Real-time kinematic positioning of LEO satellites using a single-frequency GPS receiver

Due to their low cost and low power consumption, single-frequency GPS receivers are considered suitable for low-cost space applications such as small satellite missions. Recently, requirements have emerged for real-time accurate orbit determination at sub-meter level in order to carry out onboard geocoding of high-resolution imagery, open-loop operation of altimeters and radio occultation. This study proposes an improved real-time kinematic positioning method for LEO satellites using single-frequency receivers. The C/A code and L1 phase are combined to eliminate ionospheric effects. The epoch-differenced carrier phase measurements are utilized to acquire receiver position changes which are further used to smooth the absolute positions. A kinematic Kalman filter is developed to implement kinematic orbit determination. Actual flight data from China’s small satellite SJ-9A are used to test the navigation performance. Results show that the proposed method outperforms traditional kinematic positioning method in terms of accuracy. A 3D position accuracy of 0.72 and 0.79 m has been achieved using the predicted portion of IGS ultra-rapid products and broadcast ephemerides, respectively.     

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).     

Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers

Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.     

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.     

区域电离层建模的单频伪距定位验证

针对电离层单层模型无法满足单频用户定位精度要求的问题,该文建立了区域电离层斜路径模型和单星多项式函数模型。基于河北省区域CORS站的实验结果表明:该文建立的区域电离层模型的拟合精度比CODE中心的格网电离层模型提高了近80%。并将其应用于北斗、GPS单频伪距单点定位,得出北斗的单点定位高程和平面定位精度分别优于3和2m,GPS的单点定位高程和平面定位精度分别优于1.5和1m;相对于CODE,GPS和北斗在平面及高程方向的定位精度均提高了50%左右。结果证明,采用斜路径电离层模型和多项式函数模型,可以较好地反映区域电离层的精细结构。     

Performance evaluation of different ionospheric models in single-frequency code-based differential GPS positioning

Differential ionospheric slant delays are obtained from a quiet-time, three-dimensional ionospheric electron density model, called the TaiWan Ionosphere Model (TWIM), to be used in code-based differential GPS positioning. The code observations are acquired from nine continuously operating GPS stations around Taiwan whose baseline ranged from 19 to 340 km. Daily 24-hour epoch-per-epoch positioning obtained for 70 most geomagnetic quiet days (2008–2010) for each of the 72 baselines. The performance of TWIM has been compared with the standard operational Klobuchar model (KLB) used by typical single-frequency receivers and the IGS global ionospheric model (GIM). Generally, TWIM performed well in reducing the differential ionospheric delay especially for long baselines and different levels of low solar activity. It has a much better performance compared to the operational KLB model. TWIM also performed similarly with GIM, though GIM has the best performance overall. GIM has the best ionospheric gradient estimates among the three models whose differential ionospheric delay-to-horizontal error ratio is more than 0.25. This is followed closely by TWIM with about 0.20. KLB only has a ratio of <0.10. The similarity of the performance of TWIM and GIM demonstrates the feasibility of TWIM in correcting for differential ionospheric delays in the C/A code pseudorange that is caused by electron density gradients in the ionosphere. It can provide decimeter-to-centimeter level accuracy in differential GPS positioning for single-frequency receivers during geomagnetic quiet conditions across all seasons and different levels of low solar activities.     

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.     

Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50–70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.     

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.     

北斗三号全球导航卫星系统全球广播电离层延迟修正模型(BDGIM)应用性能评估

2020年6月23日,我国北斗三号全球导航卫星系统正式完成星座全球组网.北斗三号全球导航卫星系统采用新一代全球广播电离层延迟修正模型(BDGIM),为用户提供电离层延迟改正服务.本文利用高精度全球电离层格网(GIM)以及实测BDS/GPS数据提供的电离层TEC作为参考,从延迟改正精度及北斗单频伪距单点定位应用、模型系数...     

