Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

GPS/Galileo精密单点定位模糊度解算与实验分析

针对提高多频模糊度固定解的GNSS精密单点定位的可靠性与稳定性的问题,该文基于实时非组合相位偏差产品,对三频非差非组合GPS/Galileo PPP的浮点解、固定解模型进行深入研究,并设计了3种定位策略,选取了17个MGEX跟踪站7d的实测数据,分析了三频非差模糊度固定解对静态、仿动态PPP定位精度与滤波收敛时间的影响。结果表明,滤波收敛后,与浮点解策略相比较,固定三频模糊度对高程、水平方向定位精度均有提高,在静态定位模式中提升幅度分别约为20.45%和37.50%,在仿动态定位模式中提升幅度分别约为22.41%和33.33%。在滤波收敛时间方面,相较于浮点解策略的收敛时间,静态与仿动态定位中模糊度固定策略的收敛时间分别提升了约12.57%和6.41%。     

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wübbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.     

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.     

多系统实时精密单点定位及非差模糊度固定

正精密单点定位(precise point positioning,PPP)技术能够在全球区域获取用户在国际地球参考框架下的精确三维坐标,打破了以往只能够使用差分定位技术才能够实现高精度定位的局面,是继RTK/NRTK技术之后出现的又一次技术革命。论文旨在构建实时GNSS PPP服务系统,围绕GNSS卫星钟差估计、多系统融合PPP、卫星姿态、GPS未校准相位延迟(uncalibrated phase delays,UPD)估计、PPP模糊度固定等展开研究,为用户获取实时、高精度和高可靠性的GNSS PPP服务奠定理论和实践基础。本文的主要工作和贡献如下:     

BDS静态精密单点定位模糊度固定解精度分析

针对BDS单系统未校准相位延迟(UPD)估计以及不同时长精密单点定位(PPP)模糊度固定对定位精度影响的问题,该文选取56个测站估计UPD,利用未参与UPD计算的8个测站进行不同时长BDS静态PPP模糊度固定实验。结果表明:BDS星间单差宽巷和窄巷UPD在连续时段内具有一定的稳定性,其估计精度满足用于PPP模糊度固定要求。时长越短模糊度固定率越低。以IGS周解为参考值,不同时长模糊度固定解较浮点解三维定位精度均提高12%以上,时长越短模糊度固定解精度提高越显著。因此,模糊度固定是提高BDSPPP定位精度的重要手段。     

Integer ambiguity resolution in precise point positioning: method comparison

Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below 0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better positioning quality.     

BDS-3精密单点定位模糊度解算及性能评估

基于国际GNSS服务(IGS)提供的MGEX (Multi-GNSS Experiment)的观测数据,对北斗三号卫星导航系统(BDS-3)相位小数偏差(UPD)进行估计,进一步开展基于精密单点定位(PPP)的浮点/固定解试验,分析评估其定位性能. 结果表明:北斗卫星导航系统(BDS)定位精度与GPS大致相当; BDS-3 PPP在东(E)、北(N)、天顶(U)三个方向上浮点解的平均均方根(RMS)分别为1.4 cm、1.0 cm、1.6 cm;通过模糊度固定算法,可将三个方向的定位精度提升至0.9 cm、0.7 cm、1.4 cm.      

Regional reference network augmented precise point positioning for instantaneous ambiguity resolution

Integer ambiguity fixing can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP), but it still takes approximate 15 min of time to achieve reliable integer ambiguity solutions. In this contribution, we present a new strategy to augment PPP estimation with a regional reference network, so that instantaneous ambiguity fixing is achievable for users within the network coverage. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to, and interpolated at user stations to correct for L1, L2 phase observations or their combinations. With the corrected observations, instantaneous ambiguity resolution can be carried out within the user PPP software, thus achieving the position solutions equivalent to the network real-time kinematic positioning (NRTK). The strategy is validated experimentally. The derived atmospheric delays and the interpolated corrections are investigated. The ambiguity fixing performance and the resulted position accuracy are assessed. The validation confirms that the new strategy can provide comparable service with NRTK. Therefore, with this new processing strategy, it is possible to integrate PPP and NRTK into a seamless positioning service, which can provide an accuracy of about 10 cm anywhere, and upgrade to a few centimeters within a regional network.     

Three-frequency BDS precise point positioning ambiguity resolution based on raw observables

All BeiDou navigation satellite system (BDS) satellites are transmitting signals on three frequencies, which brings new opportunity and challenges for high-accuracy precise point positioning (PPP) with ambiguity resolution (AR). This paper proposes an effective uncalibrated phase delay (UPD) estimation and AR strategy which is based on a raw PPP model. First, triple-frequency raw PPP models are developed. The observation model and stochastic model are designed and extended to accommodate the third frequency. Then, the UPD is parameterized in raw frequency form while estimating with the high-precision and low-noise integer linear combination of float ambiguity which are derived by ambiguity decorrelation. Third, with UPD corrected, the LAMBDA method is used for resolving full or partial ambiguities which can be fixed. This method can be easily and flexibly extended for dual-, triple- or even more frequency. To verify the effectiveness and performance of triple-frequency PPP AR, tests with real BDS data from 90 stations lasting for 21 days were performed in static mode. Data were processed with three strategies: BDS triple-frequency ambiguity-float PPP, BDS triple-frequency PPP with dual-frequency (B1/B2) and three-frequency AR, respectively. Numerous experiment results showed that compared with the ambiguity-float solution, the performance in terms of convergence time and positioning biases can be significantly improved by AR. Among three groups of solutions, the triple-frequency PPP AR achieved the best performance. Compared with dual-frequency AR, additional the third frequency could apparently improve the position estimations during the initialization phase and under constraint environments when the dual-frequency PPP AR is limited by few satellite numbers.     

