Real-time precise point positioning augmented with high-resolution numerical weather prediction model

GPS Solutions - The tropospheric delay is one of the major error sources in precise point positioning (PPP), affecting the accuracy and precision of estimated coordinates and convergence time,...     

Voxel-optimized regional water vapor tomography and comparison with radiosonde and numerical weather model

Water vapor tomography has been developed as a powerful tool to model spatial and temporal distribution of atmospheric water vapor. Global navigation satellite systems (GNSS) water vapor tomography refers to the 3D structural construction of tropospheric water vapor using a large number of GNSS signals that penetrate the tomographic modeling area from different positions. The modeling area is usually discretized into a number of voxels. A major issue involved is that some voxels are not crossed by any GNSS signal rays, resulting in an undetermined solution to the tomographic system. To alleviate this problem, the number of voxels crossed by GNSS signal rays should be as large as possible. An important way to achieve this is to optimize the geographic distribution of tomographic voxels. We propose an approach to optimize voxel distribution in both vertical and horizontal domains. In the vertical domain, water vapor profiles derived from radiosonde data are exploited to identify the maximum height of tomography and the optimal vertical resolution. In the horizontal domain, the optimal horizontal distribution of voxels is obtained by searching the maximum number of ray-crossing voxels in both latitude and longitude directions. The water vapor tomography optimization procedures are implemented using GPS water vapor data from the Hong Kong Satellite Positioning Reference Station Network. The tomographic water vapor fields solved from the optimized tomographic voxels are evaluated using radiosonde data and a numerical weather prediction non-hydrostatic model (NHM) obtained for the Hong Kong station. The comparisons of tomographic integrated water vapor (IWV) with the radiosonde and NHM IWV show that RMS errors of their differences are 1.41 and 3.09 mm, respectively. Moreover, the tomographic water vapor density results are compared with those of radiosonde and NHM. The RMS error of the density differences between tomography and radiosonde data is 1.05  \(\mathrm{g/m}^{3}\) . For the comparison between tomography and NHM, an overall RMS error of \(1.43\,\mathrm{g/m^{3}}\) is achieved.     

Comparing GPS-only with GPS + GLONASS positioning in a regional permanent GNSS network

Within the regional EUREF Permanent Network (EPN) all positioning is purely based on GPS. This paper investigates, using the Bernese GNSS analysis software, the influence of adding GLONASS observations to the EPN processing using fixed orbits from the International GNSS Service (IGS) as well as from the CODE analysis centre. The GPS-only coordinates and GPS + GLONASS coordinates will be compared and the change in their repeatabilities will be investigated. The influence of the used orbits will also be outlined. The results show that a combined GPS + GLONASS data analysis can be set up without major efforts and that it will not degrade the positions obtained within the EPN.     

Improving BeiDou real-time precise point positioning with numerical weather models

Precise positioning with the current Chinese BeiDou Navigation Satellite System is proven to be of comparable accuracy to the Global Positioning System, which is at centimeter level for the horizontal components and sub-decimeter level for the vertical component. But the BeiDou precise point positioning (PPP) shows its limitation in requiring a relatively long convergence time. In this study, we develop a numerical weather model (NWM) augmented PPP processing algorithm to improve BeiDou precise positioning. Tropospheric delay parameters, i.e., zenith delays, mapping functions, and horizontal delay gradients, derived from short-range forecasts from the Global Forecast System of the National Centers for Environmental Prediction (NCEP) are applied into BeiDou real-time PPP. Observational data from stations that are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiments network are processed, with the introduced NWM-augmented PPP and the standard PPP processing. The accuracy of tropospheric delays derived from NCEP is assessed against with the IGS final tropospheric delay products. The positioning results show that an improvement in convergence time up to 60.0 and 66.7% for the east and vertical components, respectively, can be achieved with the NWM-augmented PPP solution compared to the standard PPP solutions, while only slight improvement in the solution convergence can be found for the north component. A positioning accuracy of 5.7 and 5.9 cm for the east component is achieved with the standard PPP that estimates gradients and the one that estimates no gradients, respectively, in comparison to 3.5 cm of the NWM-augmented PPP, showing an improvement of 38.6 and 40.1%. Compared to the accuracy of 3.7 and 4.1 cm for the north component derived from the two standard PPP solutions, the one of the NWM-augmented PPP solution is improved to 2.0 cm, by about 45.9 and 51.2%. The positioning accuracy for the up component improves from 11.4 and 13.2 cm with the two standard PPP solutions to 8.0 cm with the NWM-augmented PPP solution, an improvement of 29.8 and 39.4%, respectively.     

