Precise Point Positioning Ambiguity Resolution Research Articles

GNSS satellite yaw attitude laws and impact on satellite clock, phase OSB and PPP-AR

Satellite yaw attitudes have significant impact on Global Navigation Satellite System (GNSS) data processing in two ways: the satellite horizontal phase center offset (PCO) corrections and phase wind-up corrections. When the Sun elevation angle is small, GNSS satellites are unable to maintain the nominal attitude and take place the yaw maneuvers. Generally, different types of satellites adopt different yaw attitudes during the yaw maneuver periods. In this research, the yaw attitude laws of different types of GPS, Galileo and BDS-3 satellites are comprehensively investigated, and the impact of yaw attitudes on satellite clock, phase observable-specific signal bias (OSB) and precise point positioning with ambiguity resolution (PPP-AR) are deeply evaluated. The main results show that for GPS Block IIF satellites, the maximum differences between the nominal yaw angles and the modeled yaw angles can reach to 360°. With the nominal attitude, the estimated phase OSB changes approximately 1 cycle and a 10 cm bias is observed in the U component positioning solutions of kinematic PPP-AR. After applying the modeled attitude, these obvious errors disappear. In addition, for BDS-3 SECM satellites, the mismodeling of the nominal attitude and CSNO modeled attitude results in 4-6 cm jumps in the detrended satellite clock residuals, and a 40 cm bias is observed in the U component positioning solutions of BDS-3 kinematic PPP-AR. After applying the modified CSNO modeled attitude to BDS-3 SECM satellites, the stability of satellite clocks and the positioning accuracy of PPP-AR are significantly improved.

Estimation of GNSS satellite bias corrections using non-common frequency model with application to PPP-AR

Abstract Corrections of satellite phase biases (SPBs) enable precise point positioning with ambiguity resolution (PPP-AR), which shortens the convergence time and improves positioning precision compared with precise point positioning (PPP). Extending PPP-AR from dual-frequency to multi-frequency can further enhance the positioning performance by correcting satellite code biases (SCBs) at the third frequency and above. In formulating a multi-frequency model to estimate satellite bias corrections (SBCs), including SPBs and SCBs, existing studies use only satellite observations collected at common frequencies (CF). This study proposes a non-common frequency (NCF) model that utilizes dual- and multi-frequency satellites to estimate SBCs simultaneously. To validate the NCF model, we collect data from an Australian network to estimate the SBCs and apply these corrections to the PPP-AR user positioning. The results show that the NCF model can provide SBCs for more satellites and frequencies than the CF model. After correction of SBCs, the proportion of fractional parts of float PPP ambiguities, which are less than 0.1 cycles, has a significant increase from 20% to
70%, indicating the successful restoration of the integer properties of PPP ambiguities by the
SBCs. Moreover, a comparable experiment between the NCF and CF PPP-AR models is conducted. The NCF PPP-AR model demonstrates superior performance over the CF model using triple-frequency satellites in convergence speed and positioning precision, achieving improvements of 41.16% and 39.52%, respectively. Meanwhile, compared to the CF model using dual-frequency satellites, the NCF PPP-AR model shows improvements of 17.16% and 7.46% in these aspects. The positioning performance of the NCF PPP-AR model is evaluated across ten user stations sampled over three days. The results indicate the root mean square
(RMS) positioning errors for the east, north and up components are 0.41, 0.51 and 2.46 cm, respectively. Additionally, the average convergence time for achieving 3D positioning errors within 1 dm is 9.75 min.

A New Precise Point Positioning with Ambiguity Resolution (PPP-AR) Approach for Ground Control Point Positioning for Photogrammetric Generation with Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) are now widely preferred systems that are capable of rapid mapping and generating topographic models with relatively high positional accuracy. Since the integrated GNSS receivers of UAVs do not allow for sufficiently accurate outcomes either horizontally or vertically, a conventional method is to use ground control points (GCPs) to perform bundle block adjustment (BBA) of the outcomes. Since the number of GCPs to be installed limits the process in UAV operations, there is an important research question whether the precise point positioning (PPP) method can be an alternative when the real-time kinematic (RTK), network RTK, and post-process kinematic (PPK) techniques cannot be used to measure GCPs. This study introduces a novel approach using precise point positioning with ambiguity resolution (PPP-AR) for ground control point (GCP) positioning in UAV photogrammetry. For this purpose, the results are evaluated by comparing the horizontal and vertical coordinates obtained from the 24 h GNSS sessions of six calibration pillars in the field and the horizontal length differences obtained by electronic distance measurement (EDM). Bartlett’s test is applied to statistically determine the accuracy of the results. The results indicate that the coordinates obtained from a two-hour PPP-AR session show no significant difference from those acquired in a 30 min session, demonstrating PPP-AR to be a viable alternative for GCP positioning. Therefore, the PPP technique can be used for the BBA of GCPs to be established for UAVs in large-scale map generation. However, the number of GCPs to be selected should be four or more, which should be homogeneously distributed over the study area.

