Ambiguity-fixed Precise Point Positioning Research Articles

Performance analysis of four PPP service software under different intensity geomagnetic storms

Currently, many precise point positioning (PPP) services provide through software or online websites for GNSS positioning studies and applications. Various PPP service software has different positioning performances due to their respective algorithms and versions. In addition, the positioning accuracy and reliability of PPP services lack systematic evaluation, especially in the case of geomagnetic storms. This study presents the PPP performance analysis of the common GNSS PPP software as CSRS-PPP (https://www.geod.nrcan.gc.ca/), APPS (https://apps.gdgps.net/), Net_Diff (http://center.shao.ac.cn/shao_gnss_ac/), and GAMP (https://www.ngs.noaa.gov/gps-toolbox/GAMP) under different geomagnetic storm intensities. The PPP experiments involve data from 916, 885, and 676 GPS stations data on 17 March 2015 (severe), 26 August 2018 (strong), and 15 January 2022 (moderate), respectively. The results showed that the positioning performance of the four PPP software is different in the magnetic storm environment. We found that during geomagnetic storms, the CSRS-PPP software has the highest positioning accuracy and reliability, while the APPS software shows the worst positioning performance. The performance of Net_Diff and GAMP during geomagnetic storms are comparable but are better than that of APPS. Statistical results indicate that the average values of 3D RMS of CSRS-PPP, APPS, Net_Diff, and GAMP under severe storm are 0.14 m, 0.60 m, 0.40 m, and 0.33 m, under strong storm are 0.18 m, 0.65 m, 0.27 m, and 0.33 m, and under moderate storm are 0.25 m, 1.66 m, 0.26 m, and 0.34 m, respectively. The main reason why the CSRS-PPP has the best positioning accuracy under different intensity storms is that it uses the ambiguity-fixed PPP solution, while the other three software use float solution.

Continuous Decimeter-Level Positioning in Urban Environments Using Multi-Frequency GPS/BDS/Galileo PPP/INS Tightly Coupled Integration

Time- and precision-critical applications, such as autonomous driving, have extremely rigorous standards for continuous high-precision positioning. The importance of precise point positioning (PPP) technology for self-navigation equipment is self-evident by delivering decimeter-/centimeter-level absolute position accuracy in a global coordinate framework. Nevertheless, the prolonged initialization period renders PPP almost too difficult to be widely used for time-critical applications in real transportation scenarios, for example, in city canyons and overpasses. We proposed a method to accomplish continuous decimeter-level positioning by leveraging triple-frequency GNSS observations with an Inertial Navigation System (INS) aiding in urban environments. In the proposed method, the inertial measurements and the original tri-frequency pseudorange and carrier phase measurements are tightly fused in an extended Kalman filter to obtain the optimal state estimate. Afterwards, with precise extra-wide-lane (EWL) and wide-lane (WL) Uncalibrated Phase Delay (UPD) products, the EWL and WL ambiguities can be resolved sequentially to implement instantaneous decimeter-level positioning. Exploiting the short-term high-precision characteristic of the INS, the continuity of the PPP solution can be ameliorated noticeably, and the ability of decimeter-level positioning can be maintained effortlessly throughout the navigation process. With land vehicle data collected, several experiments are undertaken to comprehensively assess the capability of the proposed system in urban scenarios, taking the solution obtained by a commercial post-processing software as the reference. The single-epoch decimeter-level position estimation can be captured instantaneously for WL ambiguity-fixed PPP solutions. Furthermore, for WL ambiguity-fixed PPP/INS-integrated solutions, the position estimation is better than 0.2 m for horizontal components and improved by 40–90% compared with that of the WL ambiguity-fixed PPP solutions. More importantly, the availability rate of positioning accuracy is better than 0.3 m in the horizontal direction and 0.5 m in the up direction reaching 93.91%, whereas it is only 53.78% for WL ambiguity-fixed PPP solutions. Overall, the WL ambiguity-fixed PPP/INS-integrated solutions have the favorable performance to maintain continuous decimeter-level positioning for self-navigation equipment, even if full GNSS outages are encountered.

