Ambiguity resolution in precise point positioning with hourly data for global single receiver

Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1 cm in horizontal and 1–2 cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7 mm to 12.2, 13.3 and 34.3 mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions.     

Predicting atmospheric delays for rapid ambiguity resolution in precise point positioning

Integer ambiguity resolution in precise point positioning (PPP) can shorten the initialization and re-initialization time, and ambiguity-fixed PPP solutions are also more reliable and accurate than ambiguity-float PPP solutions. However, signal interruptions are unavoidable in practical applications, particularly while operating in urban areas. Such signal interruptions can cause discontinuity of carrier phase arc, which introduces new integer ambiguities. Usually it will take approximately 15 min of continuous tracking to a reasonable number of satellites to fix new integer ambiguities. In many applications, it is impractical for a PPP user to wait for such a long time for the re-initialization. In this paper, a method for rapid ambiguity fixing in PPP is developed to avoid such a long re-initialization time. Firstly, the atmospheric delays were estimated epoch by epoch from ambiguity-fixed PPP solutions before the data gap or cycle slip occurs. A random walk procedure is then applied to predict the atmospheric delays accurately over a short time span. The predicted atmospheric delays then can be used to correct the observations which suffer from signal interruptions. Finally, the new ambiguities can be fixed with a distinct WL-LX-L3 (here LX denotes either of L1, L2) cascade ambiguity resolution strategy. Comprehensive experiments have demonstrated that the proposed method and strategy can fix zero-difference integer ambiguities successfully with only a single-epoch observation immediately after a short data gap. This technique works even when all satellites are interrupted at the same time. The duration of data gap bridged by this technique could be possibly extended if a more precise atmospheric delay prediction is found or on-the-fly (OTF) technology is applied. Based on the proposed method, real-time PPP with integer ambiguity fixing becomes more feasible in practice.     

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.     

BDS-2/BDS-3 uncalibrated phase delay estimation considering the intra-system bias

Intra-system biases (ISBs) between BDS-2 and BDS-3 are of critical importance when combining observations from the BDS-2 and BDS-3 systems, which is meaningful to fully take advantage of the BDS positioning capability. Meanwhile, ISBs should also be considered in the estimation of BDS uncalibrated phase delays (UPDs). In this research, we present a BDS-2/BDS-3 joint-processing scheme, as well as a method for estimating BDS UPDs. The characteristics of ISBs and the quality of BDS UPDs are analyzed based on 30-day data from 130 multi-GNSS experimental (MGEX) stations. Our results indicate that the ISBs are related to the type and version of the receiver. The ISBs can be regarded as constant across the course of a given day, and the mean standard deviation (STD) values of ISBs over one month for different types of receivers are generally within 0.2 m. Moreover, to assess the quality of UPD products, the residuals of the estimated UPDs and the utilization rates of the observation data are computed. The results show that the quality of BDS UPDs can be improved by correcting the satellite-induced pseudo-range variations, and by estimating the wide-lane (WL) UPD difference between BDS-2 and BDS-3. The average RMS values of the estimated residuals of WL UPD and narrow-lane (NL) UPD are 0.07 and 0.09 cycles, respectively; moreover, the utilization rate of the observation data of WL UPD and NL UPD can reach above 90 %. The performance of BDS precise point positioning (PPP) and PPP ambiguity resolution (PPP-AR) is analyzed in terms of positioning accuracy and convergence performance in both the static and kinematic modes. Compared with PPP ambiguity-float solutions, the positioning accuracy of PPP-AR is significantly improved, especially in the east direction. The impact of ISBs on PPP and PPP-AR is also analyzed, and the results indicate that ISBs can improve the convergence speed of float PPP, but can be disregarded in PPP-AR.     

