Using Allan variance to analyze the error characteristics of GNSS positioning

Currently, we evaluate the positioning accuracy of GNSS mainly by providing statistical values that can represent the overall error level, such as CEP, RMS, 2DRMS, and maximum error. These are solid indicators of the general performance of the GNSS positioning. But some applications like GNSS/INS integrated system require a detailed analysis of the error characteristics and knowledge of the precise error model. This requirement necessitates the modeling of the error components of the GNSS positioning solutions. In our research, the Allan variance method is proposed to analyze the GNSS positioning errors, describe the error characteristics, and build the corresponding error models. Based on our research, four dominant noise terms are identified in the GNSS positioning solutions, that is, 1st order Gauss-Markov process, Gaussian white noise, random walk noise, and flicker noise, which indicates that white noise is not always enough and appropriate to model GNSS positioning errors for some applications. The results show that the Allan variance is a feasible and effective way to analyze the error characteristics of the GNSS positioning solutions.     

Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning

During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.     

Analysis of GPS RTK performance using external NOAA tropospheric corrections integrated with a multiple reference station approach

For high-accuracy geodetic applications, time-variable tropospheric propagation delay errors limit global positioning system real-time kinematic positioning accuracy. Potential improvements in positioning accuracy are evaluated by using the National Oceanic and Atmospheric Administration (NOAA) real-time tropospheric corrections (herein called NOAA model) within a multiple reference station network approach. The results are compared with those for modified Hopfield tropospheric model corrections, for six scenarios in three geographical regions in the U.S. National Geodetic Survey network of Continuously Operating Reference Stations, for baseline lengths of 60~150 km. Analyses are conducted at rover locations for relatively humid days, and misclosures for various double difference observations are computed; these observations include each frequency (L1 and L2) and three linear combinations [wide lane, ionosphere free (IF), and geometry free]. The effectiveness of the network approach is demonstrated, with overall performance improvements of 15 and 19%, using the modified Hopfield and the NOAA model, respectively. The IF linear combination, a measure of tropospheric and orbital errors, shows a 3% improvement for the NOAA model compared with the modified Hopfield model.     

Using a regional numerical weather prediction model for GNSS positioning over Brazil

The global navigation satellite system (GNSS) can provide centimeter positioning accuracy at low costs. However, in order to obtain the desired high accuracy, it is necessary to use high-quality atmospheric models. We focus on the troposphere, which is an important topic of research in Brazil where the tropospheric characteristics are unique, both spatially and temporally. There are dry regions, which lie mainly in the central part of the country. However, the most interesting area for the investigation of tropospheric models is the wet region which is located in the Amazon forest. This region substantially affects the variability of humidity over other regions of Brazil. It provides a large quantity of water vapor through the humidity convergence zone, especially for the southeast region. The interconnection and large fluxes of water vapor can generate serious deficiencies in tropospheric modeling. The CPTEC/INPE (Center for Weather Forecasting and Climate Studies/Brazilian Institute for Space Research) has been providing since July 2012 a numerical weather prediction (NWP) model for South America, known as Eta. It has yield excellent results in weather prediction but has not been used in GNSS positioning. This NWP model was evaluated in precise point positioning (PPP) and network-based positioning. Concerning PPP, the best positioning results were obtained for the station SAGA, located in Amazon region. Using the NWP model, the 3D RMS are less than 10 cm for all 24 h of data, whereas the values reach approximately 60 cm for the Hopfield model. For network-based positioning, the best results were obtained mainly when the tropospheric characteristics are critical, in which case an improvement of up to 7.2 % was obtained in 3D RMS using NWP models.     

Using Allan variance to improve stochastic modeling for accurate GNSS/INS integrated navigation

MEMS-based integrated system of a global navigation satellite system (GNSS) and an inertial navigation system (INS) has been widely used in various navigation applications. However, such integration encounters some major limitations. On the one hand, the noisy MEMS-based INS undermines the accuracy with time during the frequently occurring GNSS outages caused by signal blockage or attenuation in certain situations such as urban canyon, tunnels, and high trees. On the other hand, the model mismatch between actual GNSS error and the assumed one would also degrade the obtained accuracy even with continuous GNSS aiding. To improve the overall performance for GNSS/MEMS-INS, better error models can be obtained using Allan variance (AV) analysis technique for modeling inertial sensor errors instead of the commonly recommended auto-regressive processes, and on the other hand, the measurement update in Kalman filter is improved using innovation filtering and AV calculation. The performance of each method and the combined algorithm is evaluated by a field test with either differential GNSS (DGNSS) or single-point positioning (SPP) as external aid. In addition to the considerable navigation enhancement brought by each method, the experimental results show the combined algorithm accomplishes overall accuracy improvements by about 18% (position), 8% (velocity), and 38% (attitude) for integration with DGNSS, and by about 15% (position), 75% (velocity), and 77% (attitude) for that with SPP, compared with corresponding traditional counterparts.     

