Precise Point Positioning Ambiguity Resolution Research Articles

Real-time Precise Point Positioning Ambiguity Resolution Based on Phase Biasesormalsize

采用CNES发布的实时相位偏差数据，实现包含模糊度固定的实时精密单点定位.对全球10个IGS测站10天观测数据进行RTPPP解算，分别统计模糊度首次固定时间和定位精度，结果显示利用实时相位偏差数据能在平均30min内实现模糊度首次固定，模糊度固定时水平位置误差由6cm迅速降低至2cm左右，三维位置误差由10cm迅速降低至5cm左右，同时RTPPP模糊度固定在3h观测内可保持水平3cm、三维5cm左右的定位精度.通过分析得出，基于相位偏差的RTPPP模糊度固定技术具有较高的定位精度和定位稳定性，能够快速实现cm级定位.

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 De...

Optimal Carrier-Phase Integer Combinations for Modernized Triple-Frequency BDS in Precise Point Positioning

The latest generation of Global Navigation Satellite System (GNSS) satellites are transmitting signals on three or more frequencies, it brings new opportunities and challenges for data integration in Multi–GNSS Experiment (MGEX). To reduce the convergence time, less computationally intensive method is three-carrier ambiguity resolution (TCAR). But the three combinaitons can not be found in precise point positioning (PPP) yet, especially for the third generation BeiDou Navigation Satellite System (BDS-3). This contribution concentrates on the multi-frequency carrier-phase integer combinations for BDS-3 in PPP. More specifically, the triple-frequency plane is degraded to two-dimensional plane for BDS-3 under the assumption of a low observation noise. And then third frequency coefficient should be limited as a constraint, considering that inter frequency bias (IFB) is dynamic quantity. Thereafter, a new searching algorithm based on the Satisfiability Modulo Theories (SMT) is presented to search the optimal integer combinations fast. Meanwhile, ionosphere-free combinations are exhibited and are not suitable for TCAR. Futhermore, the availability of the SMT-based searching algorithm (SMTSA) is verified. Finally, the most interesting carrier-phase combinations that can be used for PPP ambiguity resolution are screened out for later research. Meanwhile, in order to give a referenced comprehensive assessment of the integer combination, some valuable combinations for BDS-3 are displayed. It provides scientific support for the triple-frequency AR which has less convergence time than dual-frequency AR. Moreover, it also gives the important and valuable reference for future research on multi-frequency ambiguity–enabled PPP.

Capturing coseismic displacement in real time with mixed single- and dual-frequency receivers: application to the 2018 Mw7.9 Alaska earthquake

High-density GPS monitoring networks have been built in seismically active areas to obtain high-precision real-time seismic displacements with high spatial resolution, which is necessary for rapid source inversion and decreasing the blind zone for earthquake early warning. To reduce the costs for large regions such as China, single-frequency (SF) receivers are preferred to densify the current sparse dual-frequency (DF) GPS network. We developed a new approach for SF precise point positioning ambiguity resolution (PPP-AR) with mixed SF and DF receivers. The ionospheric corrections, the main issue in processing SF data, were derived directly from geometry-free carrier-phase observations with fixed ambiguities, and then interpolated to the SF stations using the Kriging interpolator. The uncalibrated phase-delay (UPD) at L1 frequency was also estimated based on a regional network to enable PPP-AR. A dataset of 30 days from SAPOS network with different station densities was utilized to validate the performance of SF PPP-AR. The experimental results show that the accuracy of original ionospheric estimates is about 0.016 m, which is better than 0.035 m obtained from interpolation for an average station separation of less than 56 km. The L1 UPDs can be estimated hourly due to its high temporal stability; all of the phase residuals are within 0.3 cycle. Compared with the post-processed daily solutions, the positioning accuracies of SF kinematic PPP-AR can reach 1–2 cm and 2–3.5 cm for the horizontal and vertical components, respectively. Convergence time can be achieved within 10 min when the station spacing is less than 52 km, but it will increase to more than 20 min when the station spacing is larger than 99 km since most ambiguities cannot be fixed correctly. Finally, we applied this approach to the 2018 Mw7.9 Alaska earthquake and successfully retrieved the seismic displacement waveforms at a comparable accuracy level when compared to the ionospheric-free (IF) PPP solutions. The accuracy of the coseismic offset estimates relative to the final solutions based on the combination of GPS and accelerometer daily solutions, and is about 5–7 mm which demonstrates the capability for capturing the coseismic displacements.

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.