Comparison of convergence time and positioning accuracy among BDS,GPS and BDS/GPS precise point positioning with ambiguity resolution

Precise point positioning (PPP) usually takes about 30?min to obtain centimetre-level accuracy, which greatly limits its application. To address the drawbacks of convergence speed and positioning accuracy, we develop a PPP model with integrated GPS and BDS observations. Based on the method, stations with global coverage are selected to estimate the fractional cycle bias (FCB) of GPS and BDS. The short-term and long-term time series of wide-lane (WL) FCB, and the single day change of narrow-lane (NL) FCB are analysed. It is found that the range of GPS and BDS non-GEO (IGSO and MEO) WL FCB is stable at up to a 30-day-time frame. At times frame of up to 60?days, the stability is reduced a lot. Whether for short-term or long-term, the changes in the BDS GEO WL FCB are large. Moreover, BDS FCB sometimes undergoes a sudden jump. Besides, 17 and 10 stations were used respectively to investigate the convergence speed and positioning errors with six strategies: BDS ambiguity-float PPP (Bfloat), GPS ambiguity-float PPP (Gfloat), BDS/GPS ambiguity-float PPP (BGfloat), BDS ambiguity-fixed PPP (Bfix), GPS ambiguity-fixed (Gfix), and BDS/GPS ambiguity-fixed (BGfix). The average convergence speed of the ambiguity-fixed solution is greatly improved compared with the ambiguity-float solution. In terms of the average convergence time, the Bfloat is the longest and the BGfix is the shortest among these six strategies. Whether for ambiguity-float PPP or ambiguity-fixed PPP, the convergence reduction time in three directions for the combined system is the largest compared with the single BDS. The average RMS value of the Bfix in three directions (easting (E), northing (N), and up (U)) are 2.0?cm, 1.5?cm, and 5.9?cm respectively, while those of the Gfix are 0.8?cm, 0.5?cm, and 1.7?cm. Compared with single system, the BDS/GPS combined ambiguity-fixed system (BGfix) has the fastest convergence speed and the highest accuracy, with average RMS as 0.7?cm, 0.5?cm, and 1.9?cm for the E, N, U components, respectively.     

Performance analysis of PPP ambiguity resolution with UPD products estimated from different scales of reference station networks

Integer ambiguity fixing with uncalibrated phase delay (UPD) products can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP). Since the tracking arcs of satellites and the behavior of atmospheric biases can be very different for the reference networks with different scales, the qualities of corresponding UPD products may be also various. The purpose of this paper is to comparatively investigate the influence of different scales of reference station networks on UPD estimation and user ambiguity resolution. Three reference station networks with global, wide-area and local scales are used to compute the UPD products and analyze their impact on the PPP-AR. The time-to-first-fix, the unfix rate and the incorrect fix rate of PPP-AR are analyzed. Moreover, in order to further shorten the convergence time for obtaining precise positioning, a modified partial ambiguity resolution (PAR) and corresponding validation strategy are presented. In this PAR method, the ambiguity subset is determined by removing the ambiguity one by one in the order of ascending elevations. Besides, for static positioning mode, a coordinate validation strategy is employed to enhance the reliability of the fixed coordinate. The experiment results show that UPD products computed by smaller station network are more accurate and lead to a better coordinate solution; the PAR method used in this paper can shorten the convergence time and the coordinate validation strategy can improve the availability of high precision positioning.     

Using only observation station data for PPP ambiguity resolution by UPD estimation

This article proposes a new method for uncalibrated phase delay (UPD) estimation to improve the accuracy of precise point positioning (PPP), which uses only observation station data. This means that the station used to generate the UPDs is the same station to which they are applied. First, dual-frequency observation equations based on a raw PPP model are developed. Then, the UPDs are calculated from integer linear combinations of float ambiguities. Third, with the UPD corrections, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to obtain the integer ambiguities. Since only observation station data are used for UPD estimation, the partial ambiguity resolution (PAR) method is adopted to increase the possibility of finding a subset of integer ambiguities. The UPD estimation and ambiguity resolution are performed in each epoch. To obtain the correct integer ambiguity, the ratio test and success rate (bootstrapping) are used to evaluate the estimated integer ambiguity. Finally, by treating the integer ambiguities as constants, fixed solutions can be obtained. Quality control is also applied throughout the entire data processing procedure to obtain high quality float and fixed solutions. Data from 22 stations of the International Global Navigation Satellite System (GNSS) Service (IGS) in East Asia on day of year (DOY) 206, 2017, are used to verify the feasibility of this method. The experimental results show that compared with the float solution, the proposed method can significantly improve the accuracy in the east, north and up directions by 24%, 21% and 18% for static PPP and 36%, 18% and 34% for dynamic PPP, respectively. However, the accuracy of the proposed method is still lower than that of the fixed solutions obtained by the PRIDE-PPPAR software, in which the fractional cycle bias is computed based on reference network data. These findings sufficiently show that the proposed method can offer better solution accuracy than the float solution. However, the quality of the UPDs estimated only from observation station data is not as good as that of the estimates obtained based on reference network data.     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

