Modeling and Prediction of Inter-System Bias for GPS/BDS-2/BDS-3 Combined Precision Point Positioning

The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System(BDS).However,the Inter-System Bias(ISB)measurement of Multi-GNSS,including the time system offset,the coordinate system difference,and the inter-system hardware delay bias,must be considered for Multi-GNSS data fusion processing.The detected ISB can be well modeled and predicted by using a quadratic model(QM),an autoregressive integrated moving average model(ARIMA),as well as the sliding window strategy(SW).In this study,the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used.However,an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used.Meanwhile,the precision of the Predicted ISB(PISB)on the next day of all stations is about 0.1−0.6 ns.Besides,to effectively utilize the PISB,a new strategy for predicting the PISB for MGPPP is proposed.In the proposed strategy,the PISB is used by adding two virtual observation equations,and an adaptive factor is adopted to balance the contribution of the Observed ISB(OISB)and the PISB to the final estimations of ISB.To validate the effectiveness of the proposed method,some experimental schemes are designed and tested under different satellite availability conditions.The results indicate that in open sky environment,the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB,but the convergence time of MGPPP is reduced by 7.1%at most in the north(N),east(E),and up(U)components.In the blocked sky environment,the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment.Compared with the direct utilization of the PISB,the selective utilization of the PISB improves the positioning precision and convergence time by 6.7%and 12.7%at most in the N,E,and U components,respectively.

Comparison of availability and reliability among different combined-GNSS/RNSS precise point positioning

With emergence of the BeiDou Navigation Satellite System(BDS), the Galileo Satellite Navigation System(Galileo), the Quasi-Zenith Satellite System(QZSS)and the restoration of the Global Navigation Satellite System(GLONASS), the single Global Positioning System(GPS) has been gradually expanded into multiple global and regional navigation satellite systems(multi-GNSS/RNSS). In view of differences in these 5 systems, a consolidated multi-GNSS/RNSS precise point positioning(PPP) observation model is deduced in this contribution. In addition, the performance evaluation of PPP for multi-GNSS/RNSS is conducted using a large number of the multi-GNSS experiment(MGEX) station datasets. Experimental results show that multi-GNSS/RNSS can guarantee plenty of visible satellites effectively. Compared with single-system GPS, PDOP, HDOP, and VDOP values of the multi-GNSS/RNSS are improved by 46.8%, 46.5% and 46.3%, respectively. As for convergence time, the static and kinematic PPP of multi-GNSS/RNSS are superior to that of the single-system GPS, whose reliability, availability, and stability drop sharply with the increasing elevation cutoff. At satellite elevation cutoff of 40 °, the single-system GPS fails to carry out continuous positioning because of the insufficient visible satellites, while the multi-GNSS/RNSS PPP can still get positioning solutions with relatively high accuracy, especially in the horizontal direction.

Performance of GNSS positioning in PPP mode using MADOCA precise products

The Global Navigation Satellite System (GNSS) is widely utilized for accurate positioning.One commonly applied method to obtain precise coordinate estimates is by implementing the relative positioning in network mode.However,this approach can be complex and challenging.Fortunately,The Japan Aerospace Exploration Agency (JAXA) offers freely available satellite orbit and clock correction products called Multi-GNSS Advanced Demonstration Tool for Orbit and Clock Analysis (MADOCA),which can enhance positioning accuracy through the precise point positioning (PPP) method.This study focuses on evaluating PPP static mode positioning using MADOCA products and comparing the results with the highly precise relative positioning method.By analyzing a network of 20 GNSS stations in Indonesia,we found that the PPP method using MADOCA products provided favorable positioning estimates.The median discrepancies and the corresponding median absolute deviation (MAD) for easting,northing,and up components were estimated as 9±18 mm,10±9 mm,and 3±40 mm,respectively.These results indicate that PPP with MADOCA products can be a reliable alternative for establishing Indonesia's horizontal control networks,particularly for orders 0,1,2,and 3,and for a broad spectrum of geoscience monitoring activities.However,considerations such as epoch transformations and seismic activities should be taken into account for accurate positioning applications that comply with the definition of the national reference framework.