GPS-PWV estimation and validation with radiosonde data and numerical weather prediction model in Antarctica

Three permanent GPS tracking stations in the trans Antarctic mountain deformation (TAMDEF) network were used to estimate precipitable water vapor (PWV) using measurement series covering the period of 2002–2005. TAMDEF is a National Science Foundation funded joint project between The Ohio State University and the United States Geological Survey. The TAMDEF sites with the longest GPS data spans considered in this research are Franklin Island East (FIE0), the International GNSS Service site McMurdo (MCM4), and Cape Roberts (ROB1). For the experiment, PWV was extracted from the ionosphere-free double-difference carrier phase observations, processed using the adjustment of GPS ephemerides (PAGES) software. The GPS data were processed with a 30 s sampling rate, 15-degree cutoff angle, and precise GPS orbits disseminated by IGS. The time-varying part of the zenith wet delay is estimated using the Marini mapping function, while the constant part is evaluated using the corresponding Marini tropospheric model. Previous studies using TAMDEF data for PWV estimation show that the Marini mapping function performs the best among the models offered by PAGES. The data reduction to compute the zenith wet delay follows the step piecewise linear strategy, which is subsequently transformed to PWV. The resulting GPS-based PWV is compared to the radiosonde observations and to values obtained from the Antarctic mesoscale prediction system (AMPS). This comparison revealed a consistent bias of 1.7 mm between the GPS solution and the radiosonde and AMPS reference values.     

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.     

Using external tropospheric corrections to improve GNSS positioning of hot-air balloon

High accurate global navigation satellite systems (GNSS) require to correct a signal delay caused by the troposphere. The delay can be estimated along with other unknowns or introduced from external models. We assess the impact of the recently developed augmentation tropospheric model on real-time kinematic precise point positioning (PPP). The model is based on numerical weather forecast and thus reflects the actual state of weather conditions. Using the G-Nut/Geb software, we processed GNSS and meteorological data collected during the experiment using a hot-air balloon flying up to an altitude of 2000 m. We studied the impacts of random walk noise setting of zenith total delay (ZTD) on estimated parameters and the mutual correlations, the use of external tropospheric corrections, the use of data from a single or dual GNSS constellation and the use of Kalman filter and backward smoothing processing methods. We observed a significant negative correlation of the estimated rover height and ZTD which depends on constraining ZTD estimates. Such correlation caused a degraded performance of both parameters when estimated simultaneously, in particular for a single GNSS constellation. The impact of ZTD constraining reached up to 50-cm differences in the rover height. Introducing external tropospheric corrections improved the PPP solution regarding: (1) shortened convergence, (2) better overall robustness, particularly, in case of degraded satellite geometry, (3) less adjusted parameters with lower correlations. The numerical weather model-driven PPP resulted in 9–12- and 5–6-cm uncertainties in the rover altitude using the Kalman filter and the backward smoothing, respectively. Compared to standard PPP, it indicates better performance by a factor of 1–2 depending on the availability of GNSS constellations, the troposphere constraining and the processing strategy.     

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.      

