Fast error analysis of continuous GPS observations

It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods require calculating the data covariance matrix and inverting it, which is a significant computational burden. Analysing 10 years of daily GPS solutions of a single station can take around 2 h on a regular computer such as a PC with an AMD Athlon^TM 64 X2 dual core processor. When one analyses large networks with hundreds of stations or when one analyses hourly instead of daily solutions, the long computation times becomes a problem. In case the signal only contains power-law noise, the MLE computations can be simplified to a process where N is the number of observations. For the general case of power-law plus white noise, we present a modification of the MLE equations that allows us to reduce the number of computations within the algorithm from a cubic to a quadratic function of the number of observations when there are no data gaps. For time-series of three and eight years, this means in practise a reduction factor of around 35 and 84 in computation time without loss of accuracy. In addition, this modification removes the implicit assumption that there is no environment noise before the first observation. Finally, we present an analytical expression for the uncertainty of the estimated trend if the data only contains power-law noise. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

含缺值GNSS基准站坐标序列的非插值小波分析与信号提取

受多种因素影响,GNSS基准站坐标序列通常都含有缺值,传统小波分析需要对缺值数据进行内插或补零处理。本文基于小波系数与时间序列观测数据的重构关系,提出了一种非插值的二进小波变换的最小范数解法,导出了相应的计算式,并严格证明了传统的补零处理算法与本文的最小范数解法等价。最后利用中国地壳运动观测网络一期27个基准站实测数据以及模拟数据进行了验证分析。结果表明,本文的非插值算法与插值算法提取的信号差异较小,27个基准站坐标序列的平均残差中误差仅相差2.01%(North),0.54%(East)和1.26%(Up),两种算法提取的信号之差与信号平均方差比仅相差1.16%(North),0.54%(East)和1.62%(Up)。     

三种GNSS数据下载方法对比分析CSCD

为综合评估单线程、多线程和多协程在全球卫星导航系统(GNSS)数据下载中的性能,以武汉大学国际GNSS服务(IGS)数据中心为下载源,从下载文件的时间跨度和量级大小两个方面对三种方法的下载效果进行对比分析.结果表明:在中小型文件下载过程中多线程的优势大于单线程和多协程;在大型文件下载中,多协程的下载效果略优于多线程,且都相较单线程性能更佳;由于GNSS数据普遍是中小型文件,所以多线程更适用于GNSS数据下载工作.     

数据缺失情况下BDS定位性能分析

针对观测数据的缺失会影响数据处理效果、降低定位精度的问题,该文为了探明缺失数据是如何影响定位,进行静态定位实验分析3类卫星对定位误差的影响,进行动态定位实验测试了在缺失数据的真实情况下北斗卫星系统的定位性能。静态实验结果表明,在伪距单点定位中缺失GEO卫星时三维点位精度下降了85%,在缺失IGSO时定位精度下降了43.8%,缺失MEO卫星时定位精度下降了6%,在载波相位定位中缺失3类卫星数据对定位精度虽然也有影响,但不如伪距定位的影响大。在动态实验中发现在无遮挡的环境中,BDS定位精度不受影响,且定位精度较高,可与GPS相媲美;在遮挡的环境中,GPS和BDS都出现了信号质量下降的情况,BDS数据缺失比GPS严重,缺失严重时定位出现较大的误差,结果不可靠。     

A MATLAB-based Kriged Kalman Filter software for interpolating missing data in GNSS coordinate time series

GNSS coordinate time series data for permanent reference stations often suffer from random, or even continuous, missing data. Missing data interpolation is necessary due to the fact that some data processing methods require evenly spaced data. Traditional missing data interpolation methods usually use single point time series, without considering spatial correlations between points. We present a MATLAB software for dynamic spatiotemporal interpolation of GNSS missing data based on the Kriged Kalman Filter model. With the graphical user interface, users can load source GNSS data, set parameters, view the interpolated series and save the final results. The SCIGN GPS data indicate that the software is an effective tool for GNSS coordinate time series missing data interpolation.     

Android智能手机GNSS数据质量分析

随着全球卫星导航系统(GNSS)的不断建设,智能手机基于移动位置服务(LBS)得到了迅猛发展.文中选取市面上常见的3种手机机型,包括:三星S9+(Exynos)、华为Mate30和华为P40 Pro作为研究对象,并使用北斗星通UR4B0-D高性能GNSS接收机进行同步静态观测实验,从卫星可见数、载噪比(CNR)、卫星高...     

基于独立分量法的新疆GNSS时间序列共模误差分析CSCD

共模误差(CME)是区域连续全球卫星导航系统(GNSS)网中的主要误差来源之一.针对GNSS时间序列具有非高斯分布特征,基于二阶统计量的主成分分析(PCA)难以准确提取出CME分量问题,采用具有高阶统计量的独立分量分析(ICA)对CME进行提取.以2011—2018年新疆区域GNSS坐标时间序列为例,将PCA滤波效果进行对比验证,分析了CME对GNSS坐标时间序列的影响,并对CME序列进行周期分析.结果表明:前6个独立分量包含CME分量,这可能与卫星轨道、地表质量负荷和时钟误差有关,ICA滤波后东(N)、北(E)、天顶(U)三个方向的均方根(RMS)值分别降低31.83%、32.29%、35.49%,速度不确定度分别降低44.14%、38.49%、43.32%,各测站的周期项振幅较滤波前更一致,有效地剔除了CME,提高了坐标时间序列的精度.     