The effect of ambiguity resolution on the precision of the GPS/Galileo PPP using a u-blox ZED-F9P low-cost GNSS receiver

Thanks to the increasing number of low-cost dual-frequency GNSS receivers available on the market, the usability of these receivers for geodetic applications is increasing. Recently, PRIDE Lab at GNSS Research Center of Wuhan University has started to produce GNSS observable-specific phase biases for all-frequency. This enables precise point positioning with ambiguity resolution (PPP-AR) not only for conventional frequencies but also for other arbitrary frequencies. In this work, static and kinematic PPP-AR precision of the u-blox ZED-F9P low-cost GNSS receiver are investigated by comparing it with a geodetic-grade GNSS receiver using GPS-only, Galileo-only, and GPS + Galileo combinations for nearly two months period. Wide-lane (WL) and Narrow-lane (NL) AR fixing rates, cycle slips, code multipath, and frequency availability are also investigated for both receivers. In the positioning domain, GPS-only, Galileo-only, and GPS + Galileo PPP positioning precision using float ambiguities is significantly improved after AR for both receivers. GPS + Galileo PPP provides the best precision comparing with the other PPP solutions for both receivers using float and fix ambiguities. For static GPS + Galileo PPP-AR, the standard deviation of north, east, and up components are computed as 2.7/1.7/3.2 mm and 2.2/2.3/5.4 mm for the geodetic receiver and the u-blox receiver, respectively. The results also reveal that kinematic PPP-AR for the u-blox receiver is not as reliable as the geodetic-grade receiver yet suggesting potential for improvement in future iterations.

Cube: An Open-Source Software for Clock Offset Estimation and Precise Point Positioning with Ambiguity Resolution

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube’s performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime.

Elevating performance in BDS-3 Precise Point Positioning Ambiguity Resolution through LEO augmented constellations

With the help of constellations combined BDS-3 (BeiDou Navigation Satellite System) and LEO (Low Earth Orbit), we aim to improve the performances of PPP (Precise Point Positioning) and PPP Ambiguity Resolution (PPP-AR). First, LEO constellations with 66, 96, 156, 192, 270, and 288 satellites are designed to establish six LEO augmented constellations. Based on four challenge scenarios, PPP of six LEO augmented constellations are performed. Even in the strip-shaped obstruction area losing more than 60% of observations, the positioning accuracies of static PPP are improved by (1.0%, 5.7%, 0.2%) for BDS+66LEO, and (14.9%, 33.7%, 7.5%) for BDS+288LEO in the east, north, and up components. The positioning accuracy and convergence time improve quickly as the number of LEO satellites increased from 66 to 156, and slowdown from 192 to 288. Two constellations, BDS+156LEO and BDS+192LEO, are considered to strike the balance of acceptable PPP performance and constellation load. Then, the performance of PPP-AR is realized with the estimated UPD (Uncalibrated Phase Delay). The correlations among geodetic parameters and ambiguities deriving from the post-fit variance–covariance matrix are analyzed to illustrate the enhancement of LEO augmented constellations. Under the condition of 20°elevation angle occlusion with azimuth ranging from 0 to 360°, BDS+156LEO can achieve an ambiguity fix rate of up to 98.37% with a faster mean TTFF (Time To First Fix) of 12.76 min, and the positioning accuracies in the east, north, and up components are improved by 28.2%, 21.4%, and 15.1% respectively, compared with BDS-3. BDS+192LEO realized an 98.42% ambiguity fixing rate, and improved BDS-3 by 31.4%, 26.7% and 11.5% with its TTFF been 12.25 min.