Performance assessment of high-rate GPS/BDS precise point positioning for vibration monitoring based on shaking table tests

For modern engineering infrastructures, the vibration information is critical in identifying the dynamic characteristics and assessing the structural health. Over the past few decades, Global Navigation Satellite System (GNSS) has played an increasingly important role in the monitoring of surface dynamic movement. The GNSS-based precise point positioning (PPP) has received much attention due to its technical feasibility and economic efficiency. More efforts are expected to be made in the research of high-rate PPP and the integration of multiple GNSSs for structural health monitoring. This study evaluates the performance of GPS/BDS kinematic PPP with 20-Hz observations in capturing vibrations generated from a linear shaker. A comparative analysis of the solutions obtained from GPS/BDS high-rate PPP, real-time kinematic (RTK) positioning, total station and accelerometer is performed in both frequency and displacement domains. The experimental results show that the displacement time series captured by GPS/BDS PPP and RTK can achieve an accuracy of 5.7–8.4 and 4.5–6.6 mm with respect to those from total station, respectively. The PPP-derived vibration frequency is consistent with that from RTK, total station and accelerometer, with a deviation less than 0.008 Hz among each other. For comparison, the GPS-only and BDS-only PPP results are also provided, and it is indicated that the dual-system integration can enhance the reliability and accuracy of monitoring results. For completeness, another experiment is conducted to investigate the performance difference between ambiguity-float and ambiguity-fixed PPP for vibration monitoring.

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.

Algorithm and Assessment of Ambiguity-Fixed PPP with BeiDou Observations and Regional Network Augmentation

AbstractIn precise point positioning (PPP) applications, uncalibrated phase delays (UPD) are applied to retrieve the ambiguity integers for achieving precise solutions over a short period. Also, th...

Multi-GNSS fractional cycle bias products generation for GNSS ambiguity-fixed PPP at Wuhan University

The School of Geodesy and Geomatics (SGG) at Wuhan University has been generating GPS fractional cycle bias (FCB) products for users to realize ambiguity-fixed precise point positioning (PPP) since 2015. Along with the development of multiple Global Navigation Satellite Systems (GNSS), there is an urgent need to provide multi-GNSS FCB products for the PPP ambiguity resolution (AR) with multi-constellation observations. This study focuses on the multi-GNSS FCB estimation, in which the FCB products of GPS, Galileo, BDS and QZSS are generated. We describe here the detailed estimation method and the significant improvements to the new service. The FCB quality, as well as the PPP AR performance, is evaluated. The mean standard deviations of wide-lane FCBs relative to CODE are 0.019, 0.005, 0.015 and 0.008 cycles, while those of narrow-lane are 0.021, 0.021, 0.057 and 0.010 cycles for GPS, Galileo, BDS and QZSS, respectively. The comparison with CNES GPS and Galileo FCBs indicates their good consistency with the corresponding FCBs. Compared with GPS-only PPP AR, the convergence time and time to first fix of the four-system PPP AR can be reduced by 27.3 and 29.4% in the static mode, respectively, while the corresponding improvements are 42.6 and 51.9% in the kinematic mode, respectively. These results demonstrate that our SGG FCB service can provide high-precision and reliable four-system FCB corrections for worldwide users to conduct ambiguity-fixed PPP processing.