Spatial–temporal characteristic of BDS phase delays and PPP ambiguity resolution with GEO/IGSO/MEO satellites

GPS precise point positioning (PPP) ambiguity resolution (AR) can improve the positioning accuracy and shorten the convergence time. However, for the BeiDou Satellite Navigation System (BDS), the problems of satellite-induced code bias, imperfections in the error models and the inadequate accuracy of orbit products limit the applications of the BDS PPP AR system, which requires more than 6 h to achieve the first ambiguity-fixed solution. In this study, the accuracy of a wide-lane (WL) uncalibrated phase delay (UPD) is improved after careful consideration of the code bias and multipath. Meanwhile, the accuracy of the BDS float ambiguity is also improved by multi-GNSS fusion and improved precise orbit and clock products, which are critical for high-quality narrow-lane (NL) UPD estimations. With three tracking networks of different scales, including Hong Kong, the Crustal Movement Observation Network of China (CMONOC) and the multi-GNSS experiment (MGEX) networks, the spatial–temporal characteristics of WL and NL UPDs for BDS GEO/IGSO/MEO satellites are analyzed, and the PPP AR is performed. Numerous results show that WL and NL UPDs with a standard deviation (STD) of less than 0.15 cycles can be achieved for BDS GEO satellites, while a STD of less than 0.1 cycles can be obtained for IGSO and MEO satellites. With the precise UPD estimation, for the first time, the BDS PPP rapid ambiguity resolution for GEO/IGSO/MEO satellites is achieved. We found that the average time to first fix (TTFF) of the BDS PPP AR is shortened significantly, to approximately 40 min for Hong Kong and the CMONOC, while the TTFF was 57.4 min for the MGEX networks. With ambiguity resolution, the accuracy of the daily BDS PPP in the east, north and vertical directions improves from 1.74 cm, 1.08 cm, and 5.52 cm to 0.72 cm, 0.54 cm, and 3.21 cm for the Hong Kong network, 2.24 cm, 2.31 cm, and 5.64 cm to 1.18 cm, 0.79 cm, and 3.30 cm for the CMONOC, and 2.71 cm, 1.80 cm, and 6.00 cm to 1.58 cm, 1.15 cm, and 4.33 cm for the MGEX networks. Significant improvement is also achieved for kinematic PPP, with improvements of 40.41%, 34.33% and 37.17% in the east, north and vertical directions for the MGEX networks, respectively.

Real‐Time Sensing of Precipitable Water Vapor From BeiDou Observations: Hong Kong and CMONOC Networks

AbstractThe development of BeiDou Navigation Satellite System (BDS) provides opportunities for real‐time retrieval of precipitable water vapor (PWV), which is expected to significantly contribute to time‐critical meteorological applications. In this study, observations from 17 stations of the Hong Kong Continuously Operating Reference Stations and 15 stations of the Crustal Movement Observation Network of China (CMONOC) are used to retrieve PWV based on the real‐time precise point positioning ambiguity resolution approach. Real‐time PWV products, retrieved from BDS observations of both summer (day of year 183–192) and winter (day of year 024–033) periods, are analyzed and validated using postprocessed Global Positioning System products. The results show that the real‐time BDS PWV series agree well with the Global Positioning System PWV series. Root‐mean‐square values for the Hong Kong Continuously Operating Reference Stations and CMONOC stations are 2.0–3.5 and 2.5–4.0 mm, respectively. In addition, short initialization time, strong reliability, and good distribution could be achieved by applying the fixed solution instead of the float solution. With the gradual completion of BDS constellation, the BDS can independently contribute to real‐time sensing of PWV and potentially contribute to time‐critical meteorological applications.

Real-Time Phase Bias Estimation for BeiDou Satellites Based on Consideration of Orbit Errors

Correction of the fractional cycle bias (FCB) in the undifferenced ambiguity allows precise point positioning (PPP) integer ambiguity resolution (IAR) to be achieved, which can improve positioning accuracy significantly. In addition, in real-time PPP-IAR, integration of the BeiDou Navigation Satellite System (BDS) can provide a significant reduction in the initial fixing time of global positioning system (GPS)-only PPP-IAR. However, the FCB quality can be considerably affected by the low precision of the BDS orbit, which then severely hampers the GPS + BDS PPP-IAR performance. Therefore, a real-time FCB estimation strategy that takes the BDS satellite orbit error into consideration was developed in this study. The slant orbit error can be absorbed by the ionosphere-free (IF) ambiguity, which can then be recovered by fixing all IF ambiguities from all the tracking stations. The estimated orbit error is then used to refine the orbit, which is broadcast along with the FCBs to enable PPP ambiguity resolution. To evaluate the proposed strategy, an experiment using 60 tracking stations covering the China region is performed in a simulated real-time mode. The a posteriori residuals of both the wide- and narrow-lane ambiguities are checked to validate the efficiency of the proposed FCB strategy. The results show that when the proposed strategy is applied, the effect of the BDS orbit error on narrow-lane FCB estimation is eliminated and more than 94% of the narrow-lane residuals are within 0.1 cycles for both the GPS and the BDS. The fixing percentage within 20 min is 46.3% for the GPS-only solution but is only 4.8% when using GPS + BDS with the traditional method. However, when the proposed strategy is used, the fixing percentage for GPS + BDS improves significantly to 91.7%.