Precision spacecraft navigation using a low-cost GPS receiver

Within the PROBA-2 microsatellite mission, a miniaturized single-frequency GPS receiver based on commercial-off-the-shelf (COTS) technology is employed for onboard navigation and timing. A rapid electronic fuse protects against destructive single-event latch-ups (SEL) and enables a quasi-continuous receiver operation despite the inherent sensitivity to space radiation. While limited to single-frequency C/A-code tracking with a narrow-band frontend, the receiver is able to provide precision navigation services through processing of raw GPS measurements on ground as well as a built-in real-time navigation system. In both cases, ionospheric path delays are eliminated through a combination of L1 pseudorange and carrier phase measurements, which also offers a factor-of-two noise reduction relative to code-only processing. By comparison with satellite laser ranging (SLR) measurements, a 0.3-m (3D rms) accuracy is demonstrated for the PROBA-2 reduced dynamic orbit determinations using post-processed GPS orbit and clock products. Furthermore, the experimental onboard navigation system is shown to provide real-time position information with a 3D rms accuracy of about 1?m, which notably outperforms the specification of the Standard Positioning Service (SPS). In view of their lower hardware complexity, mass budget and power requirements as well as the reduced interference susceptibility, legacy C/A-code receivers can thus provide an attractive alternative to dual-frequency receivers even for demanding navigation applications in low Earth orbit.     

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     

Ionospheric error contribution to GNSS single-frequency navigation at the 2014 solar maximum

For single-frequency users of the global satellite navigation system (GNSS), one of the main error contributors is the ionospheric delay, which impacts the received signals. As is well-known, GPS and Galileo transmit global models to correct the ionospheric delay, while the international GNSS service (IGS) computes precise post-process global ionospheric maps (GIM) that are considered reference ionospheres. Moreover, accurate ionospheric maps have been recently introduced, which allow for the fast convergence of the real-time precise point position (PPP) globally. Therefore, testing of the ionospheric models is a key issue for code-based single-frequency users, which constitute the main user segment. Therefore, the testing proposed in this paper is straightforward and uses the PPP modeling applied to single- and dual-frequency code observations worldwide for 2014. The usage of PPP modeling allows us to quantify—for dual-frequency users—the degradation of the navigation solutions caused by noise and multipath with respect to the different ionospheric modeling solutions, and allows us, in turn, to obtain an independent assessment of the ionospheric models. Compared to the dual-frequency solutions, the GPS and Galileo ionospheric models present worse global performance, with horizontal root mean square (RMS) differences of 1.04 and 0.49 m and vertical RMS differences of 0.83 and 0.40 m, respectively. While very precise global ionospheric models can improve the dual-frequency solution globally, resulting in a horizontal RMS difference of 0.60 m and a vertical RMS difference of 0.74 m, they exhibit a strong dependence on the geographical location and ionospheric activity.     

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。     

基于北斗GEO的电离层延迟修正方法比较与分析

电离层延迟是影响导航定位精度的最主要因素。北斗卫星导航系统采用Klobuchar模型修正单频接收机用户的电离层延迟误差,对于双频接收机,可以利用不同频率信号的伪距观测数据解算得到电离层延迟值。为比较两种方法在天津地区的电离层延迟修正效果,利用NovAtel GPStation6接收机(GNSS电离层闪烁和TEC监测接收机)采集到的卫星实测数据进行计算。以国际全球导航卫星系统服务组织(IGS)发布的全球电离层格网数据为参考,对两种方法的修正效果进行比较分析。结果表明,在天津地区,利用双频观测值解算电离层延迟比Klobuchar模型计算结果更加精确,且平均每天的修正值达到IGS发布数据的82.11％,比Klobuchar模型计算值高948％      

