Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing

The network-based real-time kinematic (RTK) positioning has been widely used for high-accuracy applications. However, the precise point positioning (PPP) technique can also achieve centimeter to decimeter kinematic positioning accuracy without restriction of inter-station distances but is not as popular as network RTK for real-time engineering applications. Typically, PPP requires a long initialization time and continuous satellite signals to maintain the high accuracy. In case of phase breaks or loss of signals, re-initialization is usually required. An approach of instantaneous cycle slips fixing using undifferenced carrier phase measurements is proposed, which leads to instantaneous re-initialization for real-time PPP. In the proposed approach, various errors such as real-time orbit and clock errors, atmosphere delay and wind-up effects are first refined and isolated from integer cycle slips. The integer values of cycle slips can then be estimated and fixed with the LAMBDA technique by applying a cascade cycle slip resolution strategy. Numerical experiments with different user dynamics are carried out to allow a comprehensive evaluation of efficiency and robustness of the cycle slip fixing algorithm. The results show that the cycle slips can be fixed correctly in all cases considered and that data gaps of up to 300?s can be connected with high confidence. As a result, instantaneous re-initialization is achieved in the real-time PPP processing.     

基于几何模型的惯性辅助PPP周跳修复与快速重新收敛

在复杂观测环境下,GNSS信号容易发生周跳和失锁现象,导致精密单点定位技术（PPP）模糊度重新初始化,影响定位精度及可靠性。本文基于PPP／SINS紧组合,提出了利用短时间内惯导递推的高精度位置信息辅助PPP周跳修复的几何模型。该模型采用原始观测值建立历元间差分方程,将周跳作为参数进行估计,而惯导提供的高精度位置作为带权的虚拟观测值参与平差解算,在固定周跳整数值后修复相位观测值,从而保持高精度的连续定位。以车载和机载两组数据分析了该方法的有效性,结果表明,引入惯性辅助能够显著加快PPP定位的重新收敛,实现周跳的准确修复。      

Performance of the L2C civil GPS signal under various ionospheric scintillation effects

As GPS is modernizing, there are currently fourteen satellites transmitting L2C civil code and seven satellites transmitting L5 signal. While the GPS observables are subject to several sources of errors, the ionosphere is one of the largest error sources affecting GPS signals. Small irregularities in the electrons density along the GPS radio signal propagation path cause ionospheric scintillation that is characterized by rapid fluctuations in the signal amplitude and phase. The ionospheric scintillation effects are stronger in equatorial and high-latitude geomagnetic latitude regions and occur mainly due to equatorial anomaly and solar storms. Several researchers have analyzed the L2C signal quality since becoming available in December, 2005. We analyze the performance of L2C using GPS data from stations in the equatorial region of Brazil, which is subject of weak, moderate and strong ionospheric scintillation conditions. The GPS data were collected by Septentrio PolaRxS–PRO receivers as part of the CIGALA/CALIBRA network. The analysis was performed as a function of scintillations indexes S4 and Phi60, lock time (time interval in seconds that the carrier phase is tracked continuously without cycle slips), multipath RMS and position variation of precise point positioning solutions. The analysis shows that L2C code solutions are less affected by multipath effects than that of P2 when data are collected under weak ionospheric scintillation effects. In terms of analysis of positions, the kinematic PPP results using L2C instead P2 codes show accuracy improvements up to 33 % in periods of weak or strong ionospheric scintillation. When combining phase and code collected under weak scintillation effects, the results by applying L2C against P2 provide improvement in accuracy up to 59 %. However, for data under strong scintillation effects, the use of L2C for PPP with code and phase does not provide improvements in the positioning accuracy.     

Mitigating the impact of ionospheric cycle slips in GNSS observations

Processing of data from global navigation satellite systems (GNSS), such as GPS, GLONASS and Galileo, can be considerably impeded by disturbances in the ionosphere. Cycle-slip detection and correction thus becomes a crucial component of robust software. Still, dealing with ionospheric cycle slips is not trivial due to scintillation effects in both the phase and the amplitude of the signals. In this contribution, a geometry-based approach with rigorous handling of the ionosphere is presented. A detailed analysis of the cycle-slip correction process is also tackled by examining its dependence on phase and code noise, non-dispersive effects and, of course, the ionosphere. The importance of stochastic modeling in validating the integer cycle-slip candidates is emphasized and illustrated through simulations. By examining the relationship between ionospheric bias and ionospheric constraint, it is shown that there is a limit in the magnitude of ionospheric delay variation that can be handled by the cycle-slip correction process. Those concepts are applied to GNSS data collected by stations in northern Canada, and show that enhanced cycle-slip detection can lead to decimeter-level improvements in the accuracy of kinematic PPP solutions with a 30-s sampling interval. Cycle-slip correction associated with ionospheric delay variations exceeding 50 cm is also demonstrated, although there are risks with such a procedure and these are pointed out.     