Contribution of ionospheric irregularities to the error of dual-frequency GNSS positioning

This paper investigates the third-order residual range error in the dual-frequency correction of ionospheric effects on satellite navigation. We solve the two-point trajectory problem using the perturbation method to derive second-approximation formulas for the phase path of the wave propagating through an inhomogeneous ionosphere. It is shown that these formulas are consistent with the results derived from applying perturbation theory directly to the eikonal equation. The resulting expression for the phase path is used in calculating the residual range error of dual-frequency global positioning system (GPS) observations, in view of second- and third-order terms. The third-order correction includes not only the quadratic correction of the refractive index but also the correction for ray bending in an inhomogeneous ionosphere. Our calculations took into consideration that the ionosphere has regular large-scale irregularities, as well as smaller-scale random irregularities. Numerical examples show that geomagnetic field effects, which constitute a second-order correction, typically exceed the effects of the quadratic correction and the regular ionospheric inhomogeneity. The contribution from random irregularities can compare with or exceed that made by the second-order correction. Therefore, random ionospheric irregularities can make a significant (sometimes dominant) contribution to the residual range error.     

Android智能手机GNSS定位性能分析

随着全球卫星导航系统(GNSS)的发展和移动通信技术的进步,用户对位置服务(LBS)提出了更高的要求. 本文采用市面上常见的两部Android智能手机采集GNSS数据,对Android智能手机伪距单点定位(SPP)和单频精密单点定位(PPP)算法进行研究,分析了在不同条件下智能手机的SPP、单频PPP定位性能. 结果表明:在使用多普勒平滑伪距和信噪比随机模型的基础上,Android智能手机GPS单系统的SPP定位精度可达3 m,GPS、Galileo、GLONASS、北斗卫星导航系统(BDS)四系统定位精度可达亚米级. 在单频PPP静态定位中,在GPS单系统下,定位精度仅能达到米级,且收敛时间较长;在GPS、Galileo、GLONASS、BDS四系统下,定位精度可达亚米级,且平面方向可在40 min内收敛. 在单频PPP动态定位中,手机的定位精度仅能达到米级.      

GNSS偏心观测在卫星天线定位定向中的应用

由于现地观测条件限制,GNSS天线无法架设在需要观测的目标点上,无法实现精确对中观测目标所对应的地面点中心,此时就需要进行GNSS偏心观测。文中从解决卫星天线定位定向的工程出发,研究GNSS偏心观测三角形法和经纬仪交会法计算归心元素。依据模拟实测计算结果以及实际卫星天线定位定向的结果,分析了两种方法的优缺点。     

一种机载GNSS高精度定位算法

提出部分模糊度固定的加权电离层模型提高大范围全球卫星导航系统(GNSS)航空定位的精度、可靠性及连续性.该方法的主要思路包括:自适应调整大气扰动等误差影响以实现短基线与长基线两类解算模式之间的灵活切换;施加虚拟电离层观测约束信息,提高基线动态定位的浮点解精度;采用部分模糊度固定方法有效挖掘若干模糊度参数的整周约束.试验表明,提出的方法可提高模糊固定效率与定位精度,克服传统方法有效观测信息利用率不足、定位精度较差、可靠性不高以及连续性较差的问题.实验结果表明,部分模糊度固定算法可在2 min内固定95%以上宽巷模糊度解算与80%以上窄巷模糊度,约20 min后可固定所有模糊度.     

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。     

GNSS对流层天顶延迟模型及映射函数研究EI北大核心CSCD

对流层延迟是指电磁波信号穿透中性大气层时速度和路径均发生改变的效应,具有非色散性,无法通过多频组合方式消除;由于水汽具有典型的时空非平稳特征,难以对非流体静力学分量进行精确建模。如何妥善处理对流层延迟,是提高GNSS定位精度的重点和难点问题。     

GNSS对流层水汽监测研究进展与展望EI北大核心CSCD

对流层是近地空间环境中与人类活动联系最为密切的大气层,而水汽是低层大气圈中最重要的组成部分之一。尽管水汽在对流层中所占比例较小,但在一系列天气和多种气候变化中都扮演着重要角色。随着全球导航卫星系统(GNSS)的快速发展,GNSS对流层水汽监测成为重要的研究和应用方向。本文系统介绍了GNSS多维水汽监测及其在相关方面应用的研究现状和进展。GNSS水汽监测研究方面,当前主要集中在二维大气可降水量监测和三维湿折射率/水汽密度廓线反演两部分;GNSS水汽应用研究方面,当前主要包括定位、短临降雨及旱涝监测、数值同化预报等。     

网格化GNSS弱干扰源定位方法

介绍了网格化全球卫星导航系统(GNSS)弱干扰源定位的系统组成,针对该场景下现有方法对信噪比低的情况适应能力较差的问题,提出了一种基于信号噪声分离的差方均值函数拟合(MFDSS)的网格化GNSS弱干扰源定位方法,方法采用MFDSS方法实现时差估计,并利用Chan双曲线定位算法解算干扰源位置.文章对比仿真了该方法和常用网格化定位方法的定位效果,在对GNSS弱干扰源定位的场景下,该方法表现出优越性能.      

