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.

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....     

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.     

Multifrequency algorithms for precise point positioning: MAP3

We present the new MAP3 algorithms to perform static precise point positioning (PPP) from multifrequency and multisystem GNSS observations. MAP3 represents a two-step strategy in which the least squares theory is applied twice to estimate smoothed pseudo-distances, initial phase ambiguities, and slant ionospheric delay first, and the absolute receiver position and its clock offset in a second adjustment. Unlike the classic PPP technique, in our new approach, the ionospheric-free linear combination is not used. The combination of signals from different satellite systems is accomplished by taking into account the receiver inter-system bias. MAP3 has been implemented in MATLAB and integrated within a complete PPP software developed on site and named PCube. We test the MAP3 performance numerically and contrast it with other external PPP programs. In general, MAP3 positioning accuracy with low-noise GPS dual-frequency observations is about 2.5 cm in 2-h observation periods, 1 cm in 10 h, and 7 mm after 1 day. This means an improvement in the accuracy in short observation periods of at least 7 mm with respect to the other PPP programs. The MAP3 convergence time is also analyzed and some results obtained from real triple-frequency GPS and GIOVE observations are presented.     

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。     

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.     

Kinematic precise point positioning at remote marine platforms

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g. <500 km) to a land-based reference station. As an alternative, precise point positioning (PPP) is normally considered free from this limiting requirement. However, due to the prerequisite of network-based satellite products, PPP at a remote marine platform may still be affected by its distance to the reference network. Hence, this paper investigates this scenario by configuring rings of reference stations with different radii centered on a to-be-positioned marine platform. Particularly, we applied ambiguity resolution at a single station to PPP by estimating uncalibrated phase delays (UPDs). We used three rings of reference stations centered on a vessel, with radii of roughly 900, 2,000 and 3,600 km, to determine satellite clocks and UPDs independently. For comparison, we also performed differential positioning based on a single reference station with baseline lengths of about 400, 1,700 and 2,800 km. We demonstrate that, despite the increasing ring-network radius to a few 1,000 km, the overall change in accuracy of the satellite clocks that are used at the vessel is smaller than 0.02 ns, and the RMS values of differences between the three sets of narrow-lane UPD estimates are around 0.05 cycles only. Moreover, the kinematic positioning accuracy of PPP is affected by the increasing ring-network radius, but can still achieve several centimeters after ambiguity resolution when the vessel is over a few 1,000 km away from the ring network, showing better performance than that of differential positioning. Therefore, we propose that ambiguity-fixed PPP can be used at remote marine platforms that support precise oceanographic and geophysical applications in open oceans.     

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。     

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.     

PPPH: a MATLAB-based software for multi-GNSS precise point positioning analysis

The integration of different GNSS constellations offers considerable opportunities to improve Precise Point Positioning (PPP) performance. Being aware of the limited number of the alternatives that utilize the potential advantages of the multi-constellation and multi-frequency GNSS, we developed a MATLAB-based GNSS analysis software, named PPPH. PPPH is capable of processing GPS, GLONASS, Galileo and BeiDou data, and forming their different combinations depending on user’s preference. Thanks to its user-friendly graphical interface, PPPH allows users to determine a variety of processing options and parameters. In addition to an output file including the estimated parameters for every single epoch, PPPH also presents several analyzing and plotting tools for evaluating the results, such as positioning error, tropospheric zenith total delay, receiver clock estimation, satellite number, dilution of precisions. On the other hand, we conducted experimental tests to both validate the performance of PPPH and assess the potential benefits of multi-GNSS on PPP. The results indicate that PPPH provides comparable PPP solution with the general standards and also contributes to the improvement of PPP performance with the integration of multi-GNSS. Consequently, we introduce a GNSS analysis software that is easy to use, has a robust performance and is open to progress with its modular structure.     