Integrity monitoring of fixed ambiguity Precise Point Positioning(PPP)solutions

Traditional positioning methods,such as conventional Real Time Kinematic(cRTK)rely upon local reference networks to enable users to achieve high-accuracy positioning.The need for such relatively dense networks has significant cost implications.Precise Point Positioning(PPP)on the other hand is a positioning method capable of centimeter-level positioning without the need for such local networks,hence providing significant cost benefits especially in remote areas.This paper presents the state-of-the-art PPP method using both GPS and GLONASS measurements to estimate the float position solution before attempting to resolve GPS integer ambiguities.Integrity monitoring is carried out using the Imperial College Carrier-phase Receiver Autonomous Integrity Monitoring method.A new method to detect and exclude GPS base-satellite failures is developed.A base-satellite is a satellite whose measurements are differenced from other satellite’s measurements when using between-satellite-differenced measurements to estimate position.The failure detection and exclusion methods are tested using static GNSS data recorded by International GNSS Service stations both in static and dynamic processing modes.The results show that failure detection can be achieved in all cases tested and failure exclusion can be achieved for static cases.In the kinematic processing cases,failure exclusion is more difficult because the higher noise in the measurement residuals increases the difficulty to distinguish between failures associated with the base-satellite and other satellites.

Status of UnDifferenced and Uncombined GNSS Data Processing Activities in China

With the continued development of multiple Global Navigation Satellite Systems(GNSS)and the emergence of various frequencies,UnDifferenced and UnCombined(UDUC)data processing has become an increasingly attractive option.In this contribution,we provide an overview of the current status of UDUC GNSS data processing activities in China.These activities encompass the formulation of Precise Point Positioning(PPP)models and PPP-Real-Time Kinematic(PPP-RTK)models for processing single-station and multi-station GNSS data,respectively.Regarding single-station data processing,we discuss the advancements in PPP models,particularly the extension from a single system to multiple systems,and from dual frequencies to single and multiple frequencies.Additionally,we introduce the modified PPP model,which accounts for the time variation of receiver code biases,a departure from the conventional PPP model that typically assumes these biases to be time-constant.In the realm of multi-station PPP-RTK data processing,we introduce the ionosphere-weighted PPP-RTK model,which enhances the model strength by considering the spatial correlation of ionospheric delays.We also review the phase-only PPP-RTK model,designed to mitigate the impact of unmodelled code-related errors.Furthermore,we explore GLONASS PPP-RTK,achieved through the application of the integer-estimable model.For large-scale network data processing,we introduce the all-in-view PPP-RTK model,which alleviates the strict common-view requirement at all receivers.Moreover,we present the decentralized PPP-RTK data processing strategy,designed to improve computational efficiency.Overall,this work highlights the various advancements in UDUC GNSS data processing,providing insights into the state-of-the-art techniques employed in China to achieve precise GNSS applications.

基于伪距/相位OSB的多频多模PPP-AR及其性能评估

在进行多频多模全球导航卫星系统(global navigation satellite system,GNSS)精密单点定位(precise point positioning,PPP)时,以相对形式表达的伪距差分码偏差(differential code bias,DCB)和相位小数周偏差(fractional cycle bias,FCB)种类繁多且修正方法较为复杂。基于此,首先给出了相对形式的伪距/相位偏差与原始观测值上的绝对偏差(observable-specific signal bias,OSB)的转换方法,以及利用该偏差进行非差模糊度固定的具体流程;然后通过实测数据分析不同偏差形式下的PPP模糊度解算(PPP-ambiguity resolution,PPP-AR)定位性能。结果表明,无论是多系统PPP还是多频PPP,其基于OSB的PPP-AR定位精度、收敛时间及固定率均与相对形式DCB/FCB的PPP-AR定位结果相当。其中,三频PPP-AR的动态和静态收敛时间均优于双频,多系统PPP-AR定位的初始化时间和定位精度也均优于单系统。伪距/相位OSB可直接用于修正对应的观测值,减少偏差处理中的组合与转换,并简化GNSS PPP数据处理流程,提高了频率选择的灵活性,使用户端算法更简单方便。