A modified phase clock/bias model to improve PPP ambiguity resolution at Wuhan University

Precise point positioning ambiguity resolution (PPP-AR) is a valuable tool for high-precision geodetic observations, while phase bias products are critical to implementing GNSS PPP-AR. Based on the conventional integer clock and uncalibrated phase delay (UPD) models, we proposed a modified phase clock/bias model to enable undifferenced ambiguity fixing where it is the phase clocks, rather than the International GNSS Service (IGS) legacy clocks, which are estimated in a network solution by first correcting carrier-phase data for both pre-resolved integer ambiguities and predetermined phase biases. Such phase clock/bias product is compatible with IGS legacy clock and code bias products as opposed to the integer clock model, while ensuring more accurate daily positions in contrast to the UPD model. We carried out precise point positioning (PPP) ambiguity fixing using 1 year of GPS data from about 500 stations and took the IGS weekly solutions as benchmarks: The phase clock/bias model reproduced the positioning achievement of the integer clock model without biasing pseudorange processing, whereas improving markedly the east component of daily positions by 20% compared to the UPD model; interestingly, negligible differences exist between the UPD-based hourly positions and those based on the phase clock/bias model, corroborating that the UPD model is a good approximation to the phase clock/bias model in case of short observation periods. Finally, since phase biases are linearly dependent on clocks, we suggest to compute daily phase bias products, instead of the usual 15-min UPDs, by driving all their temporal variations to the phase clocks, which will greatly facilitate ambiguity-fixed PPP (ftp://igs.gnsswhu.cn/pub/whu/phasebias).

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.

Estimating and assessing Galileo satellite fractional cycle bias for PPP ambiguity resolution

Due to the rapid deployment of the Galileo constellation, Galileo is now able to contribute to GNSS precise point positioning (PPP) ambiguity resolution (AR) with 17 operational satellites as of December 2017. We estimate the satellite fractional cycle bias (FCB) based on globally distributed MGEX stations and assess the Galileo FCB quality by a comparison with that of GPS and BDS. Results of 60 days indicate that the quality of Galileo wide-lane (WL) FCB is better than GPS and BDS in terms of data usage rate, residual distribution, as well as standard deviation of daily estimates. The RMS of Galileo WL FCB residuals is 0.071 cycles, while that of GPS and BDS are 0.089 and 0.117 cycles, respectively. The standard deviation of Galileo daily WL FCB is 0.010 cycles, while that of GPS and BDS is 0.018 and 0.043 cycles. We attribute the better quality of Galileo WL FCB to its signal modulation, AltBOC, which significantly compresses the multipath effect for pseudorange measurement. Within the Galileo constellation, the performance of In-Orbit Validation (IOV) satellites WL FCB is worse than that of Full Operational Capability (FOC) satellites as a result of a reduction in the power of the transmitted signal. The performance of the two highly eccentric satellites is comparable to other FOC satellites. The overall quality of Galileo narrow-lane (NL) FCB is slightly worse than that of GPS but better than that of BDS. The RMS of Galileo NL FCB residuals is 0.062 cycles, while that for GPS and BDS is 0.050 and 0.086 cycles respectively. In addition, the NL FCB quality of FOC, IOV (except E19), as well as the two eccentric satellites, shows no significant difference in terms of data usage rates and residuals. Galileo PPP AR solutions are conducted at 20 MGEX stations with 3-h sessions for 10 days. The positional biases of AR solutions are 0.7, 0.6, and 2.1 cm for east, north and up components respectively, while those for float solutions are 2.1, 1.1, and 2.7 cm, corresponding to the improvements of 67, 45, and 22%, respectively. These results demonstrate that, currently, Galileo FCB can be estimated with accuracy comparable with GPS and BDS, and the Galileo observations can bring an obvious benefit to ambiguity-fixed PPP.

Improved method to estimate undifferenced satellite fractional cycle biases using network observations to support PPP ambiguity resolution