基于X-11-ARIMA模型在GNSS定位数据后处理的应用

定位数据分析及后处理是卫星导航定位系统在测绘和地灾监测应用中的关键环节. 通常,在卡尔曼滤波处理定位数据后得到的平滑数据,能够剔除噪声干扰得到贴近真值的数据. 但在长时间跨度的情况下,周期性发生的干扰难以在短时间内被识别和滤除,从而反映为一种频率较低的噪声波动. 假设该波动干扰存在周期性,以X-11分解时间序列分析方法进行数据处理,平滑后定位数据的方差从4.733减小至2.683,精度提高了43.3%. 并对拆分数据进行差分自回归移动平均模型(ARIMA)建模预测. 还原数据对比直接预测数据的分析结果表明:拆分后分别预测再整合还原精度高于直接预测5%～10%,可以应对平滑处理实时性差的问题.      

鞍山区域电离层模型构建及GNSS应用研究

针对电离层延迟误差目前是GNSS导航定位精度最重要误差源的现状,通过GNSS参考站或跟踪站实测数据计算电子总含量值,建立区域电离层模型,监测区域电离层变化,进而找到削弱或消除电离层延迟误差影响方法。利用曲面拟合实现建模,在模型的建立过程中通过对不同的模型阶数进行设置,对比不同情况下的模型精度,从而确定特定区域内最佳数据采样间隔及阶数设置,并在最佳阶数设置情况下,比较了预报不同时段的精度,进而对延迟量预报问题进行探讨,得出一些有益结论。可以通过该模型单独解算流动站站点的实时电离层延迟信息,这对多基站CORS的站间距离选择和单基站CORS基准站和流动站之间距离设计,尤其对提高单频接收机以及GIS产品用户的定位精度和差分模型的覆盖范围都具有实际参考意义。     

Improving the GNSS positioning stochastic model in the presence of ionospheric scintillation

Ionospheric scintillations are caused by time- varying electron density irregularities in the ionosphere, occurring more often at equatorial and high latitudes. This paper focuses exclusively on experiments undertaken in Europe, at geographic latitudes between ~50°N and ~80°N, where a network of GPS receivers capable of monitoring Total Electron Content and ionospheric scintillation parameters was deployed. The widely used ionospheric scintillation indices S4 and s_j{\sigma_{\varphi}} represent a practical measure of the intensity of amplitude and phase scintillation affecting GNSS receivers. However, they do not provide sufficient information regarding the actual tracking errors that degrade GNSS receiver performance. Suitable receiver tracking models, sensitive to ionospheric scintillation, allow the computation of the variance of the output error of the receiver PLL (Phase Locked Loop) and DLL (Delay Locked Loop), which expresses the quality of the range measurements used by the receiver to calculate user position. The ability of such models of incorporating phase and amplitude scintillation effects into the variance of these tracking errors underpins our proposed method of applying relative weights to measurements from different satellites. That gives the least squares stochastic model used for position computation a more realistic representation, vis-a-vis the otherwise ‘equal weights’ model. For pseudorange processing, relative weights were com- puted, so that a ‘scintillation-mitigated’ solution could be performed and compared to the (non-mitigated) ‘equal weights’ solution. An improvement between 17 and 38% in height accuracy was achieved when an epoch by epoch differential solution was computed over baselines ranging from 1 to 750 km. The method was then compared with alternative approaches that can be used to improve the least squares stochastic model such as weighting according to satellite elevation angle and by the inverse of the square of the standard deviation of the code/carrier divergence (sigma CCDiv). The influence of multipath effects on the proposed mitigation approach is also discussed. With the use of high rate scintillation data in addition to the scintillation indices a carrier phase based mitigated solution was also implemented and compared with the conventional solution. During a period of occurrence of high phase scintillation it was observed that problems related to ambiguity resolution can be reduced by the use of the proposed mitigated solution.     

融合GNSS气象参数的PM2.5随机森林预测模型

针对PM2.5浓度的预报问题,该文结合国家GNSS服务(IGS)分析中心获取的北京房山站的气象数据及同期的PM2.5实测数据,分析了气象因子和环境污染物因子对PM2.5浓度的影响,并提出 了基于随机森林算法的PM2.5浓度预测方法,建立了融合GNSS气象参数的PM2.5随机森林预测模型.实验结果表明:该算法的时效性达6 h,在一定精度范围内能够取得较好的预测效果,同时能够有效地抑制过拟合的现象.     