Extraction of line-of-sight ionospheric observables from GPS data using precise point positioning

Here we propose a method for extracting line-of-sight ionospheric observables from GPS data using precise point positioning(PPP).The PPP-derived ionospheric observables(PIOs) have identical form with their counterparts obtained from leveling the geometry-free GPS carrier-phase to code(leveling ionospheric observables,LIOs),and are affected by the satellite and receiver inter-frequency biases(IFBs).Based on the co-location experiments,the effects of extracting error arising from the observational noise and multipath on the PIOs and the LIOs are comparatively assessed,and the considerably reduced effects ranging from 70% to 75% on the PIOs with respect to the LIOs can be verified in our case.In addition,based on 26 consecutive days' GPS observations from two international GNSS service(IGS) sites(COCO,DAEJ) during disturbed ionosphere period,the extracted PIOs and LIOs are respectively used as the input of single-layer ionospheric model to retrieve daily satellite IFBs station-by-station.The minor extracting errors underlying the PIOs in contrast to the LIOs can also be proven by reducing day-to-day scatter and improving between-receiver consistency in the retrieved satellite IFBs values.

New methods for dual constellation single receiver positioning and integrity monitoring

Navigation system integrity monitoring is crucial for mission(e.g.safety)critical applications.Receiver autonomous integrity monitoring(RAIM)based on consistency checking of redundant measurements is widely used for many applications.However,there are many challenges to the use of RAIM associated with multiple constellations and applications with very stringent requirements.This paper discusses two positioning techniques and corresponding integrity monitoring methods.The first is the use of single frequency pseudorange-based dual constellations.It employs a new cross constellation single difference scheme to benefit from the similarities while addressing the differences between the constellations.The second technique uses dual frequency carrier phase measurements from GLONASS and the global positioning system for precise point positioning.The results show significant improvements both in positioning accuracy and integrity monitoring as a result of the use of two constellations.The dual constellation positioning and integrity monitoring algorithms have the potential to be extended to multiple constellations.

GNSS smartphones positioning: advances, challenges, opportunities, and future perspectives

Starting from 2016,the raw Global Navigation Satellite System(GNSS)measurements can be extracted from the Android Nougat(or later)operating systems.Since then,GNSS smartphone positioning has been given much attention.A high number of related publications indicates the importance of the research in this field,as it has been doing in recent years.Due to the cost-effectiveness of the GNSS smartphones,they can be employed in a wide variety of applications such as cadastral surveys,mapping surveying applications,vehicle and pedestrian navigation and etc.However,there are still some challenges regarding the noisy smartphone GNSS observations,the environment effect and smartphone holding modes and the algorithm development part which restrict the users to achieve high-precision smartphone positioning.In this review paper,we overview the research works carried out in this field with a focus on the following aspects:first,to provide a review of fundamental work on raw smartphone observations and quality assessment of GNSS observations from major smart devices including Google Pixel 4,Google Pixel 5,Xiaomi Mi 8 and Samsung Ultra S20 in terms of their signal strengths and carrier-phase continuities,second,to describe the current state of smartphone positioning research field until most recently in 2021 and,last,to summarize major challenges and opportunities in this filed.Finally,the paper is concluded with some remarks as well as future research perspectives.

Impact of different sampling rates on precise point positioning performance using online processing service