Development of GNSS Buoy for a Synthetic Geohazard Monitoring System

The GNSS buoy system for early tsunami warnings has been under development for about 20 years. A small prototype buoy was first deployed in Sagami Bay, Japan, in 1997. Then, after a series of experiments aiming for operational use, the system was implemented as a part of national wave monitoring system NOWPHAS. The NOWPHAS system had set up more than 10 GNSS buoys around Japan by 2011, and it recorded the tsunami caused by the 11 March 2011 Tohoku-oki earthquake. The records were used to update the tsunami warning at the time of the 2011 Tohoku-oki earthquake. However, the buoys were placed less than 20 km from the coast, as the system used the baseline mode RTK-GPS algorithm, which was not far enough for effective evacuation of people. Thus, we began trying to improve the system by putting the buoys much farther from the coast. The new system employs a newly developed positioning algorithm, Precise Point Positioning with Ambiguity Resolution (PPP-AR), together with satellite data transmission. A series of experiments involving the new system successfully indicated changes in sea level with an accuracy of a few centimeters. Given the success of the experiments, we are trying to use the GNSS buoys not only to provide early tsunami warnings but also to monitor various other geohazards. For example, we are trying to use the GNSS-Acoustic system to continuously monitor crustal movements on the ocean floor, to monitor the ionosphere, and to monitor the atmosphere. Ancillary sensors on the buoys will be utilized for oceanographic monitoring as well.

Accelerating real-time PPP ambiguity resolution by incorporating multi-GNSS observations

The performance of Real-Time (RT) Precise Point Positioning (PPP) ambiguity resolution can be further improved by incorporating multiple Global Navigation Satellite System (GNSS) observations. RT PPP with ambiguity resolution based on raw GNSS observations, aided by the satellite clock offsets and GPS un-calibrated phase delays (UPDs), is realized to evaluate the effect of GNSS observations. Compared with previous studies, Galileo observations are integrated in this analysis and the effect of new BeiDou/Galileo systems in RT PPP ambiguity resolution is analyzed for global users. Comparing with the GPS-only and GPS/GLONASS solution, the time to first fix (TTFF) is 18.8% and 7.9% improved for those users in the Asia-Pacific regions, while it is 9.6% and 3.8% improved for other users by adding the BeiDou/Galileo observations. The improvement of the fixing rate and positioning accuracy is similar for users in different regions. The fixing rate is 2.1% and 0.5% improved when adding BeiDou/Galileo observations on top of GPS and GPS/GLONASS respectively. The accuracy of the north, east and up components are 0.4, 0.0 and 0.5 mm improved when adding on top of GPS, while 0.2, 0.1 and 0.4 mm when adding on top of GPS/GLONASS. By utilizing observations of four systems, an accuracy of 9.0, 9.1 and 28.3 mm is achieved for the fixed kinematic PPP solution after a mean initialization time of 797.9 s.

An Improved BeiDou-2 Satellite-Induced Code Bias Estimation Method.

Different from GPS, GLONASS, GALILEO and BeiDou-3, it is confirmed that the code multipath bias (CMB), which originate from the satellite end and can be over 1 m, are commonly found in the code observations of BeiDou-2 (BDS) IGSO and MEO satellites. In order to mitigate their adverse effects on absolute precise applications which use the code measurements, we propose in this paper an improved correction model to estimate the CMB. Different from the traditional model which considering the correction values are orbit-type dependent (estimating two sets of values for IGSO and MEO, respectively) and modeling the CMB as a piecewise linear function with a elevation node separation of 10°, we estimate the corrections for each BDS IGSO + MEO satellite on one hand, and a denser elevation node separation of 5° is used to model the CMB variations on the other hand. Currently, the institutions such as IGS-MGEX operate over 120 stations which providing the daily BDS observations. These large amounts of data provide adequate support to refine the CMB estimation satellite by satellite in our improved model. One month BDS observations from MGEX are used for assessing the performance of the improved CMB model by means of precise point positioning (PPP). Experimental results show that for the satellites on the same orbit type, obvious differences can be found in the CMB at the same node and frequency. Results show that the new correction model can improve the wide-lane (WL) ambiguity usage rate for WL fractional cycle bias estimation, shorten the WL and narrow-lane (NL) time to first fix (TTFF) in PPP ambiguity resolution (AR) as well as improve the PPP positioning accuracy. With our improved correction model, the usage of WL ambiguity is increased from 94.1% to 96.0%, the WL and NL TTFF of PPP AR is shorten from 10.6 to 9.3 min, 67.9 to 63.3 min, respectively, compared with the traditional correction model. In addition, both the traditional and improved CMB model have a better performance in these aspects compared with the model which does not account for the CMB correction.