GNSS navigation and positioning for the GEOHALO experiment in Italy

GEOHALO is a joint experiment of several German institutes for atmospheric research and earth observation where exploring airborne gravimetry over Italy using the High Altitude and LOng Range (HALO) aircraft data is one of the major goals. The kinematic positioning of the aircraft, on which all remote sensing instruments are located, by Global Navigation Satellite System (GNSS) is affected by the characteristics of long-distance, long-time duration, and high-platform dynamics which are a key factor for the success of the GEOHALO project. We outline the strategy and method of GNSS data processing which takes into account multiple GNSS systems (GPS and GLONASS), multiple static reference stations including stations from the International GNSS Service (IGS) and the EUropean REFerence network (EUREF), multiple GNSS-receiving equipments mounted on the kinematic platform, geometric relations between multiple antennas, and assumptions of similar characteristic of atmospheric effects within a small area above the aircraft. From this precondition, various data processing methods for kinematic positioning have been developed, applied and compared. It is shown that the proposed method based on multiple reference stations and multiple kinematic stations with a common atmospheric delay parameter can effectively improve the reliability and accuracy of GNSS kinematic positioning.     

GNSS/INS组合车辆协同精密定位方法

自动驾驶和智能交通要求载体的高精度定位,更要求载体之间的高精度协同控制。当前依靠增加传感器来提升载体定位精度的研究思路依然无法有效解决卫星信号长时间失锁的复杂情况。本文提出了基于GNSS/INS组合的载体协同高精度定位方法,通过建立载体之间的相对位置关系来实现载体间观测值的共享,从而提升载体的定位精度和可信度。试验结果表明,GNSS/INS组合的协同定位模式相比于单独定位模式能显著改善载体恶劣环境下的定位精度。     

导航卫星信号湿延迟参数化模型和数值模式的比较

对高精度导航卫星处理软件(GAMIT)确定的卫星信号湿延迟和香港天文台中尺度数值模式(ORSM)所计算的湿延迟进行了比较,发现二者相关系数为0.99,偏差为3mm,平均绝对偏差为26.7mm,基本不存在系统性的偏差。卫星在天顶时,两者偏差最小,随着卫星仰角的降低,偏差增大,在天顶角70-80°时,两者确定信号湿延迟平均绝对偏差可达30mm。     

Tropospheric delay gradients from numerical weather prediction models: effects on GPS estimated parameters

Several numerical weather prediction (NWP) models provide information on the 3D state of the neutral atmosphere which has enabled GNSS researchers to have improved a priori information of the delay induced in the GNSS signals. However, the quality of weather models on the one hand and computational difficulties on the other, are motivations to develop an algorithm based partly on NWP models, while still estimating the remaining residual delay through GNSS processing strategies. An algorithm has been developed to estimate horizontal delay gradients from Meteorological Service of Canada NWP models. The GNSS software “Bernese” has also been modified to handle these gradients, as well as zenith delay and mapping functions based on NWP models in phase and code observation equations. Month-long precise point positioning results show strong correlation between north–south hydrostatic gradients and latitude differences, with significant but less strong correlation with the height and zenith total delay parameters. The longitude components were not sensitive to the implementation of gradients. High precision GNSS applications such as long term geodynamics studies, realization of terrestrial reference frames and climatology and consequential interpretations may be affected by ignoring the asymmetry of the neutral atmosphere. In addition to estimating the gradients, implementing a priori information on gradients in the processing software may have an impact on estimated results and consequential interpretations.     

Analytical 2D GNSS PVT solutions from a hyperbolic positioning approach

GNSS receivers estimate 3D antenna position and receiver clock bias when at least four satellites are tracked. If only three satellites are available, a 2D antenna position solution is still possible. We derive an almost exact algorithm for the determination of two possible antenna positions and the corresponding receiver clock biases based on pseudorange measurements to three GNSS satellites and a height measurement. The two ambiguous solutions exactly reflect the same height measurement. One of the solutions can be eliminated if some prior knowledge of the user position, for example, near the Earth, is available. In general, a less accurate height measurement gives a less accurate 2D GNSS solution, and vice versa. The determination of the receiver antenna position is based upon the intersection of two confocal hyperboloid sheets and the ellipsoid, resulting in a hyperbola along which the user is located. The algorithm is verified by numerical computations.     

