS solutions obtained by applying different troposphere models: the Global Mapping Function (GMF) and the Vienna Mapping Function 1 (VMF1) as well as a priori hydrostatic zenith delays derived from the Global Pressure and Temperature (GPT) model and from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data. The station height differences between terrestrial reference frames computed with GMF/GPT and with VMF1/ECMWF are in general below 1 mm, and the horizontal differences are even smaller. The differences of annual amplitudes in the station height can also reach up to 1 mm. Modeling hydrostatic zenith delays with mean (or slowly varying empirical) pressure values instead of the true pressure values results in a partial compensation of atmospheric loading. Therefore, station height time series based on the simple GPT model have a better repeatability than those based on more realistic ECMWF troposphere a priori delays if atmospheric loading corrections are not included. On the other hand, a priori delays from numerical weather models are essential to reveal the full atmospheric loading signal.     

对流层映射函数对精密单点定位的影响分析

分析对流层映射函数(NMF、VMF1和GMF)对精密单点定位(PPP)精度的影响,对分布于南北半球不同纬度地区的IGS跟踪站的观测数据进行解算。首先比较PPP坐标与IGS发布的日解SNX文件坐标差异和模型间PPP坐标差异,然后分析不同季节对模型差异的影响。实验结果表明,3种映射函数均可提高PPP精度,精度控制在1cm左右。整体而言,VMF1和GMF对PPP精度的影响相当,且优于NMF。在不同季节里,模型差异会发生mm级的变化。     

TEQC单点定位的系统性偏差分析

TEQC是由UNAVCO Facility研制的GPS数据预处理软件,可进行单历元C/A码伪距单点定位的计算,获得各历元GPS接收机的WGS84坐标。利用TEQC对大量GPS观测数据的计算表明:TEQC软件的单点定位结果在东坐标和高程方向上带有明显的系统性偏差。作者研制的单点定位软件GPP,由于考虑了地球自转、对流层折射和电离层折射等误差对GPS定位的影响,因此单点定位的结果较为准确,而且对上述系统性偏差产生的原因进行了分析和探讨。     

Adaptive mapping functions to the azimuthal anisotropy of the neutral atmosphere

The anisotropy of propagation of radio waves used by global navigation satellite systems is investigated using high-resolution observational data assimilations produced by the European Centre for Medium-range Weather Forecast. The geometry and the refractivity of the neutral atmosphere are built introducing accurate geodetic heights and continuous formulations of the refractivity and its gradient. Hence the realistic ellipsoidal shape of the refractivity field above the topography is properly represented. Atmospheric delays are obtained by ray-tracing through the refractivity field, integrating the eikonal differential system. Ray-traced delays reveal the anisotropy of the atmosphere. With the aim to preserve the classical mapping function strategy, mapping functions can evolve to adapt to high-frequency atmospheric fluctuations and to account for the anisotropy of propagation by fitting at each site and time the zenith delays and the mapping functions coefficients. Adaptive mapping functions (AMF) are designed with coefficients of the continued fraction form which depend on azimuth. The basic idea is to expand the azimuthal dependency of the coefficients in Fourier series introducing a multi-scale azimuthal decomposition which slightly changes the elevation functions with the azimuth. AMF are used to approximate thousands of atmospheric ray-traced delays using a few tens of coefficients. Generic recursive definitions of the AMF and their partial derivatives lead to observe that the truncation of the continued fraction form at the third term and the truncation of the azimuthal Fourier series at the fourth term are sufficient in usual meteorological conditions. Delays’ and elevations’ mapping functions allow to store and to retrieve the ray-tracing results to solve the parallax problem at the observation level. AMF are suitable to fit the time-variable isotropic and anisotropic parts of the ray-traced delays at each site at each time step and to provide GPS range corrections at the measurement level with millimeter accuracy at low elevation. AMF to the azimuthal anisotropy of the neutral atmosphere are designed to adapt to complex weather conditions by adaptively changing their truncations.     

基于C#的简码法数字化测图技术在测量中的应用

随着计算机技术与测绘科学技术的发展,传统的模拟测图方法已被高度自动化的数字化测图技术所替代。通过大量实践探索,提出一种在测量中实用、经济、高效的测图方法一一简码法,并通过C#语言编程将野外测点简码转化成CASS成图系统默认的编程实现野外数据的转换,并实现内业自动成图。文中利用该方法对昆明理工大学校园进行了数字化测图验证。结果表明：该方法相对其他测图方法外业数据采集速度更快,内业工作量及测量成本大大减少,且该方法能方便地与GIS系统进行数据交换以及更好地服务于测绘行业,提高工作效率。     

Assessment of troposphere mapping functions using three-dimensional ray-tracing

The troposphere delay is an important source of error for precise GNSS positioning due to its high correlation with the station height parameter. It has been demonstrated that errors in mapping functions can cause sub-annual biases as well as affect the repeatability of GNSS solutions, which is a particular concern for geophysical studies. Three-dimensional ray-tracing through numerical weather models (NWM) is an excellent approach for capturing the directional and daily variation of the tropospheric delay. Due to computational complexity, its use for positioning purposes is limited, but it is an excellent tool for evaluating current state-of-the-art mapping functions used for geodetic positioning. Many mapping functions have been recommended in the past such as the Niell Mapping Function (NMF), Vienna Mapping Function 1 (VMF1), and the Global Mapping Function (GMF), which have been adopted by most IGS analysis centers. A new Global Pressure Temperature model (GPT2) has also been developed, which has been shown to improve upon the original atmospheric model used for the GMF. Although the mapping functions mentioned above use the same functional formulation, they vary in terms of their atmospheric source and calibration approach. A homogeneous data set of three-dimensional ray-traced delays is used to evaluate all components of the mapping functions, including their underlying functional formulation, calibration, and compression method. Additionally, an alternative representation of the VMF1 is generated using the same atmospheric source as the truth data set to evaluate the differences in ray-tracing methods and their effect on the end mapping function. The results of this investigation continue to support the use of the VMF1 as the mapping function of choice when geodetic parameters are of interest. Further support for the GPT2 and GMF as reliable back-ups when the VMF1 is not available was found due to their high consistency with the NWM-derived mapping function. Additionally, a small latitude-dependent bias in station height was found in the current mapping functions. This bias was identified to be due to the assumption of a constant radius of the earth and was largest at the poles and at the equator. Finally, an alternative version of the VMF1 is introduced, namely the UNB-VMF1 which provides users with an independent NWM-derived mapping function to support geodetic positioning.     