Improving multi-GNSS ultra-rapid orbit determination for real-time precise point positioning

Currently, with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSS), the real-time positioning and navigation are undergoing dramatic changes with potential for a better performance. To provide more precise and reliable ultra-rapid orbits is critical for multi-GNSS real-time positioning, especially for the three merging constellations Beidou, Galileo and QZSS which are still under construction. In this contribution, we present a five-system precise orbit determination (POD) strategy to fully exploit the GPS $$+$$ GLONASS $$+$$ BDS $$+$$ Galileo $$+$$ QZSS observations from CDDIS $$+$$ IGN $$+$$ BKG archives for the realization of hourly five-constellation ultra-rapid orbit update. After adopting the optimized 2-day POD solution (updated every hour), the predicted orbit accuracy can be obviously improved for all the five satellite systems in comparison to the conventional 1-day POD solution (updated every 3 h). The orbit accuracy for the BDS IGSO satellites can be improved by about 80, 45 and 50% in the radial, cross and along directions, respectively, while the corresponding accuracy improvement for the BDS MEO satellites reaches about 50, 20 and 50% in the three directions, respectively. Furthermore, the multi-GNSS real-time precise point positioning (PPP) ambiguity resolution has been performed by using the improved precise satellite orbits. Numerous results indicate that combined GPS $$+$$ BDS $$+$$ GLONASS $$+$$ Galileo (GCRE) kinematic PPP ambiguity resolution (AR) solutions can achieve the shortest time to first fix (TTFF) and highest positioning accuracy in all coordinate components. With the addition of the BDS, GLONASS and Galileo observations to the GPS-only processing, the GCRE PPP AR solution achieves the shortest average TTFF of 11 min with $$7{^{\circ }}$$ cutoff elevation, while the TTFF of GPS-only, GR, GE and GC PPP AR solution is 28, 15, 20 and 17 min, respectively. As the cutoff elevation increases, the reliability and accuracy of GPS-only PPP AR solutions decrease dramatically, but there is no evident decrease for the accuracy of GCRE fixed solutions which can still achieve an accuracy of a few centimeters in the east and north components.

Real-Time Tropospheric Delay Retrieval from Multi-GNSS PPP Ambiguity Resolution: Validation with Final Troposphere Products and a Numerical Weather Model

The multiple global navigation satellite systems (multi-GNSS) bring great opportunity for the real-time retrieval of high-quality zenith tropospheric delay (ZTD), which is a critical quality for atmospheric science and geodetic applications. In this contribution, a multi-GNSS precise point positioning (PPP) ambiguity resolution (AR) analysis approach is developed for real-time tropospheric delay retrieval. To validate the proposed multi-GNSS ZTD estimates, we collected and processed data from 30 Multi-GNSS Experiment (MGEX) stations; the resulting real-time tropospheric products are evaluated by using standard post-processed troposphere products and European Centre for Medium-Range Weather Forecasts analysis (ECMWF) data. An accuracy of 4.5 mm and 7.1 mm relative to the Center for Orbit Determination in Europe (CODE) and U.S. Naval Observatory (USNO) products is achievable for real-time tropospheric delays from multi-GNSS PPP ambiguity resolution after an initialization process of approximately 5 min. Compared to Global Positioning System (GPS) results, the accuracy of retrieved zenith tropospheric delay from multi-GNSS PPP-AR is improved by 16.7% and 31.7% with respect to USNO and CODE final products. The GNSS-derived ZTD time-series exhibits a great agreement with the ECMWF data for a long period of 30 days. The average root mean square (RMS) of the real-time zenith tropospheric delay retrieved from multi-GNSS PPP-AR is 12.5 mm with respect to ECMWF data while the accuracy of GPS-only results is 13.3 mm. Significant improvement is also achieved in terms of the initialization time of the multi-GNSS tropospheric delays, with an improvement of 50.7% compared to GPS-only fixed solutions. All these improvements demonstrate the promising prospects of the multi-GNSS PPP-AR method for time-critical meteorological applications.