Study of cloud liquid water path and total precipitable water from irs-p4/msmr and numerical weather prediction model output

A global weather analysis-forecast system is used to produce six hourly analysis of meteorological fields at roughly 150 km × 150 km resolution at the National Center for Medium Range Weather Forecast (NCMRWF). In this paper, we have studied the Total Precipitable Water Content (TPWC) and Cloud Liquid Water Path (CLWP) derived from the Indian Remote Sensing (IRS-P4) Satellite over the Indian Ocean region in relation to operational numerical weather prediction (NWP) model analysis and short-range forecasts. An objective analysis was carried out by introducing the observations of CLWP, TPWC and their values (six hour forecasts) from the T80 model as the first guess, for a 20 days period of August 1999 using the standard Cressman’s technique. The reanalysis could capture the signature of TPWC and CLWP data from IRS-P4 satellite. In general the observed values of TPWC and CLWP from IRS-P4 have a positive bias compared to NCMRWF analysis over the region where the satellite passed. The CLWP values have been compared with Special Sensor Microwave/Imager (SSM/I) products from the Defense Meteorological Satellite Program (DMSP) satellites. Results indicate that the model derived CLWP values were within acceptable limits, whereas the observations from the Multi-channel Scanning Microwave Radiometer (MSMR) showed slightly larger values.     

A closed-loop EKF and multi-failure diagnosis approach for cooperative GNSS positioning

Current cooperative positioning with global navigation satellite system (GNSS) for connected vehicle application mainly uses pseudorange measurements. However, the positioning accuracy offered cannot meet the requirements for lane-level positioning, collision avoidance and future automatic driving, which needs real-time positioning accuracy of better than 0.5 m. Furthermore, there is an apparent lack of research into the integrity issue for these new applications under emerging driverless vehicle applications. In order to overcome those problems, a new extended Kalman filter (EKF) and a multi-failure diagnosis algorithm are developed to process both GNSS pseudorange and carrier phase measurements. We first introduce a new closed-loop EKF with partial ambiguity resolution as feedback to address the low accuracy issue. Then a multi-failure diagnosis algorithm is proposed to improve integrity and reliability. The core of this new algorithm includes using Carrier phase-based Receiver Autonomous Integrity Monitoring method for failure detection, and the double extended w test detectors to identify failure. A cooperative positioning experiment was carried out to validate the proposed method. The results show that the proposed closed-loop EKF can provide highly accurate positioning, and the multi-failure diagnosis method is effective in detecting and identifying failures for both code and carrier phase measurements.     

基于一阶模型补偿的GNSS RTK参考站数据预报策略

针对相对定位过程中基准站通信中断的情况,本文作者提出了一种对基准站数据进行高精度预报,维持向参考站提供延迟差分修正信息的思路. 对影响全球卫星导航系统(GNSS)观测值预报的卫星星历误差、电离层、对流层等误差源进行分析,比较了各类误差源对延迟时长的敏感程度. 实验结果显示:预报误差随着预报时长增加线性累积,且与卫星高度角负相关;当高度角低于10°时,预报5 min造成的误差可达174.6 cm. 同时,为提高数据预报精度,利用一阶线性模型计算误差累积速率,并补偿至预报观测值. 补偿后,上述预报累积误差削弱至64.4 cm. 定位结果表明:当基准站数据缺失1 min时,经一阶线性模型补偿预报后,零基线实时定位(RTK)定位结果在,东(E)、北(N)、天(U)三个方向均方根误差(RMSE)分别为0.37 cm、0.41 cm、0.86 cm,较未补偿时提升71.1%、77.2%和90.0%;当预报延迟为5 min时,仍能保持cm级解算精度.