Fixing ambiguities is beneficial to improve accuracy and convergence time of precise point positioning (PPP). In recent years, several methods have been proposed to estimate fractional cycle biases (FCBs) to realize ambiguity-fixed PPP. Existing single-difference models are mostly for GPS-only ambiguity-fixed PPP. However, the use of a single-difference model to achieve fixed ambiguities in GPS + GLONASS PPP is complicated because GLONASS uses frequency division multiple access modulation. This study presents an improved method to estimate undifferenced FCBs using network observations. The periodic feature of a trigonometric function is utilized to eliminate the integer ambiguity. Therefore, the proposed method avoids the difficulty of ambiguity fixing in undifferenced FCBs estimation at the network. Thus, it is a very simple method. GPS + GLONASS observation data of the Chinese reference station network are used to achieve ambiguity fixing for GPS-only and GPS + GLONASS PPP using the estimated FCBs. Experimental results show that the FCBs estimated with the proposed method can satisfy the accuracy requirement for ambiguity-fixed PPP. The root-mean-squares of the resolutions of GPS-only ambiguity-fixed PPP in the N, E, and U directions can reach 0.8, 0.9, and 2.5 cm, respectively, which are comparable with existing ambiguity-fixed resolutions in PPP. The resolutions of fixed ambiguity in GPS + GLONASS PPP can reach 0.7, 0.7, and 2.0 cm, which is an improvement by approximately 13, 22, and 20%, respectively, compared to the fixed solution of GPS-only PPP.

Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP

The main challenge of ambiguity resolution in precise point positioning (PPP) is that it requires 30 min or more to succeed in the first fixing of ambiguities. With the full operation of the BeiDou (BDS) satellite system in East Asia, it is worthwhile to investigate the performance of GPS + BDS PPP ambiguity resolution, especially the improvements of the initial fixing time and ambiguity-fixing rate compared to GPS-only solutions. We estimated the wide- and narrow-lane fractional-cycle biases (FCBs) for BDS with a regional network, and PPP ambiguity resolution was carried out at each station to assess the contribution of BDS. The across-satellite single-difference (ASSD) GPS + BDS combined ambiguity-fixed PPP model was used, in which the ASSD is applied within each system. We used a two-day data set from 48 stations. For kinematic PPP, the percentage of fixing within 10 min for GPS only (Model A) is 17.6 %, when adding IGSO and MEO of BDS (Model B), the percentage improves significantly to 42.8 %, whereas it is only 23.2 % if GEO is added (Model C) due to the low precision of GEO orbits. For static PPP, the fixing percentage is 32.9, 53.3 and 28.0 % for Model A, B and C, respectively. In order to overcome the limitation of the poor precision of GEO satellites, we also used a small network of 10 stations to analyze the contribution of GEO satellites to kinematic PPP. We took advantage of the fact that for stations of a small network the GEO satellites appear at almost the same direction, such that the GEO orbit error can be absorbed by its FCB estimates. The results show that the percentage of fixing improves from 39.5 to 57.7 % by adding GEO satellites.

On biases in precise point positioning with multi-constellation and multi-frequency GNSS data

Various types of biases in Global Navigation Satellite System (GNSS) data preclude integer ambiguity fixing and degrade solution accuracy when not being corrected during precise point positioning (PPP). In this contribution, these biases are first reviewed, including satellite and receiver hardware biases, differential code biases, differential phase biases, initial fractional phase biases, inter-system receiver time biases, and system time scale offset. PPP models that take account of these biases are presented for two cases using ionosphere-free observations. The first case is when using primary signals that are used to generate precise orbits and clock corrections. The second case applies when using additional signals to the primary ones. In both cases, measurements from single and multiple constellations are addressed. It is suggested that the satellite-related code biases be handled as calibrated quantities that are obtained from multi-GNSS experiment products and the fractional phase cycle biases obtained from a network to allow for integer ambiguity fixing. Some receiver-related biases are removed using between-satellite single differencing, whereas other receiver biases such as inter-system biases are lumped with differential code and phase biases and need to be estimated. The testing results show that the treatment of biases significantly improves solution convergence in the float ambiguity PPP mode, and leads to ambiguity-fixed PPP within a few minutes with a small improvement in solution precision.

Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning

With the development of precise point positioning (PPP), the School of Geodesy and Geomatics (SGG) at Wuhan University is now routinely producing GPS satellite fractional cycle bias (FCB) products with open access for worldwide PPP users to conduct ambiguity-fixed PPP solution. We provide a brief theoretical background of PPP and present the strategies and models to compute the FCB products. The practical realization of the two-step (wide-lane and narrow-lane) FCB estimation scheme is described in detail. With GPS measurements taken in various situations, i.e., static, dynamic, and on low earth orbit (LEO) satellites, the quality of FCB estimation and the effectiveness of PPP ambiguity resolution (AR) are evaluated. The comparison with CNES FCBs indicated that our FCBs had a good consistency with the CNES ones. For wide-lane FCB, almost all the differences of the two products were within ±0.05 cycles. For narrow-lane FCB, 87.8 % of the differences were located between ±0.05 cycles, and 97.4 % of them were located between ±0.075 cycles. The experimental results showed that, compared with conventional ambiguity-float PPP, the averaged position RMS of static PPP can be improved from (3.6, 1.4, 3.6) to (2.0, 1.0, 2.7) centimeters for ambiguity-fixed PPP. The average accuracy improvement in the east, north, and up components reached 44.4, 28.6, and 25.0 %, respectively. A kinematic, ambiguity-fixed PPP test with observation of 80 min achieved a position accuracy of better than 5 cm at the one-sigma level in all three coordinate components. Compared with the results of ambiguity-float, kinematic PPP, the positioning biases of ambiguity-fixed PPP were improved by about 78.2, 20.8, and 65.1 % in east, north, and up. The RMS of LEO PPP test was improved by about 23.0, 37.0, and 43.0 % for GRACE-A and GRACE-B in radial, tangential, and normal directions when AR was applied to the same data set. These results demonstrated that the SGG FCB products can be produced with high quality for users anywhere around the world to carry out ambiguity-fixed PPP solutions.

Ionospheric effects in uncalibrated phase delay estimation and ambiguity-fixed PPP based on raw observable model

Zero-difference (ZD) ambiguity resolution (AR) reveals the potential to further improve the performance of precise point positioning (PPP). Traditionally, PPP AR is achieved by Melbourne–Wubbena and ionosphere-free combinations in which the ionosphere effect are removed. To exploit the ionosphere characteristics, PPP AR with L1 and L2 raw observable has also been developed recently. In this study, we apply this new approach in uncalibrated phase delay (UPD) generation and ZD AR and compare it with the traditional model. The raw observable processing strategy treats each ionosphere delay as an unknown parameter. In this manner, both a priori ionosphere correction model and its spatio-temporal correlation can be employed as constraints to improve the ambiguity resolution. However, theoretical analysis indicates that for the wide-lane (WL) UPD retrieved from L1/L2 ambiguities to benefit from this raw observable approach, high precision ionosphere correction of better than 0.7 total electron content unit (TECU) is essential. This conclusion is then confirmed with over 1 year data collected at about 360 stations. Firstly, both global and regional ionosphere model were generated and evaluated, the results of which demonstrated that, for large-scale ionosphere modeling, only an accuracy of 3.9 TECU can be achieved on average for the vertical delays, and this accuracy can be improved to about 0.64 TECU when dense network is involved. Based on these ionosphere products, WL/narrow-lane (NL) UPDs are then extracted with the raw observable model. The NL ambiguity reveals a better stability and consistency compared to traditional approach. Nonetheless, the WL ambiguity can be hardly improved even constrained with the high spatio-temporal resolution ionospheric corrections. By applying both these approaches in PPP-RTK, it is interesting to find that the traditional model is more efficient in AR as evidenced by the shorter time to first fix, while the three-dimensional positioning accuracy of the RAW model outperforms the combination model by about \(7.9\,\%\). This reveals that, with the current ionosphere models, there is actually no optimal strategy for the dual-frequency ZD ambiguity resolution, and the combination approach and raw approach each has merits and demerits.

