On the estimation of higher-order ionospheric effects in precise point positioning

GPS Solutions - Higher-order ionospheric effects, if not properly accounted for, can propagate into geodetic parameter estimates. For this reason, several investigations have led to the development...     

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.     

On the effects of the ionospheric disturbances on precise point positioning at equatorial latitudes

In precise point positioning (PPP), the ionospheric delay is corrected in a first-order approximation from GPS dual-frequency observations, which should eliminate almost completely the ionosphere as a source of error. However, sudden plasma density variations can adversely affect the GPS signal, degrading accuracy and reliability of positioning techniques. The occurrence of plasma density irregularities is frequent at equatorial latitudes and is reflected in large total electron content (TEC) variations. We study the relation between large changes in the rate of TEC (ROT) and positioning errors in single-epoch PPP. At equatorial latitudes and during post-sunset hours, the estimated altitudes contain errors of several meters for a single-epoch position determination, and latitude and longitude estimates are also degraded. These results have been corroborated by the online CSRS-PPP (NRCan) program. Moreover, abrupt changes in the satellite geometry have been discarded as possible cause of such errors, suggesting an apparent relation between the occurrence of large ROT and degraded position estimates.     

Higher order ionospheric effects in precise GNSS positioning

With the increasing number of precise navigation and positioning applications using Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS), higher order ionospheric effects and their correction become more and more important. Whereas the first-order error can be completely eliminated by a linear combination of dual- frequency measurements, the second- and third-order residual effects remain uncorrected in this approach. To quantify the second-order residual effect, a simple formula has been derived for GNSS users in Germany. Our proposed correction algorithm reduces the second-order effects to a residual error of fractions of 1 mm up to 2 mm at a vertical total electron content level of 10¹⁸ electrons/m² (100 TECU), depending on satellite azimuth and elevation angles. The correction formula can be implemented in real-time applications as it does not require the knowledge of the geomagnetic field or the electron density distribution in the ionosphere along the signal path. It is expected that the correction will enable more accurate positioning using the line-of-sight carrier-phase measurements.     

Real-time multi-GNSS single-frequency precise point positioning

GPS Solutions - Precise Point Positioning (PPP) is a popular Global Positioning System (GPS) processing strategy, thanks to its high precision without requiring additional GPS infrastructure....     

基于神经网络的区域电离层模型及其在单频PPP中的应用

基于武汉市CORS系统的双频非差载波相位观测数据,利用改进的神经网络方法建立区域电离层模型,并通过单频GPS精密单点定位的计算实例来分析该模型的精度。计算实例表明,当基准站间的距离小于100km时,基于神经网络的区域电离层模型的平均外符合精度为0．03m,对于时段长度为4h的单频PPP静态时段解可以达到厘米级的定位精度。     

精密单点定位技术在空中三角测量中的应用研究

在常规的GPS辅助空中三角测量中,摄站点坐标的获取主要通过差分定位的方法,这种定位方法增加了航空摄影测量的外业作业过程和经费投入。本文主要研究了将精密单点定位技术应用于GPS辅助空中三角测量的原理和方法,并且通过大量的试验和分析发现,基于精密单点定位技术的GPS辅助空中三角测量可以大大简化航测外业作业过程,并且其定位精度能够满足大比例尺成图的精度要求。     

多卫星系统融合精密单点定位性能分析

随着全球四大卫星导航系统格局的成型,卫星定位系统已从单系统模式发展为如今多系统、多频率融合定位、交互操作的模式。在分析多系统精密单点定位模型及各误差项处理策略的基础上,利用RTKLIB进行GPS,GLONASS,GALILEO,BDS多系统融合精密单点定位试验,并分析其动/静态定位性能。实验结果表明:在单系统空间几何构型较差的情况下,多系统融合精密单点定位较单GPS定位精度可提高20%~40%,收敛时间可缩短35%~50%;在截止高度角超过40°的情况下,单系统会因可见卫星数量不足而无法完成连续定位,而多系统仍能实现高精度的连续定位。这在城区、山区或卫星遮蔽较严重的不利环境中有重要的利用价值。     

Single-frequency precise point positioning with optimal filtering

The accuracy of standalone GPS positioning improved significantly when Selective Availability was turned off in May 2000. With the availability of various public GPS related products including precise satellite orbits and clocks, and ionosphere maps, a single-frequency standalone user can experience even a further improvement of the position accuracy. Next, using carrier phase measurements becomes crucial to smoothen the pseudorange noise. In this contribution, the most critical sources of error in single-frequency standalone positioning will be reviewed and different approaches to mitigate the errors will be considered. An optimal filter (using also carrier phase measurements) will be deployed. The final approach will then be evaluated in a decently long static test with receivers located in different regions of the world. Kinematic experiments have also been performed in various scenarios including a highly dynamic flight trial. The accuracy, in general, can be confirmed at 0.5 m horizontal and 1 m vertical, with static tests. Ultimate results demonstrate an accuracy close to 2 dm (95%) for the horizontal position components and 5 dm (95%) for the vertical in the flight experiment.

Analyzing GNSS data in precise point positioning software

This work demonstrates that precise point positioning (PPP) can be used not only for positioning, but for a variety of other tasks, such as signal analysis. The fact that the observation model used for accurate error modeling has to take into consideration the several effects present in GPS signals, and that observations are undifferenced, makes PPP a powerful data analysis tool sensitive to a variety of parameters. The PPP application developed at the University of New Brunswick, which is called GAPS (GPS Analysis and Positioning Software), has been designed and built in order to take advantage of available precise products, resulting in a data analysis tool for determining parameters in addition to position, receiver clock error, and neutral atmosphere delay. These other estimated parameters include ionospheric delays, code biases, satellite clock errors, and code multipath among others. In all cases, the procedures were developed in order to be suitable for real-time as well as post-processing applications. One of the main accomplishments in the development described here is the use of very precise satellite products, coupled with a very complete observation error modeling to make possible a variety of analyses based on GPS data. In this paper, several procedures are described, their innovative aspects are pointed out, and their results are analyzed and compared with other sources. The procedures and software are readily adaptable for using data from other global navigation satellite systems.     