Improvement of PPP-inferred tropospheric estimates by integer ambiguity resolution

Integer ambiguity resolution in Precise Point Positioning (PPP) can improve positioning accuracy and reduce convergence time. The decoupled clock model proposed by Collins (2008) has been used to facilitate integer ambiguity resolution in PPP, and research has been conducted to assess the model’s potential to improve positioning accuracy and reduce positioning convergence time. In particular, the biggest benefits have been identified for the positioning solutions within short observation periods such as one hour. However, there is little work reported about the model’s potential to improve the estimation of the tropospheric parameter within short observation periods. This paper investigates the effect of PPP ambiguity resolution on the accuracy of the tropospheric estimates within one hour.     

Mitigation of receiver biases in ionospheric observables from PPP with ambiguity resolution

PPP (Precise Point Positioning) is a GNSS (Global Navigation Satellite Systems) positioning method that requires SSR (State Space Representation) corrections in order to provide solutions with an accuracy of centimetric level. The so-called RT-PPP (Real-time PPP) is possible thanks to real-time precise SSR products, for orbits and clocks, provided by IGS (International GNSS Service) and its associate analysis centers such as CNES (Centre National d'Etudes Spatiales). CNES SSR products also enable RT-PPP with integer ambiguity resolution. In GNSS related literature, PPP with ambiguity resolution (PPP-AR) in real-time is often referred as PPP-RTK (PPP – Real Time Kinematic). PPP-WIZARD (PPP - With Integer and Zero-difference Ambiguity Resolution Demonstrator) is a software that is made available by CNES. This software is capable of performing PPP-RTK. It estimates slant ionospheric delays and other GNSS positioning parameters. Since ionospheric effects are spatially correlated by GNSS data from active networks, it is possible to model and provide ionospheric delays for any position in the network coverage area. The prior knowledge ionospheric delays can reduce positioning convergence for PPP-RTK users. Real-time ionospheric models could benefit from highly precise ionospheric delays estimated in PPP-AR. In this study, we demonstrate that ionospheric delays obtained throughout PPP-AR estimation are actu ally ionospheric observables. Ionospheric observables are biased by an order of few meters caused by the receiver hardware biases. These biases prohibit the use of PPP-WIZARD ionospheric delays to produce ionospheric models. Receiver biases correction is essential to provide ionospheric delays while using PPP-AR based ionospheric observables. In this contribution, a method was implemented to estimate and mitigate receiver hardware biases influence on slant ionospheric observables from PPP-AR. In order to assess the proposed approach, PPP-AR data from 12 GNSS stations were processed over a two-month period (March and April 2018). A comparison between IGS ionospheric products and PPP-AR based ionospheric observables corrected for receiver biases, resulted in a mean of differences of −39 cm and 51 cm standard deviation. The results are consistent with the accuracy of the IGS ionospheric products, 2–8 TECU, considering that 1 TECU is ~16 cm in L1. In another analysis, a comparison of ionospheric delays from 5 pairs of short baselines GNSS stations found an agreement of 0.001 m in mean differences with 22 cm standard deviation after receiver biases were corrected. Therefore, the proposed solution is promising and could produce high quality (1–2 TECU) slant ionospheric delays. This product can be used in a large variety of modeling approaches, since ionospheric delays after correction are unbiased. These results indicate that the proposed strategy is promising, and could benefit applications that require accuracy of 1–2 TECU (~16–32 cm in L1).     

两步法快速解算编队卫星GPS模糊度

为克服卫星编队飞行实时相对定位中双频模糊度解算速度慢的缺点,结合扩展Kalman滤波(EKF,Extended Kalman Filter),首先采用少数个历元(如10个)相位平滑伪距相对定位结果与 L₆的平均值对滤波初始化,再根据两步法解算双频模糊度,即先解算并正确固定宽巷模糊度,获得较准确的基线分量估值,然后采用选权拟合方法,将基线分量作为约束条件解算并固定双频模糊度.仿真算例计算结果表明,当宽巷模糊度正确固定后,编队卫星间相对定位误差在5cm以内,两步法可以在较短时间(约3min)内固定双频模糊度,为精确解算编队卫星的相对状态提供保障.     