Comparison between multi-constellation ambiguity-fixed PPP and RTK for maritime precise navigation

AbstractIn order to achieve high-accuracy positioning, either Real-Time Kinematic (RTK) or Precise Point Positioning (PPP) techniques can be used. While RTK normally delivers higher accuracy with shorter convergence times, PPP has been an attractive technology for maritime applications, as it delivers uniform positioning performance without the direct need of a nearby reference station. Traditional PPP has been based on ambiguity-­float solutions using GPS and Glonass constellations. However, the addition of new satellite systems, such as Galileo and BeiDou, and the possibility of fixing integer carrier-phase ambiguities (PPP-AR) allow to increase PPP accuracy. In this article, a performance assessment has been done between RTK, PPP and PPP-AR, using GNSS data collected from two antennas installed on a ferry navigating in Oslo (Norway). RTK solutions have been generated using short, medium and long baselines (up to 290 km). For the generation of PPP-AR solutions, Uncalibrated Hardware Delays (UHDs) for GPS, Galileo and BeiDou have been estimated using reference stations in Oslo and Onsala. The performance of RTK and multi-­constellation PPP and PPP-AR are presented.

High-Rate GPS Seismology Using Real-Time Precise Point Positioning With Ambiguity Resolution

With the availability of real-time high-rate GPS observations and precise satellite orbit and clock products, the interest in the real-time precise point positioning (PPP) technique has greatly increased to construct displacement waveforms and to invert for source parameters of earthquakes in real time. Furthermore, PPP ambiguity resolution approaches, developed in the recent years, overcome the accuracy limitation of the standard PPP float solution and achieve comparable accuracy with relative positioning. In this paper, we introduce the real-time PPP service system and the key techniques for real-time PPP ambiguity resolution. We assess the performance of the ambiguity-fixed PPP in real-time scenarios and confirm that positioning accuracy in terms of root mean square of 1.0–1.5 cm can be achieved in horizontal components. For the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor–Cucapah (Mexico) earthquakes, the displacement waveforms estimated from ambiguity-fixed PPP and those provided by the accelerometer instrumentation are consistent in the dynamic component within few centimeters. The PPP fixed solution not only can improve the accuracy of coseismic displacements but also provides a reliable recovery of earthquake magnitude and of the fault slip distribution in real time.

Near-field surface displacement and permanent deformation induced by the Alaska Mw 7.5 earthquake determined by high-rate real-time ambiguity-fixed PPP solutions

High-rate GPS data from the United States continuously operating reference stations in the Alaska region are processed using the recently developed precise point positioning (PPP) technique. The traditional PPP technique does not fix ambiguities into their integers because these ambiguities do not have an integer nature when data from a single receiver, as well as precise orbit and clock corrections, are used. Additional corrections, i.e., uncalibrated phase delay (UPD), are needed to fix integer ambiguities and consequently improve positioning accuracy. This study proposes a methodology to compute for wide-lane and L2 (the second L-band frequency) UPDs using the geometry-based model and subsequently applies these parameters to the computation for ambiguity-fixed solutions. The instantaneous displacements of near-field sites, as well as the permanent deformations after the earthquake, are therefore obtained for the January 5, 2013, Alaska earthquake. The real-time performance of PPP solutions are assessed by considering realistic data latency and data interval of corrections. Ambiguity-fixed solutions are compared with ambiguity-float ones. The comparison shows that the positioning accuracy can be improved significantly when the ambiguities are fixed correctly. The solutions using the real-time corrections are also compared with those using post-processing corrections, i.e., Center for Orbit Determination in Europe final orbit and clock. Although the accuracy is somehow degraded because of the data latency and data interval, the real-time results are satisfactory for use in monitoring the small-scale deformation (1–2 cm) caused by the Alaska earthquake. In addition, the kinematic ambiguity-fixed PPP solutions for 7 days around the earthquake are calculated to obtain permanent pre- and post-earthquake deformations. The deformations computed from real-time and post-processing corrections do not appear to be significantly different.

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.

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

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

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 15min 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.