Comparison of 4D tomographic mapping versus thin-shell approximation for ionospheric delay corrections for single-frequency GPS receivers over North America

The majority of navigation satellite receivers operate on a single frequency. They compensate for the ionospheric delay using either an ionospheric model which typically only corrects for 50% of the delay or a thin-shell map of the ionosphere. A 4D tomographic imaging technique is used to map the free electron density over the full-height of the ionosphere above North America during autumn 2003. The navigation solutions computed using correction based upon the thin-shell and the full-height maps are compared in this paper. The maps are used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across North America. The excess delay is applied to correct the single-frequency pseudorange observations at each location, and the improvements to the resulting positioning are calculated. It is shown that the thin-shell and full-height maps perform almost as well as a dual-frequency carrier-smoothed benchmark and for most receivers better than the unfiltered dual-frequency benchmark. The full-height corrections perform well and are considerably better than thin-shell corrections under extreme storm conditions.     

The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1σ).     

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.     

Understanding the role of the ionospheric delay in single-point single-epoch GPS coordinates

The ionospheric delay is the main source of error for single-point single-epoch (SPSE) GPS positioning when using single-frequency receivers. In contrast to the common slant approach, in this article we focus on its effect in final coordinates through the study of bias propagation in SPSE positioning: we first show an analytical resolution for the propagation problem with highly symmetric satellite configurations. To overcome some of the disadvantages of this first method, we use Santerre’s technique and, finally, present a new numerical methodology that allows us to generalize for a real geometry and obtain an average ionospheric positioning error over a given site. From the results obtained, four working hypotheses that relate the ionospheric shape above the receiver with final position errors are presented and tested. These four hypotheses, which agree with average ionospheric positioning error in 95% of the studied cases, can be related to the construction of the design matrix. Finally, these hypotheses have been used to address a situation where the ionospheric delay is corrected with an ionospheric model.     

GPS scintillation over the European Arctic during the November 2004 storms

Small-scale irregularities in the background electron density of the ionosphere can cause rapid fluctuations in the amplitude and phase of radio signals passing through it. These rapid fluctuations are known as scintillation and can cause a Global Positioning System (GPS) receiver to lose lock on a signal. This could compromise the integrity of a safety of life system based on GPS, operating in auroral regions. In this paper, the relationship between the loss of lock on GPS signals and ionospheric scintillation in auroral regions is explored. The period from 8 to 14 November 2004 is selected for this study, as it includes both geomagnetically quiet and disturbed conditions. Phase and amplitude scintillation are measured by GPS receivers located at three sites in Northern Scandinavia, and correlated with losses of signal lock in receivers at varying distances from the scintillation receivers. Local multi-path effects are screened out by rejection of low-elevation data from the analysis. The results indicate that losses of lock are more closely related to rapid fluctuations in the phase rather than the amplitude of the received signal. This supports the idea, suggested by Humphreys et al. (2005) (performance of GPS carrier tracking loops during ionospheric scintillations. Proceedings Internationsl Ionospheric Effects Symposium 3–5 May 2005), that a wide loop bandwidth may be preferred for receivers operating at auroral latitudes. Evidence from the Imaging Riometer for Ionospheric Studies (IRIS) appears to suggest that, for this particular storm, precipitation of particles in the D/E regions may be the mechanism that drives the rapid phase fluctuations in the signal.

利用单频GPS／Galileo组合观测值的导航性能分析

针对不同观测值的初始方差比值,对比GPS／Galileo组合单点定位的结果。利用不同测站的观测数据和广播星历数据进行单频GPS／Galileo组合单点定位试验。结果表明,组合GPS／Galileo单点定位的平面方向精度优于2m,高程方向精度优于4m,点位精度优于5m;相比于GPS单系统,GPS／Galileo组合系统在平面方向的定位精度略有提高,高程方向的定位精度改善率为11％。同时给出基于4颗IOV卫星的Galileo单点定位结果。     

论电离层对GPS定位的影响

电离层是ＧＰＳ定位的主要误差源。本文论述电离层的特征和折射系数,以及电离层的下列影响：电离层码群延、电离层载波相位超前、电离层多普勒频移、振幅闪烁、电离层相位闪烁效应、磁暴对ＧＰＳ定位测量的影响、电离层对差分ＧＰＳ的影响和ＧＰＳ接收机的电离层改正。     

An improvement to ionospheric delay correction for single-frequency GPS users – the APR-I scheme

 For the commonly used GPS wide-area augmentation systems (WAAS) with a grid ionospheric model, the efficient modelling of ionospheric delays in real time, for single-frequency GPS users, is still a crucial issue which needs further research. This is particularly necessary when differential ionospheric delay corrections cannot be broadcast, when users cannot receive them, or when there are ionospheric anomalies. Ionospheric delays have a severe effect on navigation performance of single-frequency receivers. A new scheme is proposed which can efficiently address the above problems. The robust recurrence technique is based on the efficient combination of single-frequency GPS observations by users and the high-precision differential ionospheric delay corrections from WAAS. Its effectiveness is verified with examples. Received: 24 December 1999 / Accepted 21 February 2001     

中低纬度地区连续运行参考站网络电离层扰动修正技术研究

分析了电离层扰动对中长距离连续运行参考站网络(CORS)的工作性能的影响,论证了中小尺度电离层行进式扰动是影响中低纬度地区CORS基线解算和实时定位精度的最主要误差源。本文提出了时相关电离层修正模型,通过在双线性曲面纠正模型上附加中尺度电离层扰动修正信息,实现电离层预报修正技术。在100 km以上长距离参考站网的实验验证了该技术应用于CORS领域减弱电离层强扰动影响方面的有效性。     

Double-epoch algorithm in rapid positioning using single frequency GPS receivers

A new algorithm, called as Double-Epoch Algorithm (DEA) is proposed in GPS rapid positioning using two epoch single frequency phase data in this paper. Firstly, the structure characteristic of the normal matrix in GPS rapid positioning is analyzed. Then, in the light of the characteristic, based on TIKHONOV regularization theorem, a new regularizer is designed to mitigate the ill-condition of the normal matrix. The accurate float ambiguity solutions and their MSEM (Mean Squared Error Matrix) are obtained, using two epoch single frequency phase data. Combined with LAMBDA method, DEA can fix the integer ambiguities correctly and quickly using MSEM instead of the covariance matrix of the ambiguities. Compared with the traditional methods, DEA can improve the efficiency obviously in rapid positioning. So, the new algorithm has an extensive application outlook in deformation monitoring, pseudokinematic relative positioning and attitude determination, etc.     