Anubis的GNSS数据质量检核可视化表达与分析

针对目前TEQC数据质量检核软件尚不支持同时检核GPS/BDS/GLONASS/Galileo四系统观测数据质量的现状,该文基于开源代码的Anubis命令式窗口软件,重新编译Anubis软件代码,以扩展北斗导航系统新频点新信号数据的处理功能;依托Python平台实现Anubis软件的可视化界面封装以及质量检核结果的可视化输出,并对其软件功能和检核结果有效性进行验证。实验结果表明,改进后的Anubis软件能够以多种质量指标有效检核GNSS数据,满足检核新一代iGMAS接收机数据质量的需求。     

GNSS data management and processing with the GPSTk

We organize complex problems in simple ways using a GNSS data management strategy based on “GNSS Data Structures” (GDS), coupled with the open source “GPS Toolkit” (GPSTk) suite. The code resulting from using the GDS and their associated “processing paradigm” is remarkably compact and easy to follow, yielding better code maintainability. Furthermore, the data abstraction allows flexible handling of concepts beyond mere data encapsulation, including programmable general solvers. An existing GPSTk class can be modified to achieve the goal. We briefly describe the “GDS paradigm” and show how the different GNSS data processing “objects” may be combined in a flexible way to develop data processing strategies such as Precise Point Positioning (PPP) and network-based PPP that computes satellite clock offsets on-the-fly.     

基于多通道奇异谱的GNSS坐标序列 粗差探测与数据插值

由于接收机故障、天线更换以及一些未知外界环境因素的影响,导致GPS时间序列中不可避免地存在数据缺失和粗差,数据缺失和粗差会产生各种问题,因此需要鲁棒探测粗差和缺失数据插值来获得连续完整统一的时间序列。传统方法可能需要针对不同类型的数据和不同长度的数据间隙研究不同的插值方法,这使得缺失数据的插值较为困难。针对上述问题,文中采用多通道奇异谱分析(Multichannel Singular Spectrum Analysis,MSSA)对时间序列进行粗差探测和缺失数据插值,重建非均匀采样时间序列的连续可靠模型,且不需要关于时间序列的任何先验信息。在该方法中,粗差探测与数据插值同时进行。模拟数据和实测GNSS时间序列数据测试结果都表明该方法的有效性。     

GNSS在线数据处理系统在工程控制网中的应用与分析

介绍目前几个主要的GNSS在线数据处理系统,着重利用其中5个GNSS在线数据处理系统对某工程控制网的观测数据进行多个方案的处理;对处理结果进行对比分析,检验其内符合精度;再利用框架和历元转换理论和方法,将多个系统处理获得的不同ITRF框架下2011即时历元的观测点坐标转换归算到CGCS2000坐标下进行对比,结果表明:GNSS在线数据处理系统完全能够满足工程控制网的数据处理、精度要求以及成果提交等需求。     

中国大陆导航连续站周期信号空间规律研究

为了进一步分析我国GNSS周期信号的空间分布规律,文章基于我国大陆及周边IGS站与中国地壳运动观测网络基准站的坐标时间序列,给出定量标准剔除质量差的测站;采用分段线性拟合法提取并扣除时间序列的趋势项;采用"拉依达准则"剔除时间序列中的奇异值;采用4参数三角函数拟合出时间序列的周期与幅度;分析东向、北向、垂向3个方向的年周期、半年周期的振幅与最大值出现月份在我国的空间分布情况。分析结果表明:3方向年周期的振幅都是半年周期振幅的两倍以上,3个方向不同周期振幅的空间分布规律差异明显。     

陆态网络数据的北斗观测值特性分析

为了进一步分析北斗卫星观测值的相关特性,文章对比北斗卫星与GPS卫星、以及不同类型北斗卫星之间观测值特性的差异,提出了用站间差分考察伪距多路径组合和GFIF组合观测值的方法。陆态网络数据实验结果显示,北斗卫星B1频率观测值的信噪比最低;高度角较低时,北斗卫星伪距多路径组合绝对值和离散度均较大,约为1.5m,且IGSO和MEO卫星的伪距多路径组合值随高度角增大而明显降低;北斗GEO和IGSO卫星的相位GFIF组合有日周期性,变化范围约为±2cm,伪距GFIF组合的变化范围可达±2m;站间差分可明显减弱伪距多路径组合的变化趋势和相位GFIF组合的周期性,表明这两个组合中可能包含与卫星相关的误差,为北斗观测数据误差处理提供参考。     