A double-differenced cycle slip detection and repair method for GNSS CORS network

The difficulty to detect and repair cycle slip of carrier phase measurements is a key limit for continuously high accuracy of GNSS positioning and navigation services. We propose an automated cycle slip detection and repair method for data preprocessing of a CORS network. The method jointly uses double-differenced (DD) geometry-free (GF) combination and ionospheric-free observation corrected for the computed geometrical distance (IF-OMC) to estimate the cycle slips in dual-frequency observations. The DD GF combination, which is only affected by the ionospheric residual, can be used to detect cycle slips with high reliability except for special pairs such as (77, 60) on GPS L1/L2 frequencies. The detection principle of the IF-OMC observable is such that there is a large discontinuity related to the previous epoch when cycle slips occur at the present epoch. The disadvantages of these two combinations can be overcome employing the proposed detection method. The cycle slip pair (77, 60) has no effect on the GF combination, while a change of 14.65 m is derived from GPS L1/L2 observations using the IF-OMC algorithm. Using pre-determined station coordinates as precise values, we found that the accuracy of the DD IF-OMC combination was 18 mm for a 200-km CORS baseline. Therefore, cycle slips in dual-frequency observations can be correctly and uniquely determined using DD GF and IF-OMC equations. The proposed method was verified by adding simulated cycle slips in observations collected from the CORS network under a quiet ionosphere and shown to be effective. Moreover, the method was assessed with observations made during intense ionospheric activity, which generated extensive cycle slips. The results show that the algorithm can detect and repair all cycle slips apart from two exceptions relating to long data gaps.     

CORS基准站周跳探测与修复方法研究

在高精度GNSS测量中,周跳的存在直接影响到整周模糊度的解算及最终定位精度。针对目前各省市连续运行基准站网多系统观测数据的获取导致周跳探测工作量增加,该文基于甘肃省卫星定位连续运行基准站网(GSCORS)双频观测值提出了一种满足普遍条件的多系统周跳探测方法。采用相位减伪距结合电离层残差法分别对GPS和BDS原始观测值进行周跳探测与修复,通过对相应载波的模拟周跳探测发现,BDS较大的卫星钟差和伪距噪声影响了数据质量,其周跳检测量时间序列波动大于GPS,对7周以上周跳探测的精度较GPS会有1周的偏差,但电离层残差法能对BDS相位减伪距法探测残留的1周小周跳进行二次探测并修复。实验最终证实该方法能够有效探测并且正确分离GPS和BDS每个频率1周以上的周跳。     

Benefits of the third frequency signal on cycle slip correction

Cycle slip detection and correction are important issues when carrier phase observations are used in high-precision GNSS data processing and have, therefore, been intensively investigated. Along with the GNSS modernization, the cycle slip correction (CSC) problem has been raised to deal with more signals from multi-frequencies. We extend the geometry-based approach by integrating time-differenced pseudorange and carrier phase observations to estimate the integer number of triple-frequency cycle slips together with the receiver clock offset, ionospheric delay variations and receiver displacements. The Least-squares AMBiguity Decorrelation Adjustment method can be employed. The benefit of the third frequency observation on the cycle slip estimate is first investigated with simulation tests. The results show that adding the third frequency observation can significantly improve the model strength and that a reliable triple-frequency CSC with a theoretical success rate of higher than 99.9 % can still be achieved, even under the condition that the range or ionosphere delay variation is poorly defined. The performance of triple-frequency CSC is validated with real triple-frequency BDS data since all BDS satellites in orbit are transmitting triple-frequency signals. The results show that the fixing rate of CSC can reach 99.1 % in static precise point positioning (PPP) and 98.8 % in the kinematic case. PPP solutions with cycle slip-uncorrected and cycle slip-corrected data sets are compared to validate the correctness of triple-frequency CSC. The standard deviations of the PPP solution in east, north and vertical component, respectively, can be improved by 31.1, 30.7 and 37.6 % for static, and by 42.0, 53.8 and 39.7 % for kinematic after cycle slips are corrected. The performance of dual- and triple-frequency CSC is also compared. Results show that the performance of dual-frequency CSC is slightly worse than that of triple-frequency CSC. These results demonstrate that the performance of CSC can be significantly improved with triple-frequency observations.     

A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.     