Double-epoch algorithm in rapid positioning using single frequency GPS receivers

A new algorithm, called as Double-Epoch Algorithm (DEA) is proposed in GPS rapid positioning using two epoch single frequency phase data in this paper. Firstly, the structure characteristic of the normal matrix in GPS rapid positioning is analyzed. Then, in the light of the characteristic, based on TIK-HONOV regularization theorem, a new regularizer is designed to mitigate the ill-condition of the normal matrix. The accurate float ambiguity solutions and their MSEM (Mean Squared Error Matrix) are obtained, using two epoch single frequency phase data. Combined with LAMBDA method, DEA can fix the integer ambiguities correctly and quickly using MSEM instead of the covariance matrix of the ambiguities. Compared with the traditional methods, DEA can improve the efficiency obviously in rapid positioning. So, the new algorithm has an extensive application outlook in deformation monitoring, pseudokinematic relative positioning and attitude determination, etc.     

GPS单频机电离层延迟改正新算法

探讨了几种新的电离层延迟改正算法,通过算例检验了新方案的效率和可行性,对不同精度用户选取电离层延迟改正方案给出了建议。     

Spin rate estimation of sounding rockets using GPS wind-up

Carrier phase wind-up is a well-known effect that arises from the relative rotation between a transmitting and receiving antenna. In GPS measurements at L1 frequency, this effect translates into an error of 19.029 cm per full relative rotation of antennas. Since this effect is independent of the satellite elevation for pure rotation about the antenna boresight axis, it is usually absorbed by the clock estimation in navigation algorithms. Therefore, the impact of wind-up is usually neglected for applications that do not require accuracies to the cm level like RTK. However, in receiving platforms with high rotation rate, the accumulated wind-up value can be important and actually be larger than receiver noise or even ionospheric variations. Therefore, in such scenarios, the wind-up contribution can be isolated and used as a source of information to compute the spin rate of such platforms using an appropriate combination of GPS observables. This work shows some results of a coarse, yet simple, approach to monitor the rotation angle and spin-rate of spin stabilized sounding rockets flown by DLR.     

GPS网络RTK流动站的对流层内插改正分析

介绍网络RTK常规内插模型,分析内插法的精度,从单站上分析高程对天顶距延迟的影响,分析高程差异对双差对流层延迟的影响,利用网络RTK内插法只可消除其中大部分的误差.这对利用网络RTK算法生成流动站的误差改正数具有重要的参考价值.     

单频GPS非连续历元周跳处理研究

常规的周跳处理方法大都适用于连续观测数据中的周跳处理,本文则重点针对由于建筑物遮挡或信号干扰等原因,暂时性中断的GPS数据可能出现的周跳进行正确处理的研究。本文采用基于模糊度参数重设的GPS定位模型重建以及基于变采样区间的改进的多项式拟合法的周跳处理算法,可在一定程度上有效解决GPS数据失锁对于定位解算造成的不利影响。     

GPS现代化后电离层折射误差高阶项的三频改正方法

研究了电离层对GPS观测信号的主要影响及电离层折射误差模型,总结了电离层双频改正模型。针对GPS现代化中增加的第三频率,系统推导了三个频率的电离层改正模型及相位观测值无电离层组合(LC组合)模型。该模型将电离层折射误差模型改正至二阶项,可进一步提高GPS定位精度,同时,为GPS定位中其他误差的改正及分离、周跳的探测等提供了有力的技术手段。     

GPS高程转换中考虑地形改正的几何方法

讨论了出区地形变化较大,在进行ＧＰＳ高程转换时所应加入的地形改正,给出了改正公式。     

Performance comparison of semicodeless GPS receivers for LEO satellites

This report provides a detailed performance analysis of three semicodeless dual-frequency GPS receivers for use in low Earth orbit (LEO). The test set comprises the IGOR receiver, which represents a follow-on of the flight-proven BlackJack receiver, as well as two geodetic receivers (NovAtel OEM4-G2 and Septentrio PolaRx2), which are entirely based on commercial-off-the-shelf technology (COTS). All three receivers are considered for upcoming flight projects or experiments and have undergone at least a preliminary environmental qualification program. Using extensive signal simulator tests, the cold start signal acquisition, tracking sensitivity, differential code biases, raw measurement accuracy, and navigation accuracy of each receiver have been assessed. All tests are based on a common scenario that is representative of an actual space mission and provides a realistic simulation of the signal dynamics and quality on a scientific LEO satellite. Compared to the other receivers, the IGOR instrument exhibits a superior tracking sensitivity and is thus best suited for occultation measurements with low tangent point altitudes. The OEM4-G2 and PolaRx2 receivers are likewise shown to properly track dual-frequency GPS signals and normal signal levels and to provide accurate code and carrier phase measurements. Given their limited resource requirements, these receivers appear well suited for precise orbit determination applications and ionospheric sounding onboard of microsatellites with tight mission budgets.