GPS静态精密单点定位算法精度分析

采用精密轨道和钟差,利用Bernese软件解算得到亚洲地区13个IGS跟踪站的站坐标、对流层ZTD和接收机钟差,将解算的结果与CODE发布的结果对比发现：静态PPP算法解算的N方向收敛精度明显优于E方向和U方向,4~6 h后,坐标偏差在1 cm左右;NEU RMS均值分别为0.45、0.29、0.69 cm,ZTD RMS均值为0.85 cm,接收机钟差RMS均值为0.14 ns。试验表明：精密单点定位算法具有较高的精度和可靠性,可为实际工程测量及相关地球物理信号研究提供理论依据。     

基于GPS单频接收机的精密单点定位研究

介绍了利用单频GPS接收机进行精密单点定位的数学模型及解算方案,并采用选权拟合法得到比较准确的状态参数初值及其方差-协方差,加快了卡尔曼滤波的收敛。算例结果表明,利用精密卫星星历及卫星钟改正数并采用单频观测值,半个小时后的定位精度可达1~2分米的水平。     

一种加快BDS精密单点定位初始化的方法

由于BDS卫星的星座特性及卫星的轨道和钟差的精度影响,使得传统消电离层组合精密单点定位(PPP)的初始化时间较长。针对上述问题,文中对附加电离层约束的非组合精密单点定位算法进行研究。首先介绍非组合PPP算法,分析其与传统PPP的差异;其次分别利用CODE电离层格网产品,以反距离加权算法计算的站星电离层延迟、低阶球谐函数建立的区域电离层产品等作为先验信息对非组合PPP进行约束。通过MGEX观测网实测数据静态和仿动态计算表明,相比传统消电离层组合PPP,附加电离层约束的非组合PPP能够有效缩短初始化时间,同时能够获得高精度的定位结果。     

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.     

静态精密单点定位的精度和收敛性分析

精密单点定位(PPP)是当前GPS界研究的热点之一。为讨论其精度及收敛性,应用TriP软件处理分析5 min、30 min、2 h、24 h不同时段长度的单站GPS观测值。结果表明,随着观测时间的增加,定位精度不断提高,30 min内即可稳定在厘米级,最终实现毫米级精密定位。与此同时定位结果不断收敛,且收敛速度由快变慢,前15 min收敛较快,此后随观测时间的增加收敛速度逐步变慢且逐渐趋于缓和。     

Ambiguity resolution in precise point positioning with hourly data

Precise point positioning (PPP) has become a powerful tool for the scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station in PPP has been considered difficult, due to the receiver- and satellite-dependent uncalibrated hardware delays (UHD). However, recent studies show that if these UHD can be determined accurately in advance within a network of stations, then ambiguity resolution at a single station becomes possible. In this study, the method proposed by Ge et al. J Geod 82(7):389–399, 2007 is adopted with a refinement in which only one single-difference narrow-lane UHD between a pair of satellites is determined within each full pass over a regional network. This study uses the EUREF (European Reference Frame) Permanent Network (EPN) to determine the UHD from Day 245 to 251 in 2007. Then 12 International GNSS Service stations inside the EPN and 15 outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the mean positioning accuracy in all hourly solutions for the stations inside the EPN is improved from (3.8, 1.5, 2.8) centimeters to (0.5, 0.5, 1.4) centimeters for the East, North and Up components, respectively. For the stations outside the EPN, some of which are over 2,000 km away from the nearest EPN stations, the mean positioning accuracy in the East, North and Up directions still achieves (0.6, 0.6, 2.0) centimeters, respectively, when the EPN-based UHD are applied to these stations. These results demonstrate that ambiguity resolution at a single station can significantly improve the positioning accuracy in hourly PPP. Particularly, UHD can be even applied to a station which is up to thousands of kilometers from the UHD-determination network, potentially showing a great advantage over current network-based GPS augmentation systems. Therefore, it is feasible and beneficial for the operators of GPS regional networks and providers of PPP-based online services to provide these UHD estimates as an additional product.     

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.