电离层闪烁对全球导航卫星系统（GNSS）的定位影响分析

电离层闪烁是影响卫星导航系统定位性能的重要因素之一,中国南方区域是全球电离层闪烁多发区之一,开展电离层闪烁对卫星导航系统性能的影响研究具有重要意义。利用中国区域的电离层闪烁数据和GPS测量数据,对电离层闪烁情况下的用户定位性能进行了比较分析,发现电离层闪烁将引起用户定位误差的普遍增大,严重时可能出现定位异常,电离层闪烁对不同的定位应用方式具有不同程度的影响,电离层闪烁对卫星导航系统的多种影响是卫星导航系统的重要威胁之一。     

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。     

电离层闪烁对卫星导航系统性能影响的仿真分析

电离层闪烁是影响卫星导航系统定位性能的重要因素之一。通过仿真方法对中国区域用户定位性能受电离层闪烁影响的情况进行分析研究。结合电离层闪烁模型、卫星导航接收机模型和用户定位算法,仿真了中国区域内卫星导航系统用户在电离层闪烁存在情况下的定位精度性能。仿真结果表明：电离层闪烁将引起用户接收机测量误差的增大,在受电离层闪烁影响严重的中国低纬地区,用户定位误差将有明显增大,严重时可能出现定位异常。     

Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity

We develop a new approach for cycle slip detection and repair under high ionospheric activity using undifferenced dual-frequency GPS carrier phase observations. A forward and backward moving window averaging (FBMWA) algorithm and a second-order, time-difference phase ionospheric residual (STPIR) algorithm are integrated to jointly detect and repair cycle slips. The FBMWA algorithm is proposed to detect cycle slips from the widelane ambiguity of Melbourne–Wübbena linear combination observable. The FBMWA algorithm has the advantage of reducing the noise level of widelane ambiguities, even if the GPS data are observed under rapid ionospheric variations. Thus, the detection of slips of one cycle becomes possible. The STPIR algorithm can better remove the trend component of ionospheric variations compared to the normally used first-order, time-difference phase ionospheric residual method. The combination of STPIR and FBMWA algorithms can uniquely determine the cycle slips at both GPS L ₁ and L ₂ frequencies. The proposed approach has been tested using data collected under different levels of ionospheric activities with simulated cycle slips. The results indicate that this approach is effective even under active ionospheric conditions.     

GNSS精密单点定位中的实时质量控制

提出了一套适用于GNSS精密单点定位(PPP)的实时质量控制方法,重点研究了钟跳探测与修复、周跳探测与标记、抗差估计方法,并在现有质量控制方法的基础上进行了改进。对比分析了不同质量控制方案对PPP的影响,结果表明,钟跳不利于周跳探测,严重影响非差PPP的精度和效率,必须对其进行探测与修复;联合MW、GF组合可以探测出绝大多数周跳,且较使用单一方法更为准确、可靠;采用改进的抗差估计有效抑制了残余粗差对精密定位的影响,显著提高了PPP的精度和可靠性。     

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.     

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.     

基于原始观测值的单频精密单点定位算法

研究了一种基于GPS原始观测值的单频PPP算法。该算法通过增加电离层延迟先验信息、空间和时间约束的虚拟观测方程,将电离层延迟当作未知参数与其他定位参数一并进行估计来高效修正电离层延迟误差。通过使用全球178个IGS站1d的实测数据对本算法的收敛速度、定位精度和电离层VTEC的精度进行检验与分析。结果表明,该算法的收敛速度和稳定性均得到了改善,其静态单频单天PPP解的精度可达2~3cm、模拟动态单频单天PPP解的精度可达2~3dm,并且单频PPP与双频PPP提取的电离层总电子含量平均偏差小于5个TECU,可作为一种附属定位产品使用。     

Brazilian active GNSS networks as systems for monitoring the ionosphere

This research shows the viability of using Global Navigation Satellite System (GNSS) stations from Brazilian active networks in monitoring the ionosphere. Various indexes of ionospheric irregularities and scintillation of GNSS signals, estimated in real-time and post-processed from GNSS data, are explored for this purpose. This way, an increase in the spatial resolution of ionospheric information is provided, allowing the generation of maps of scintillation and irregularities in observing the spatial and temporal behavior of the layer’s activity cycle, since the number of ionosondes, imagers, and radars is insufficient for monitoring the irregularities in Brazil. Experiments to evaluate the estimates of the indexes are performed for periods of high and low variability of electrons. Three Brazilian networks are used: the Brazilian Network for Continuous Monitoring (RBMC), the GNSS Active Network of Sao Paulo State (GNSS-SP), and CIGALA/CALIBRA. The results are compared with data from ionosondes and PolaRxS-PRO Septentrio receivers, proving compatible with moderate to high correlations. An analysis of the seasonal variation during the peak of solar cycle 24 is carried out. The maps allow identifying the displacement of ionospheric irregularities along the magnetic equator over Brazil, from northeast to southwest, starting at 7:00 pm and ending at 2:00 am local time. Real-time monitoring is carried out for the summer solstice in the southern hemisphere, and results are consistent with those from the post-processed mode. The indexes and maps can be applied to the analysis of GNSS positioning. Real-time ionospheric information can be used in important practical applications because the displacement monitoring of irregularities allows prior knowledge of whether there will be a deterioration of positioning accuracy in a certain region.     