On the probability distribution of GNSS carrier phase observations

When processing observational data from global navigation satellite systems (GNSS), the carrier phase measurements are generally assumed to follow a normal distribution. Although full knowledge of the probability distribution of the observables is not required for parameter estimation, for example when using the least-squares method, the distributional properties of GNSS observations play a key role in quality control procedures, such as outlier and cycle-slip detection, in ambiguity resolution, as well as in the reliability assessment of estimation results. In addition, when applying GNSS positioning under critical observation conditions with respect to multipath and atmospheric effects, the validity of the normal distribution assumption of GNSS observables certainly comes into doubt. This paper illustrates the discrepancies between the normal distribution assumption and reality, based on a large and representative data set of GPS phase measurements covering a range of factors, including multipath impact, baseline length, and atmospheric conditions. The statistical inferences are made using the first through fourth sample moments, hypothesis tests, and graphical tools such as histograms and quantile–quantile plots. The results show clearly that multipath effects, in particular the near-field component, produce the dominant influence on the distributional characteristics of GNSS observables. Additionally, using surface meteorological data, considerable correlations between distributional deviations from normality on the one hand and atmospheric relative humidity on the other are detected.     

Combination of GNSS and SLR observations using satellite co-locations

Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR.     

组合GNSS观测值反演海面高度EI北大核心CSCD

与验潮站技术相比,岸基全球导航卫星定位系统干涉反射技术(GNSS-IR)海面测高成本较低,且其观测量不受地壳沉降的影响,并可利用目前已有的沿海岸GNSS固定站提供的数据反演海面高度。目前常用观测量为大地测量型GNSS接收机给出的信噪比(SNR)值,然而,早期很多GNSS设备的输出文件中都不包含该值,导致无法利用它们研究海面高度长期变化趋势。但经典的码伪距和载波相位观测值中,同样包含着GNSS-IR测高信息。本文分别引入单频码伪距和单频载波相位的组合,以及单频码伪距和双频载波相位的组合GNSS两种观测值的组合实现了岸基海面测高。本文采用模拟数据证明了基于前一组合的GNSS-IR测高精度受到电离层延迟残差的影响,而后一种组合可避免该误差项的影响。为验证两种组合方法的有效性,在山东威海一海上栈桥上开展了试验,采集了全球定位系统(GPS)和北斗卫星导航系统(BDS)的观测数据,并处理得到了海面测高信息。最后,将反演结果与26 GHz雷达高度计的观测值进行了比较分析,发现二者具有较好的一致性,相关系数均优于85%。试验结果表明:两种码伪距和载波相位组合法均可用于GNSS-IR测高。另外,由于当前GNSS-IR测高受多种误差项影响,导致反演精度较低,使得后一种组合在避免电离层延迟残差方面的优越性并没有明显体现。本文组合方法的引入,增加了海面高度反演方法的多样性,提升了GNSS-IR测高技术的应用空间。     

Evaluation of the impact of atmospheric pressure loading modeling on GNSS data analysis

In recent years, several studies have demonstrated the sensitivity of Global Navigation Satellite System (GNSS) station time series to displacements caused by atmospheric pressure loading (APL). Different methods to take the APL effect into account are used in these studies: applying the corrections from a geophysical model on weekly mean estimates of station coordinates, using observation-level corrections during data analysis, or solving for regression factors between the station displacement and the local pressure. The Center for Orbit Determination in Europe (CODE) is one of the global analysis centers of the International GNSS Service (IGS). The current quality of the IGS products urgently asks to consider this effect in the regular processing scheme. However, the resulting requirements for an APL model are demanding with respect to quality, latency, and—regarding the reprocessing activities—availability over a long time interval (at least from 1994 onward). The APL model of Petrov and Boy (J Geophys Res 109:B03405, 2004) is widely used within the VLBI community and is evaluated in this study with respect to these criteria. The reprocessing effort of CODE provides the basis for validating the APL model. The data set is used to solve for scaling factors for each station to evaluate the geophysical atmospheric non-tidal loading model. A consistent long-term validation of the model over 15 years, from 1994 to 2008, is thus possible. The time series of 15 years allows to study seasonal variations of the scaling factors using the dense GNSS tracking network of the IGS. By interpreting the scaling factors for the stations of the IGS network, the model by (2004) is shown to meet the expectations concerning the order of magnitude of the effect at individual stations within the uncertainty given by the GNSS data processing and within the limitations due to the model itself. The repeatability of station coordinates improves by 20% when applying the effect directly on the data analysis and by 10% when applying a post-processing correction to the resulting weekly coordinates compared with a solution without taking APL into account.     

安卓智能手机GNSS数据质量分析

Android系统开放了全球卫星导航系统(GNSS)原始数据观测值,开发人员可以直接通过应用程序编程接口(API)获取GNSS原始观测数据．本文选取小米8和华为P30手机作为研究对象,对手机输出的原始GNSS观测数据进行研究,从多路径效应、数据载噪比方面分析数据质量．实验结果表明:相对于测量型接收机,安卓智能手机的原始观测值载噪比较低且多路径效应严重.