几种电离层模型对单频单点定位的影响分析

针对实时GNSS单频定位中电离层延迟改正问题,本文采用可用于实时GNSS单频定位的几种电离层模型对电离层延迟进行改正并分析其对GNSS单频单点定位性能的影响。其中,对单频SPP的电离层延迟采用模型直接进行改正,采用Klobuchar模型、CODE的预报产品c1pg、原国家测绘地理信息局的实时球谐电离层产品cosong和CODE事后产品codg计算的电离层精度依次提高;采用不同电离层模型作为电离层估计的先验约束进行单频PPP定位。结果表明:采用精度较好的电离层产品作为先验约束可加快单频PPP收敛。     

A preliminary evaluation of the performance of multiple ionospheric models in low- and mid-latitude regions of China in 2010–2011

Ionospheric delay is a dominant error source in Global Navigation Satellite System (GNSS). Single-frequency GNSS applications require ionospheric correction of signal delay caused by the charged particles in the earth’s ionosphere. The Chinese Beidou system is developing its own ionospheric model for single-frequency users. The number of single-frequency GNSS users and applications is expected to grow fast in the next years in China. Thus, developing an appropriate ionospheric model is crucially important for the Chinese Beidou system and worldwide single-frequency Beidou users. We study the performance of five globally accessible ionospheric models Global Ionospheric Map (GIM), International Reference Ionosphere (IRI), Parameterized Ionospheric Model (PIM), Klobuchar and NeQuick in low- and mid-latitude regions of China under mid-solar activity condition. Generally, all ionospheric models can reproduce the trend of diurnal ionosphere variations. It is found that all the models have better performances in mid-latitude than in low-latitude regions. When all the models are compared to the observed total electron content (TEC) data derived from GIM model, the IRI model (2012 version) has the best agreement with GIM model and the NeQuick has the poorest agreement. The RMS errors of the IRI model using the GIM TEC as reference truth are about 3.0–10.0 TECU in low-latitude regions and 3.0–8.0 TECU in mid-latitude regions, as observed during a period of 1 year with medium level of solar activity. When all the ionospheric models are ingested into single-frequency precise point positioning (PPP) to correct the ionospheric delays in GPS observations, the PIM model performs the best in both low and mid-latitudes in China. In mid-latitude, the daily single-frequency PPP accuracy using PIM model is ~10 cm in horizontal and ~20 cm in up direction. At low-latitude regions, the PPP error using PIM model is 10–20 cm in north, 30–40 cm in east and ~60 cm in up component. The single-frequency PPP solutions indicate that NeQuick model has the lowest accuracy among all the models in both low- and mid-latitude regions of China. This study suggests that the PIM model may be considered for single-frequency GNSS users in China to achieve a good positioning accuracy in both low- and mid-latitude regions.     

北极地区BDS-3伪距单点定位精度分析

针对北斗三号卫星导航系统（BDS-3）在北极地区的定位性能,本文基于METG站和SOD3站分析了北极地区BDS-3的卫星可见数、PDOP 值、单频和双频伪距单点定位精度.经研究发现,北极地区BDS-3卫星可见数和 PDOP 值与GPS卫星一致,B1I频率与B3I频率伪距单点定位精度相当,相比于GPS卫星L1频率伪距单点定位精度略差,B1I／B3I频率组合下的伪距单点定位精度低于任一单频伪距单点定位精度,并且相比于GPS卫星L1／L2频率组合下的伪距单点定位精度略差.      

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。     

Klobuchar电离层模型精化进展

电离层延迟是卫星导航定位的重要误差源之一。采用合适的电离层延迟模型可以有效地减弱电离层延迟误差对定位结果的影响。目前在导航定位中运用最广泛的是Klobuchar模型,但Klobuchar模型的修正率只有50%~60%。为了满足日益增长的导航定位精度的需求,不同的精化模型被提出。本文介绍了Klobuchar模型在GPS和BDS系统中的应用,比较了在两个系统应用时的差异。回顾概括了文献在Klobuchar模型的参数精化和模型精化两个方面的研究,并对各种精化模型进行了对比总结。模型精化的结果优于参数精化,未来对于Klobuchar模型的精化更趋向于模型精化。