An improved approach to model regional ionosphere and accelerate convergence for precise point positioning

Given the severe effects of the ionosphere on global navigation satellite system (GNSS) signals, single-frequency (SF) precise point positioning (PPP) users can only achieve decimeter-level positioning results. Ionosphere-free combinations can eliminate the majority of ionospheric delay, but increase observation noise and slow down dual-frequency (DF) PPP convergence. In this paper, we develop a regional ionosphere modeling and rapid convergence approach to improve SF PPP (SFPPP) accuracy and accelerate DF PPP (DFPPP) convergence speed. Instead of area model, ionospheric delay is modeled for each satellite to be used as a priori correction. With the ionospheric, wide-lane uncalibrated phase delay (UPD) and residuals satellite DCBs product, the wide-lane observations for DF users change to be high-precision pseudorange observations. The validation of a continuously operating reference station (CORS) network was analyzed. The experimental results confirm that the approach considerably improves the accuracy of SFPPP. For DF users, convergence time is substantially reduced.     

GPS/Galileo组合导航的模糊度搜索空间

为了组合导航的载波相位模糊度固定,将目前在GPS中常用的模糊度固定方法--最小二乘降相关平差（LAMBDA）法直接应用于GPS/Galileo组合模糊度固定,发现其搜索空间的确定方法并不能很好地适应GPS/Galileo组合中模糊度维数较高的情况。通过对常规LAMBDA搜索空间确定方法的分析比较,在传统方法的基础上提出了一种专门针对高维模糊度固定的搜索空间确定方法--修正法确定模糊度搜索空间。通过对修正法进行仿真试验,证明该方法能保证在GPS/Galileo组合定位模式下实际备选模糊度个数基本与预先设定的备选模糊度个数一致,进而能在不降低模糊度固定成功率的基础上有效提高LAMBDA模糊度固定的搜索效率,其性能优于传统的模糊度搜索空间确定方法。     

Long-term time-varying characteristics of UPD products generated by a global and regional network and their interoperable application in PPP

The quality and availability of Uncalibrated Phase Delay (UPD) solutions are crucial to the Precise Point Positioning (PPP) service, and the long-term temporal variability and its contributing factors should be better understood. In this paper, we comprehensively investigate the long-term time-varying characteristics of each UPD product respectively generated by a global and regional network and their interoperable application in PPP-AR (ambiguity resolution), the sampling of the WL and NL UPDs are daily and 30 s, respectively. Firstly, in terms of our 30 day Wide-Lane (WL) UPD products of 31 satellites, the Standard Deviation (STD) of each satellite WL UPDs ranges from 0.04 to 0.06 cycles, indicating that the long-term prediction accuracy of satellite WL UPD is sufficient for fixing Wide-Lane ambiguities. Secondly, when a satellite in eclipsing the discontinulity may corrupt the determination of Narrow-Lane (NL) UPD in form of offset, as a result of lacking or poor satellite attitude dynamic modeling. When the influence of discontinuity is removed, the STD of our estimated satellite NL UPDs is less than 0.05 cycles. Thirdly, the STD of our estimated receiver WL UPDs is mainly below 0.2 cycles, which implies that its stability is one order poorer that of the satellite. In addition, if they are used for stations in and around the network covered region, the stability of the UPD products from the CMONOC (Crustal Movement Observation Network of China) is better than that from a global network, benefit from the fact that all the CMONOC stations are equipped with the same receiver type. Finally, the PPP-AR results show that a rate of 82.9% for stations with a WL-ambiguity-fixed rate of over 90% while 69.5% for stations with an NL-ambiguity-fixed rate of over 80% can be achieved when using UPD from the global network, which is worse than that of using UPD from the CMONOC (85.7% for stations with a WL-ambiguity-fixed rate of over 90% while 75% for stations with an NL-ambiguity-fixed rate of over 80%). The results of the experiment on the UPD interoperable application in PPP show that the global network UPD products can provide a fast AR at any single station, and the convergence time is well below 25 min. Particularly, when the location of a station is in and around the regional network, our results show that the PPP results obtained using regional UPDs enable the consistent use of global UPDs. When the location of a station is far away from the regional network, using the regional UPDs can not achieve PPP-AR. Finally, the WL UPDs of the previous day is used for forecasting to estimate the NL UPDs, the stability analysis results of NL UPDs solution and positioning results are demonstrate the validity of forecasted UPD products.     