GPS精密单点定位中对流层延迟处理方法研究

本文首先介绍了GPS精密单点定位技术,采用宽巷组合的方法得到观测方程。然后对精密定位中的误差改正作了简述,主要讨论了处理对流层延迟的Saastamoinen模型和Niell映射函数。提出用扩展卡尔曼滤波参数估计方法来处理对流层延迟,通过实例用Saastamoinen模型、Saastamoinen模型加Niell映射函数和扩展卡尔曼滤波参数估计三种方法对对流层延迟进行改正,结果表明该方法优于Saastamoinen模型。     

BDS/GNSS融合精密单点定位性能分析

随着北斗卫星导航系统(BDS)的全球组网成功,基于BDS的应用研究正在如火如荼的进行中,尤其是包括BDS在内的多频多模融合定位正成为研究的重点.利用MGEX(Multi-GNSS Experiment)多个测站的BDS、GPS、GLONASS、Galileo观测数据,基于RTKLIB开源代码,在Visual Studi...     

Application of the TaiWan Ionospheric Model to single-frequency ionospheric delay corrections for GPS positioning

The performance of a three-dimensional ionospheric electron density model derived from FormoSat3/COSMIC GPS Radio Occultation measurements, called the TaiWan Ionosphere Model (TWIM), in removing the ionospheric delays in single-frequency pseudorange observations is presented. Positioning results using TWIM have been compared with positioning results using other ionospheric models, such as the Klobuchar (KLOB) and the global ionospheric model (GIM). C/A code pseudoranges have been observed at three International GPS Service reference stations that are representative of mid-latitude (BOR1 and IRKJ) and low-latitude (TWTF) regions of the ionosphere. The observations took place during 27 geomagnetically quiet days from April 2010 to October 2011. We perform separate solutions using the TWIM, KLOB, GIM ionospheric models and carry out a solution applying no ionospheric correction at all. We compute the daily mean horizontal errors (DMEAN) and the daily RMS (DRMS) for these solutions with respect to the published reference station coordinates. It has demonstrated that TEC maps generate using the TWIM exhibit a detailed structure of the ionosphere, particularly at low-latitude region, whereas the Klobuchar and the GIM only provide the basic diurnal and geographic features of the ionosphere. Also, it is shown that even for lower satellite elevations, the TWIM provides better positioning than the Klobuchar and GIM models. Specifically, using TWIM, the difference of the uncorrected solution (no ionospheric correction), and the other solutions, relative to the uncorrected solution, is 45 % for the mean horizontal error (DMEAN) and 42 % for the horizontal root-mean-square error (DRMS). Using Klobuchar and GIM, the percent for DMEAN only reaches to about 12 % and 3 %, while the values for the DRMS are only 12 and 4 %, respectively. In the vertical direction, all models have a percentage of about 99 and 70 % for the mean vertical error (VMEAN) and vertical root-mean-square error (VRMS), respectively. These percentages show the greater impact of TWIM on the ionospheric correction compared to the other models. In at least 40 % of the observed days and across all stations, TWIM has the smallest DMEAN, VMEAN, DRMS, and VRMS daily values. These values reach 100 % at station TWTF. This shows the overall performance of TWIM is better than the Klobuchar and GIM.     

GNSS/声学联合定位的自适应滤波算法

海底控制点布设是构建海洋时空基准的重要环节,而可靠的海洋基准定位模型及方法又是实现高精度海底控制点布设的前提和基础。应用广泛的走航船测量方式兼具灵活性和可控性,但载体异常扰动影响不可避免,易导致海底控制点联合定位模型解算失真。针对这一问题,本文提出一种基于自适应选权滤波的GNSS/声学联合解算方法。首先推导了统一海面及水下观测过程的GNSS/声学联合定位数学模型;然后研究了在联合模型的自适应滤波解算中对载体异常扰动的判别标准,给出了各状态参数自适应因子的构造方法;最后通过仿真和实测数据进行了试验验证。结果表明:引入自适应滤波算法后,能有效改善状态扰动对GNSS/声学联合定位的异常影响,提升其定位稳定性及定位精度;当分别对各类状态参数的自适应因子进行合理构造后,滤波效果可达最佳。