In this study,the effect of different sampling rates(i.e.observation recording interval)on the Precise Point Positioning(PPP)solutions in terms of accuracy was investigated.For this purpose,a field test was carried out inÇorum province,Turkey,on 11 September 2019.Within this context,a Geodetic Point(GP)was established and precisely coordinated.A static GNSS measurement was occupied on the GP for about 4-hour time at 0.10 second(s)/10 Hz measurement intervals with the Trimble R10 geodetic grade GNSS receiver.The original observation file was converted to RINEX format and then decimated into the different data sampling rates as 0.2 s,0.5 s,1 s,5 s,10 s,30 s,60 s,and 120 s.All these RINEX observation files were submitted to the Canadian Spatial Reference System-Precise Point Positioning(CSRS-PPP)online processing service the day after the data collection date by choosing both static and kinematic processing options.In this way,PPP-derived static coordinates,and the kinematic coordinates of each measurement epoch were calculated.The PPP-derived coordinates obtained from each decimated sampling intervals were compared to known coordinates of the GP for northing,easting,2D position,and height components.According to the static and kinematic processing results,high data sampling rates did not change the PPP solutions in terms of accuracy when compared to the results obtained using lower sampling rates.The results of this study imply that it was not necessary to collect GNSS data with high-rate intervals for many surveying projects requiring cm-level accuracy.

Analysis of Galileo signal-in-space range error and positioning performance during 2015-2018

A long-term analysis of signal-in-space range error (SISRE) is presented for all healthy Galileo satellites, and the first pair of full operational capability satellites in wrong elliptical orbits. Both orbit and clock errors for Galileo show an obvious convergence trend over time. The annual statistical analyses show that the average root mean squares (RMSs) of SISRE for the Galileo constellation are 0.58 m (2015), 0.29 m (2016), 0.23 m (2017), and 0.22 m (2018). Currently, the accuracy of the Galileo signal-in-space is superior to that of the global positioning system (GPS) Block IIF (0.35 m). In addition, the orbit error accounts for the majority of Galileo SISRE, while the clock error accounts for approximately one-third of SISRE due to the high stability of the onboard atomic clock. Single point positioning results show that Galileo achieves an accuracy of 2-3 m, which is comparable to that of GPS despite the smaller number of satellites and worse geometry. Interestingly, the vertical accuracy of Galileo, which uses the NeQuick ionospheric model, is higher than that of GPS. Positioning with single frequency E1 and E5 show a higher precision than E5a and E5b signals. Regarding precise point positioning (PPP), the results indicate that a comparable positioning accuracy can be achieved among different stations with the current Galileo constellation. For static PPP, the RMS values of Galileo-only solutions are within 1 cm horizontally, and the vertical RMSs are mostly within 2 cm horizontally. For kinematic PPP, the RMSs of Galileo-only solutions are mostly within 4 cm horizontally and 6 cm vertically.

Performance investigation of LAMBDA and bootstrapping methods for PPP narrow-lane ambiguity resolution

Precise point positioning with ambiguity resolution(PPP-AR)is a powerful tool for geodetic and time-constrained applications that require high precision.The performance of PPP-AR highly depends on the reliability of the correct integer carrier-phase ambiguity estimation.In this study,the performance of narrow-lane ambiguity resolution of PPP using the Least-squares AMBiguity Decorrelation(LAMBDA)and bootstrapping methods is extensively investigated using real data from 55 IGS stations over one-month in 2020.Static PPP with 24-,12-,8-,4-,2-,1-and½-h sessions using two different cutoff angles(7°and 30°)was conducted with three PPP modes:i.e.ambiguity-float and two kinds of ambiguity-fixed PPP using the LAMBDA and bootstrapping methods for narrow-lane AR,respectively.The results show that the LAMBDA method can produce more reliable results for 2 hour and shorter observation sessions com-pared with the bootstrapping method using a 7°cutoff angle.For a 30°cutoff angle,the LAMBDA method outperforms the bootstrapping method for observation sessions of 4 h and less.For long observation times,the bootstrapping method produced much more accurate coordinates compared with the LAMBDA method without considering the wrong fixes cases.The results also show that occurrences of fixing the wrong integer ambiguities using the bootstrapping method are higher than that of the LAMBDA method.