Seismic deformation of the Mw 8.0 Wenchuan earthquake from high-rate GPS observations

High-rate GPS positioning has been recognized as a powerful tool in estimating epoch-wise station displacement which is particularly useful for seismology. In this study, station displacements during the 12 May 2008 M_w 8.0 Wenchuan earthquake are derived from the 1-Hz GPS data collected at a set of stations in China. The impacts of integer ambiguity resolution and station environment-dependent effects are investigated in order to yield more accurate results. The position accuracy of horizontal components of better than 1 cm suggests that GPS can sense the rapid position oscillation of about 2 cm in amplitude. Temporal and spatial analysis is applied to the surface displacement at station XANY and the characteristics of the movements due to Rayleigh and Love waves are detected and discussed. The comparison of GPS-derived displacement with relevant synthetic data computed based on a recently published rapture model shows a reasonable agreement in waveform. The various differences in amplitude need further investigation and also imply that rapture inversion might be improved if GPS-derived displacement is assimilated.     

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.     

An Integer Precise Point Positioning technique for sea surface observations using a GPS buoy

GPS data dedicated to sea surface observation are usually processed using differential techniques. Unfortunately, the precision of resulting kinematic positions is baseline-length dependent. So, high precision sea surface observations using differential GPS techniques are limited to coasts, lakes, and rivers. Recent improvements in GPS satellite products (orbits, clocks, and phase biases) make phase ambiguity fixing at the zero difference level achievable and opens up the observation of the sea surface without geographical constraints. This paper recalls the concept of the Integer Precise Point Positioning technique and discusses the precision of GPS buoy positioning. A sequential version of the GINS software has been implemented to achieve single epoch GPS positioning. We used 1 Hz data from a two week GPS campaign conducted in the Kerguelen Islands. A GPS buoy has been moored close to a radar gauge and 90 m away from a permanent GPS station. This infrastructure offers the opportunity to compare both kinematic Integer Precise Point Positioning and classical differential GPS positioning techniques to in situ radar gauge data. We found that Precise Point Positioning results are not significantly biased with respect to radar gauge data and that horizontal time series are consistent with differential processing at the sub-centimetre precision level. Nevertheless, standard deviations of height time series with respect to radar gauge data are typically [4–5] cm. The dominant driver for noise at this level is attributed to errors in tropospheric estimates which propagate into position solutions.     

Real-time clock comparison and monitoring with multi-GNSS precise point positioning: GPS,GLONASS and Galileo

The precise point positioning (PPP) technique is widely used in time and frequency applications. Because of the real-time service (RTS) project of the International GNSS Service, we can use the PPP technique for real-time clock comparison and monitoring. As a participant in the RTS, the Centre National d’Etudes Spatiales (CNES) implements the PPPWIZARD (Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator) project to validate carrier phase ambiguity resolution. Unlike the Integer-PPP (IPPP) of the CNES, fixing ambiguities in the post-processing mode, the PPPWIZARD operates in the real-time mode, which is also called real-time IPPP (RT-IPPP). This paper focuses on applying the RT-IPPP for real-time clock comparison and monitoring. We review the principle of real-time clock comparison and monitoring, and introduce the methodology of the RT-IPPP technique. The observations of GPS, GLONASS and Galileo were processed for the experiments. Five processing modes were provided in the experiment to analyze the benefits of ambiguity resolution and multi-GNSS. In the clock comparison experiment, the average reduction ratios of standard deviations with respect to the G PPP mode range from 9.7% to 35.0%. In the clock monitoring experiment, G PPP mode can detect clock jumps whose magnitudes are larger than 0.9 ns. The RT-IPPP technique with GRE PPP AR (G) mode allows for the detection of any clock jumps larger than 0.6 ns. For frequency monitoring, G PPP mode allows detection of frequency changes larger than 1.1 × 10⁻¹⁴. When the RT-IPPP technique is applied, monitoring with GRE PPP AR (G) mode can detect frequency changes larger than 6.1 × 10⁻¹⁵.     