北京1号小卫星多光谱影像全国镶嵌技术与制图研究

北京1号小卫星在轨运行一年多成功接收了覆盖中国各个行政区域的多光谱影像数据,为全国数字镶嵌图的研究提供了丰富的数据资料.针对北京1号小卫星特点进行关键技术和方法研究,形成了北京1号小卫星多光谱影像全国范围数据获取任务测控优化模式,解决了北京1号小卫星多光谱数据预处理中去条带、波段自动配准、MTF复原处理等关键技术,系统地、全面地阐述了全国镶嵌图制作的技术流程和方法.     

基于《测绘工程》期刊的测绘技术动态可视化分析

结合文献计量方法与可视化技术,以《测绘工程》期刊1996-2015年间发表的论文为数据源,进行关键词、摘要的统计分析,并将统计结果以统计图表和地图的形式展现,直观地反映工程技术实践类测绘研究的研究热点以及核心研究区的地理分布。从研究结果可以得出我国工程技术实践类测绘研究每年的研究热点都不相同,学科的发展地理分布较不平衡,一定程度上反映我国工程技术实践类测绘研究的水平。     

基于自然样条补偿最小二乘的高程误差研究

基于非参数自然样条补偿最小二乘估计方法,把GPS高程数据与对应的水准数据的差值作为观测值,按照非参数自然样条补偿最小二乘的估计方法,得到消弱偶然误差v之后的平差值,并以此去改正GPS高程,可以取得较好的效果。并以某河道测量采集的数据作为事例,证明该方法的有效性。     

利用改进灰色模型的钟差预报算法及其精度分析

灰色模型在钟差长期预报中虽具有一定的优势,但是预测的精度还有进一步提高的可能。在本文中,采用经过数据预处理和残差修正对一阶灰色模型进行了改进,再对GPS卫星钟差进行不同时间尺度上的预报。算例利用IGS提供的精密钟差产品,建立了一个基于改进灰色模型的预报算法,改进灰色模型的预报精度较传统的二次项模型有了很大的提高,且预报结果的收敛性也获得了一定程度的改善。     

基于可拓学的测绘项目风险管理

本文介绍了风险管理的基本理论,分析了目前传统测绘项目在风险管理方面存在的不足.同时,针对测绘项目实施时如何进行有效的风险管理的难题,提出了基于可拓学的测绘项目风险管理方法.实证研究结果表明此方法合理、可行、操作简单,具有很强的实用性.     

基于方差膨胀模型的多个粗差的探测

本文将粗差归入随机模型,提出了基于方差膨胀模型的粗差探测方法。首先针对测量平差实际给出了非等权独立观测条件下的单个粗差的Score检验统计量,然后提出了基于方差膨胀模型的两种定位多个粗差的方案,最后对一边角网进行了计算和分析。大量试验表明,用本文给出的定位多个粗差的方法是切实可行的,它不仅有效地发现了粗差,而且计算简便、快捷,结果比较理想。     

基于KML的三维专题图表示方法

近几年来,虚拟地理环境系统得到广泛应用。专题图制作在制图学上有着悠久的历史。但是在虚拟地理环境浏览系统中(如Google Earth)对专题要素的表达没有得到足够的重视。文中研究如何利用KML制作专题符号,并在三维虚拟地理环境浏览系统中利用基于KML的专题符号实现定点符号法、分区图表法、质别底色法等专题图表示方法。通过实验说明KML在专题图的制作中具有巨大潜力,但同时也有一些重点问题需要解决。     

一种遗传算法优化的卫星钟差预报

针对导航卫星钟差预报精度不高的问题,该文引入了GM-LSSVM钟差预报模型,采用全局寻优能力较强的遗传算法对模型的参数选取过程进行优化,避免模型陷入局部最优,从而改善了组合模型中惩罚因子和核函数参数选择的盲目性。最后选取国际GPS服务组织提供的卫星钟差数据,分别建立GM(1,1)模型、LSSVM模型、GM-LSSVM模型和遗传算法优化的GM-LSSVM模型进行短期钟差预报分析和仿真实验。仿真结果表明,优化后的模型预报精度小于1.3ns,精度比前3种模型提高了45%~60%,符合钟差预报的要求。     

顾及映射函数误差的对流层延迟两步估计法

利用VLBI、GNSS等空间大地测量数据估计对流层延迟时,通常不考虑映射函数的误差,但这种处理策略最终会对估计结果造成不可忽略的影响。首先,根据多年的气象资料,分析了映射函数误差随高度角的变化特性,然后构建了映射函数误差模型,进而提出了一种顾及映射函数误差的对流层延迟两步估计法。试验表明,本文提出的方法可有效削弱斜路径延迟残差,并在一定程度上改善对流层湿延迟的估计精度。