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.

Improving the estimation of fractional-cycle biases for ambiguity resolution in precise point positioning

Ambiguity resolution dedicated to a single global positioning system (GPS) station can improve the accuracy of precise point positioning. In this process, the estimation accuracy of the narrow-lane fractional-cycle biases (FCBs), which destroy the integer nature of undifferenced ambiguities, is crucial to the ambiguity-fixed positioning accuracy. In this study, we hence propose the improved narrow-lane FCBs derived from an ambiguity-fixed GPS network solution, rather than the original (i.e. previously proposed) FCBs derived from an ambiguity-float network solution. The improved FCBs outperform the original FCBs by ensuring that the resulting ambiguity-fixed daily positions coincide in nature with the state-of-the-art positions generated by the International GNSS Service (IGS). To verify this improvement, 1?year of GPS measurements from about 350 globally distributed stations were processed. We find that the original FCBs differ more from the improved FCBs when fewer stations are involved in the FCB estimation, especially when the number of stations is less than 20. Moreover, when comparing the ambiguity-fixed daily positions with the IGS weekly positions for 248 stations through a Helmert transformation, for the East component, we find that on 359 days of the year the daily RMS of the transformed residuals based on the improved FCBs is smaller by up to 0.8?mm than those based on the original FCBs, and the mean RMS over the year falls evidently from 2.6 to 2.2?mm. Meanwhile, when using the improved rather than the original FCBs, the RMS of the transformed residuals for the East component of 239 stations (i.e. 96.4% of all 248 stations) is clearly reduced by up to 1.6?mm, especially for stations located within a sparse GPS network. Therefore, we suggest that narrow-lane FCBs should be determined with ambiguity-fixed, rather than ambiguity-float, GPS network solutions.     

Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization

Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s.     

精密单点定位技术在高精度GPS网数据处理中的应用探讨

本文通过对韶关市基础控制网改造中的GPS框架网的数据分别采用GAMIT解算基线的相对定位方法以及采用静态精密单点定位技术两种不同的方法分别进行了解算,解算结果表明,两种方法获得的结果是一致的.     

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....     

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。     

Assessment of correct fixing rate for precise point positioning ambiguity resolution on a global scale

Ambiguity resolution (AR) for a single receiver has been a popular topic in Global Positioning System (GPS) recently. Ambiguity-resolution methods for precise point positioning (PPP) have been well documented in recent years, demonstrating that it can improve the accuracy of PPP. However, users are often concerned about the reliability of ambiguity-fixed PPP solution in practical applications. If ambiguities are fixed to wrong integers, large errors would be introduced into position estimates. In this paper, we aim to assess the correct fixing rate (CFR), i.e., number of ambiguities correctly fixing to the total number of ambiguities correctly and incorrectly fixing, for PPP user ambiguity resolution on a global scale. A practical procedure is presented to evaluate the CFR of PPP user ambiguity resolution. GPS data of the first 3 days in each month of 2010 from about 390 IGS stations are used for experiments. Firstly, we use GPS data collected from about 320 IGS stations to estimate global single-differenced (SD) wide-lane and narrow-lane satellite uncalibrated phase delays (UPDs). The quality of UPDs is evaluated. We found that wide-lane UPD estimates have a rather small standard deviation (Std) between 0.003 and 0.004 cycles while most of Std of narrow-lane estimates are from 0.01 to 0.02 cycles. Secondly, many experiments have been conducted to investigate the CFR of integer ambiguity resolution we can achieve under different conditions, including reference station density, observation session length and the ionospheric activity. The results show that the CFR of PPP can exceed 98.0 % with only 1 h of observations for most user stations. No obvious correlation between the CFR and the reference station density is found. Therefore, nearly homogeneous CFR can be achieved in PPP AR for global users. At user end, higher CFR could be achieved with longer observations. The average CFR for 30-min, 1-h, 2-h and 4-h observation is 92.3, 98.2, 99.5 and 99.7 %, respectively. In order to get acceptable CFR, 1 h is a recommended minimum observation time. Furthermore, the CFR of PPP can be affected by diurnal variation and geomagnetic latitude variation in the ionosphere. During one day at the hours when rapid ionospheric variations occur or in low geomagnetic latitude regions where equatorial electron density irregularities are produced relatively frequently, a significant degradation of the CFR is demonstrated.