精密单点定位中对流层延迟参数的相关性研究

为了确定对流层延迟参数的自相关性及其与坐标参数的互相关性,本文研究采用随机卡尔曼滤波进行精密单点定位解算。根据自相关原理计算出对流层天顶延迟误差的自相关函数,采用4种经验函数模型分别对自相关函数进行拟合,结果表明exponential-cos为最佳拟合模型;对对流层天顶延迟误差与坐标垂直分量误差的互相关性进行了分析,结果表明二者显著负线性相关;坐标垂直分量误差波动幅度是对流层天顶延迟误差波动幅度的4倍左右;卫星截止高度角越低,参数相关性越强。     

北斗三号精密单点定位精度分析研究

2020年7月31日,北斗三号全球卫星导航系统(BDS-3)正式开通.BDS-3增加播发B1C、B2a新信号,结合原有北斗二号(BDS-2)的B1I、B2I、B3I信号,5个频点形成7种消电离层组合,进行双频精密单点定位(PPP)研究,结果表明所有组合PPP定位精度在厘米级.     

Tuning a Kalman filter carrier tracking algorithm in the presence of ionospheric scintillation

GPS Solutions - Strong ionospheric electron content gradients may lead to fast and unpredictable fluctuations in the phase and amplitude of the signals from Global Navigation Satellite Systems...     

Ambiguity resolution in precise point positioning with hourly data

Precise point positioning (PPP) has become a powerful tool for the scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station in PPP has been considered difficult, due to the receiver- and satellite-dependent uncalibrated hardware delays (UHD). However, recent studies show that if these UHD can be determined accurately in advance within a network of stations, then ambiguity resolution at a single station becomes possible. In this study, the method proposed by Ge et al. J Geod 82(7):389–399, 2007 is adopted with a refinement in which only one single-difference narrow-lane UHD between a pair of satellites is determined within each full pass over a regional network. This study uses the EUREF (European Reference Frame) Permanent Network (EPN) to determine the UHD from Day 245 to 251 in 2007. Then 12 International GNSS Service stations inside the EPN and 15 outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the mean positioning accuracy in all hourly solutions for the stations inside the EPN is improved from (3.8, 1.5, 2.8) centimeters to (0.5, 0.5, 1.4) centimeters for the East, North and Up components, respectively. For the stations outside the EPN, some of which are over 2,000 km away from the nearest EPN stations, the mean positioning accuracy in the East, North and Up directions still achieves (0.6, 0.6, 2.0) centimeters, respectively, when the EPN-based UHD are applied to these stations. These results demonstrate that ambiguity resolution at a single station can significantly improve the positioning accuracy in hourly PPP. Particularly, UHD can be even applied to a station which is up to thousands of kilometers from the UHD-determination network, potentially showing a great advantage over current network-based GPS augmentation systems. Therefore, it is feasible and beneficial for the operators of GPS regional networks and providers of PPP-based online services to provide these UHD estimates as an additional product.     

Rapid re-convergences to ambiguity-fixed solutions in precise point positioning

Integer ambiguity resolution at a single receiver can be achieved if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved positioning accuracy by such integer resolution, the convergence to an ambiguity-fixed solution normally requires a few tens of minutes. Even worse, these convergences can repeatedly occur on the occasion of loss of tracking locks for many satellites if an open sky-view is not constantly available, consequently totally destroying the practicability of real-time PPP. In this study, in case of such re-convergences, we develop a method in which ionospheric delays are precisely predicted to significantly accelerate the integer ambiguity resolution. The effectiveness of this method consists in two aspects: first, wide-lane ambiguities can be rapidly resolved using the ionosphere-corrected wide-lane measurements, instead of the noisy Melbourne–Wübbena combination measurements; second, narrow-lane ambiguity resolution can be accelerated under the tight constraints derived from the ionosphere-corrected unambiguous wide-lane measurements. In the test at 90 static stations suffering from simulated total loss of tracking locks, 93.3 and 95.0% of re-convergences to wide-lane and narrow-lane ambiguity resolutions can be achieved within five epochs of 1-Hz measurements, respectively, even though the time latency for the predicted ionospheric delays is up to 180 s. In the test at a mobile van moving in a GPS-adverse environment where satellite number significantly decreases and cycle slips frequently occur, only when the predicted ionospheric delays are applied can the rate of ambiguity-fixed epochs be dramatically improved from 7.7 to 93.6% of all epochs. Therefore, this method can potentially relieve the unrealistic requirement of a continuous open sky-view by most PPP applications and improve the practicability of real-time PPP.     

Real-time single-frequency precise point positioning: accuracy assessment

The performance of real-time single-frequency precise point positioning is demonstrated in terms of position accuracy. This precise point positioning technique relies on predicted satellite orbits, predicted global ionospheric maps, and in particular on real-time satellite clock estimates. Results are presented using solely measurements from a user receiver on the L1-frequency (C1 and L1), for almost 3?months of data. The empirical standard deviations of the position errors in North and East directions are about 0.15?m, and in Up direction about 0.30?m. The 95% errors are about 0.30?m in the horizontal directions, and 0.65?m in the vertical. In addition, single-frequency results of six receivers located around the world are presented. This research reveals the current ultimate real-time single-frequency positioning performance. To put these results into perspective, a case study is performed, using a moderately priced receiver with a simple patch antenna.