Calibration of GLONASS Inter-Frequency Code Bias for PPP Ambiguity Resolution with Heterogeneous Rover Receivers

Integer ambiguity resolution (IAR) is important for rapid initialization of precise point positioning (PPP). Whereas many studies have been limited to Global Positioning System (GPS) alone, there is a strong need to add Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) to the PPP-IAR solution. However, the frequency-division multiplexing of GLONASS signals causes inter-frequency code bias (IFCB) in the receiving equipment. The IFCB causes GLONASS wide-lane uncalibrated phase delay (UPD) estimation with heterogeneous receiver types to fail, so GLONASS ambiguity is therefore traditionally estimated as float values in PPP. A two-step method of calibrating GLONASS IFCB is proposed in this paper, such that GLONASS PPP-IAR can be performed with heterogeneous receivers. Experimental results demonstrate that with the proposed method, GLONASS PPP ambiguity resolution can be achieved across a variety of receiver types. For kinematic PPP with mixed receiver types, the fixing percentage within 10 min is only 33.5% for GPS-only. Upon adding GLONASS, the percentage improves substantially, to 84.9%.

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.

Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo

This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with $$7{^{\circ }}$$ cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to $$30{^{\circ }}$$ , the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.

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.

Assessment of PPP integer ambiguity resolution using GPS, GLONASS and BeiDou (IGSO, MEO) constellations

Although integer ambiguity resolution (IAR) can improve positioning accuracy considerably and shorten the convergence time of precise point positioning (PPP), it requires an initialization time of over 30 min. With the full operation of GLONASS globally and BDS in the Asia–Pacific region, it is necessary to assess the PPP–IAR performance by simultaneous fixing of GPS, GLONASS, and BDS ambiguities. This study proposed a GPS + GLONASS + BDS combined PPP–IAR strategy and processed PPP–IAR kinematically and statically using one week of data collected at 20 static stations. The undifferenced wide- and narrow-lane fractional cycle biases for GPS, GLONASS, and BDS were estimated using a regional network, and undifferenced PPP ambiguity resolution was performed to assess the contribution of multi-GNSSs. Generally, over 99% of a posteriori residuals of wide-lane ambiguities were within ±0.25 cycles for both GPS and BDS, while the value was 91.5% for GLONASS. Over 96% of narrow-lane residuals were within ±0.15 cycles for GPS, GLONASS, and BDS. For kinematic PPP with a 10-min observation time, only 16.2% of all cases could be fixed with GPS alone. However, adding GLONASS improved the percentage considerably to 75.9%, and it reached 90.0% when using GPS + GLONASS + BDS. Not all epochs could be fixed with a correct set of ambiguities; therefore, we defined the ratio of the number of epochs with correctly fixed ambiguities to the number of all fixed epochs as the correct fixing rate (CFR). Because partial ambiguity fixing was used, when more than five ambiguities were fixed correctly, we considered the epoch correctly fixed. For the small ratio criteria of 2.0, the CFR improved considerably from 51.7% for GPS alone, to 98.3% when using GPS + GLONASS + BDS combined solutions.

Property Analysis of the Real-Time Uncalibrated Phase Delay Product Generated by Regional Reference Stations and Its Influence on Precise Point Positioning Ambiguity Resolution

The real-time estimation of the wide-lane and narrow-lane Uncalibrated Phase Delay (UPD) of satellites is realized by real-time data received from regional reference station networks; The properties of the real-time UPD product and its influence on real-time precise point positioning ambiguity resolution (RTPPP-AR) are experimentally analyzed according to real-time data obtained from the regional Continuously Operating Reference Stations (CORS) network located in Tianjin, Shanghai, Hong Kong, etc. The results show that the real-time wide-lane and narrow-lane UPD products differ significantly from each other in time-domain characteristics; the wide-lane UPDs have daily stability, with a change rate of less than 0.1 cycle/day, while the narrow-lane UPDs have short-term stability, with significant change in one day. The UPD products generated by different regional networks have obvious spatial characteristics, thus significantly influencing RTPPP-AR: the adoption of real-time UPD products employing the sparse stations in the regional network for estimation is favorable for improving the regional RTPPP-AR up to 99%; the real-time UPD products of different regional networks slightly influence PPP-AR positioning accuracy. After ambiguities are successfully fixed, the real-time dynamic RTPPP-AR positioning accuracy is better than 3 cm in the plane and 8 cm in the upward direction.

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.