Performance assessment of RTPPP positioning with SSR corrections and PPP-AR positioning with FCB for multi-GNSS from MADOCA products

The state-space representation (SSR) product of satellite orbit and clock is one of the most essential corrections for real-time precise point positioning (RTPPP). When it comes to PPP ambiguity resolution (PPP-AR), the fractional cycle bias (FCB) matters. The Japan Aerospace Exploration Agency (JAXA) has developed a multi-GNSS (i.e., global navigation satellite system) advanced demonstration tool for orbit and clock analysis (MADOCA), providing free and precise orbit and clock products. Because of the shortage of relevant studies on performance evaluation, this paper focuses on the performance assessment of RTPPP and PPP-AR by real-time and offline MADOCA products. To begin with, the real-time MADOCA products are evaluated by comparing orbit and clock with JAXA final products, which gives an objective impression of the correction. Second, PPP tests in static and simulated kinematic mode are conducted to further verify the quality of real-time MADOCA products. Finally, the offline MADOCA products are assessed by PPP and PPP-AR comparisons. The results are as follows: (1) Orbit comparisons produced an average error of about 0.04–0.13 m for the global positioning system (GPS), 0.14–0.16 m for the global navigation satellite system (GLONASS), and 0.07–0.08 m for the quasi-zenith satellite system (QZSS). The G15 satellite had the most accurate orbit, with a difference of 0.04 m between the JAXA orbit products and MADOCA’s counterpart, while the R07 satellite had the least accurate orbit with a difference of 0.16 m. Clock products had an accuracy of 0.4–1.3 ns for GPS, 1.4–1.6 ns for GLONASS, and 0.7–0.8 ns for QZSS in general. The G15 satellite had the most accurate clock with a difference of only 0.40 ns between the JAXA clock products and MADOCA products, and the R07 satellite had the least accurate clock with a difference of 1.55 ns. The orbit and clock products for GLONASS performed worse than those of GPS and QZSS. (2) After convergence, the positioning accuracy was 3.0–8.1 cm for static PPP and 8.1–13.7 cm for kinematic PPP when using multi-GNSS observations and precise orbit and clock products. The PFRR station performed the good performance both in static and kinematic mode with an accuracy of 2.99 cm and 8.08 cm, respectively, whereas the CPNM station produced the worst static performance with an error of 8.09 cm, and the ANMG station produced the worst kinematic performance with a counterpart of 13.69 cm. (3) The PPP-AR solution was superior to the PPP solution, given that, with respect to PPP, post-processing PPP-AR improved the positioning accuracy and convergence time by 13–32 % (3–89 %) in GPS-only mode by 2–15 % (5–60 %) in GPS/QZSS mode. Thus, we conclude that the current MADOCA products can provide SSR corrections and FCB products with positioning accuracy at the decimeter or even centimeter level, which could meet the demands of the RTPPP and PPP-AR solutions.     

Real-time zenith tropospheric delays in support of numerical weather prediction applications

The Geodetic Observatory Pecný (GOP) routinely estimates near real-time zenith total delays (ZTD) from GPS permanent stations for assimilation in numerical weather prediction (NWP) models more than 12 years. Besides European regional, global and GPS and GLONASS solutions, we have recently developed real-time estimates aimed at supporting NWP nowcasting or severe weather event monitoring. While all previous solutions are based on data batch processing in a network mode, the real-time solution exploits real-time global orbits and clocks from the International GNSS Service (IGS) and Precise Point Positioning (PPP) processing strategy. New application G-Nut/Tefnut has been developed and real-time ZTDs have been continuously processed in the nine-month demonstration campaign (February–October, 2013) for selected 36 European and global stations. Resulting ZTDs can be characterized by mean standard deviations of 6–10 mm, but still remaining large biases up to 20 mm due to missing precise models in the software. These results fulfilled threshold requirements for the operational NWP nowcasting (i.e. 30 mm in ZTD). Since remaining ZTD biases can be effectively eliminated using the bias-reduction procedure prior to the assimilation, results are approaching the target requirements in terms of relative accuracy (i.e. 6 mm in ZTD). Real-time strategy and software are under the development and we foresee further improvements in reducing biases and in optimizing the accuracy within required timeliness. The real-time products from the International GNSS Service were found accurate and stable for supporting PPP-based tropospheric estimates for the NWP nowcasting.