利用北斗GEO卫星观测监测深圳市周围地区电离层空间环境

采用非差非组合精密单点定位(precise point positioning,PPP)反演北斗GEO卫星穿刺点位置的垂直方向电子总含量(vertical total electron content,VTEC),利用GEO卫星在时域上穿刺点位置近似固定的特性,反演、分析了深圳市2020年的电离层空间环境参数,并详细评估了该区域VTEC实测值与国际GNSS服务(International GNSS Service,IGS)组织提供的全球电离层模型(global ionosphere model,GIM)电离层产品间的差异。结果表明:在深圳市,北斗GEO卫星的VTEC实测值与GIM产品具有较好的一致性,全年差值的日均值和标准差分别为-0.87 TECU和3.24 TECU,各月份差值的日间时段均值略小于夜间时段,差值的标准差呈现明显的季节性特性,其中,6月、7月、8月份较低。整体上,GIM的VTEC日峰值比实测值的小,全年差值的均值和标准差分别为3.51 TECU和5.98 TECU。

LEO Enhanced Global Navigation Satellite System(LeGNSS):progress,opportunities,and challenges

With the completion of Chinese BeiDou Navigation Satellite System(BDS),the world has begun to enjoy the Positioning,Navigation,and Timing(PNT)services of four Global Navigation Satellite Systems(GNSS).In order to improve the GNSS performance and expand its applications,Low Earth Orbit(LEO)Enhanced Global Navigation Satellite System(LeGNSS)is being vigorously advocated.Combined with high-,medium-,and low-earth orbit satellites,it can improve GNSS performance in terms of orbit determination,Precise Point Positioning(PPP)convergence time,etc.This paper comprehensively reviews the current status of LeGNSS,focusing on analyzing its advantages and challenges for precise orbit and clock determination,PPP convergence,earth rotation parameter estimation,and global ionosphere modeling.Thanks to the fast geometric change brought by LEO satellites,LeGNSS is expected to fundamentally solve the problem of the long convergence time of PPP without any augmentation.The convergence time can be shortened within 1 minute if appropriate LEO constellations are deployed.However,there are still some issues to overcome,such as the optimization of LEO constellation as well as the real time LEO precise orbit and clock determination.

Orbit Fitting Based on Helmert Transformation

Orbit fitting is used in many GPS applications. For example, in Precise Point Positioning (PPP), GPS orbits (SP3 orbits) are normally retrieved either from IGS or from one of its Analysis Centers (ACs) with 15 minutes’ sampling, which is much bigger than the normal observation sampling. Therefore, algorithms should be derived to fit GPS orbits to the observation time. Many methods based on interpolation were developed. Using these methods the orbits fit well at the sampling points. However, these methods ignore the physical motion model of GPS satellites. Therefore, the trajectories may not fit the true orbits at the periods in between 2 sampling epochs. To solve this problem, we develop a dynamic approach, in which a model based on Helmert transformation is developed in GPS orbit fitting. In this orbit fitting approach, GPS orbits at sampling points are treated as pseudo-observations. Thereafter, Helmert transformation is built up between the pseudo-observations and dynamically integrated orbits at each epoch. A set of Helmert parameters together with corrections of GPS initial orbits are then modeled as unknown parameters. Results show that the final fit orbits have the same precision as the IGS final orbits.

Numerical weather modeling-based slant tropospheric delay estimation and its enhancement by GNSS data

Unmitigated tropospheric delay is one of the major error sources in precise point positioning(PPP).Precise Slant Tropospheric Delay(STD)estimation could help to provide cleaner observables for PPP,and improve its convergence,accuracy,and stability.STD is difficult to model accurately due to the rapid spatial and temporal variation of the water vapor in the troposphere.In the traditional approach,the STD is mapped from the zenith direction,which assumes a spherically symmetric local tropospheric profile and has limitations.In this paper,a new approach of directly estimating the STD from high resolution numerical weather modeling(NWM)products is introduced.This approach benefits from the best available meteorological information to improve real time STD estimation,with the RMS residual lower than 3.5 cm above 15°elevation,and 2 cm above 30°.Therefore,the new method can provide sufficient accuracy to improve PPP convergence time.To improve the performance of the new method in highly variable tropospheric conditions,a correction scheme is proposed which combines NWM information with multi-GNSS observations from a network of local continuously operating reference stations.It is demonstrated through a case study that this correction scheme is quite effective in reducing the STD estimation residuals and PPP convergence time.