Evaluation of three ionospheric delay computation methods for ground-based GNSS receivers

GNSS observables for ionospheric estimation are commonly based on carrier-to-code leveling (CCL) and precise point positioning (PPP) methods. The CCL method is a geometry-free method which uses carrier phase to level pseudorange observation for decreasing multipath error and observation noise. However, the ionospheric observable based on the CCL has been proven to be affected by leveling errors. The leveling errors are caused by pseudorange multipath and intraday variation of receiver DCB. To obtain more accurate ionospheric observable, the PPP method takes advantage of precise satellite-to-ground range for retrieving slant total electron content and is less affected by the leveling errors. Previous studies have only proven that the ionospheric observables extracted by the two methods are affected by the leveling errors. The influence on ionospheric observable by the pseudorange inter-receiver satellite bias (IRSB) of the receiver has not been taken into consideration. Also, the magnitude of the differences between the ionospheric observables extracted by the two methods has also not been given. In this work, three methods, namely, the CCL, the conventional ionospheric-free PPP method which uses the ionospheric-free Hatch–Melbourne–Wubbena (HMW) function, and the University of Calgary (UOFC) PPP method, are selected to analyze and compare the differences of ionospheric observables and the global ionospheric maps, using a large number of measured data from international GNSS service global stations. Experimental results show that the accuracy of ionospheric observables obtained by the three methods is not only related to the leveling error, but also pseudorange IRSB. The IRSB of the receiver exerts a major effect on the ionospheric observables obtained by the CCL method and a minor effect on the ionospheric observables obtained by the HMW and UOFC methods. The accuracies in the latter case are similar and superior to those obtained by the CCL. The differences of the ionospheric observables obtained by the CCL and UOFC methods, or the CCL and HMW methods, are at decimeter level, whereas the difference of the ionospheric observables obtained by the UOFC and HMW methods is at centimeter level. The UOFC method presented the highest single-frequency pseudorange positioning accuracy using estimated global ionospheric products, followed by the HMW and the CCL methods which presented the lowest positioning accuracy.     

GPS/INS紧组合的INS辅助周跳探测与修复

建立了GPS/INS紧组合定位模型,改正惯性器件误差及电离层折射误差,对不同组合观测量的误差影响进行了分析,构造不同观测值组合,提出了基于惯性信息辅助的GPS周跳自适应探测方法,分析了INS定位误差对周跳探测的影响,给出了周跳探测误报率及修复成功率评价指标,提出了一种周跳检测阈值自适应确定方法。利用实测组合导航试验数据验证本文的算法,文中模拟了不同的单历元多周跳及信号失锁条件,结果表明,在GPS信号完全失锁20 s内,该方法能准确检测和修复所有周跳,中断时间的延长降低了周跳修复的成功率;GPS信号部分失锁时,在模拟的90 s中断时段内仍能修复所有周跳;模拟了170历元的5 s间隔密集周跳,周跳探测成功率为100%,正确修复率为99.41%。     

基于无几何电离层滤波模型的北斗三号系统相位周跳与中断修复方法

高精度位置服务依赖模糊度正确固定的载波相位观测值,而复杂环境的相位周跳和中断给模糊度固定和数据处理带来了巨大挑战。北斗三号系统向全球播发四频和五频信号,为提升周跳处理性能提供了机遇。本文建立了探测多频超宽巷周跳的伪距-相位无几何组合模型,以及探测窄巷周跳的相位-相位无几何组合模型,并以周跳探测成功概率最大为准则确定了多频最优超宽巷和窄巷组合。由于电离层延迟制约了数据中断和电离层变化剧烈情况下的窄巷周跳探测,进而建立了顾及电离层延迟的窄巷周跳探测滤波模型。试验结果表明,对30 s采样间隔,基于无几何组合模型探测周跳的成功率均优于96%;对于3 min的数据中断,基于无几何组合模型的周跳探测成功率仅为70%,但补偿电离层延迟的滤波模型将成功率提升至95%以上。