5G assisted GNSS precise point positioning ambiguity resolution

5G assisted GNSS precise point positioning ambiguity resolution

Orbit and clock products for quad-system satellites with undifferenced ambiguity fixing approach

Integer Ambiguity Resolution (IAR) can significantly improve the accuracy of GNSS Precise Orbit Determination (POD). Traditionally, the IAR in POD is achieved at the Double Differenced (DD) level. In this contribution, we develop an Un-Differenced (UD) IAR method for Global Positioning System (GPS)+ BeiDou Navigation Satellite System (BDS) + Galileo navigation satellite system (Galileo)+ Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range. Based on this method, we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center (IAC) of the International GNSS Monitoring and Assessment System (iGMAS). One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products. Notably, the UD Ambiguity Resolution (AR) yields more resolved integer ambiguities than the traditional DD AR, scaling up to 9%, attributable to its avoidance of station baseline formation. Benefiting from the removal of ambiguity parameters, the computational efficiency of parameter estimation undergoes a substantial 70% improvement. Compared with the float solution, the orbit consistencies of UD AR solution achieve the accuracy of 1.9, 5.2, 2.8, 2.1, and 2.7 cm for GPS, BeiDou-2 Navigation Satellite System (BDS-2), BeiDou-3 Navigation Satellite System (BDS-3), Galileo, and GLONASS satellites respectively, reflecting enhancements of 40%, 24%, 54%, 34%, and 42%. Moreover, the standard deviations of Satellite Laser Ranging (SLR) residuals are spanning 2.5–3.5 cm, underscoring a comparable accuracy to the DD AR solution, with discrepancies below 5%. A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock (IRC), facilitating Precise Point Positioning (PPP) AR without requiring additional Uncalibrated Phase Delay (UPD) products. To assess the performance of quad-system kinematic PPP based on IRC, a network comprising 120 stations is utilized. In comparison to the float solution, the IRC-based PPP AR accelerates convergence time by 31% and enhance positioning accuracy in the east component by 54%.

GSeisRT: A Continental BDS/GNSS Point Positioning Engine for Wide-Area Seismic Monitoring in Real Time

Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety. Real-time global navigation satellite systems (GNSSs) have been a valuable tool in monitoring seismic motions, allowing permanent displacement computation to be unambiguously achieved. As a valuable tool presented to the seismic community, the GSeisRT software developed by Wuhan University (China) can realize multi-GNSS precise point positioning with ambiguity resolution (PPP-AR) and achieve centimeter-level to sub-centimeter-level precision in real time. While the stable maintenance of a global precise point positioning (PPP) service is challenging, this software is capable of estimating satellite clocks and phase biases in real time using a regional GNSS network. This capability makes GSeisRT especially suitable for proprietary GNSS networks and, more importantly, the highest possible positioning precision and reliability can be obtained. According to real-time results from the Network of the Americas, the mean root mean square (RMS) errors of kinematic PPP-AR over a 24 h span are as low as 1.2, 1.3, and 3.0 cm in the east, north, and up components, respectively. Within the few minutes that span a typical seismic event, a horizontal displacement precision of 4 mm can be achieved. The positioning precision of the GSeisRT regional PPP/PPP-AR is 30%–40% higher than that of the global PPP/PPP-AR. Since 2019, GSeisRT has successfully recorded the static, dynamic, and peak ground displacements for the 2020 Oaxaca, Mexico moment magnitude (Mw) 7.4 event; the 2020 Lone Pine, California Mw 5.8 event; and the 2021 Qinghai, China Mw 7.3 event in real time. The resulting immediate magnitude estimates have an error of around 0.1 only. The GSeisRT software is open to the scientific community and has been applied by the China Earthquake Networks Center, the EarthScope Consortium of the United States, the National Seismological Center of Chile, Institute of Geological and Nuclear Sciences Limited (GNS Science Te Pū Ao) of New Zealand, and the Geospatial Information Agency of Indonesia.

Analysis of GNSS-ZTD retrieval using dual-frequency raw observations

The Global Navigation Satellite System (GNSS) is promising technology for zenith tropospheric delay (ZTD) retrieval. With the emergence of new multi-GNSS frequencies and maturity of precise point positioning ambiguity resolution (PPP-AR) technology, opportunities and challenges have arisen in high-precision GNSS-ZTD retrieval. However, certain strategies have usually been adopted, such as the traditional dual-frequency combination of American global positioning system (GPS) technology, for ZTD retrieval, but the influence of AR on ZTD retrieval has been ignored. To address this issue, in this study, the GNSS-ZTD retrieval performance of all existing dual-frequency combinations was first comprehensively evaluated by raw observations. Then, the influences of AR and system combinations were analysed with popular dual-frequency combinations. Finally, La Niña occurred during the GNSS data period considered in this article, and the effect on GNSS-ZTD retrieval was examined. The results of this study could not only provide a reference for GNSS-ZTD retrieval but also provide insight into the relationship between La Niña occurrence and GNSS-ZTD retrieval performance.

PPP-AR reference satellite selection based on the observation quality factors

Precise point positioning ambiguity resolution (PPP-AR) can effectively improve positioning accuracy and convergence time. In PPP-AR, the double-difference ambiguity between satellite pairs must be fixed. Therefore, it requires the selection of one satellite as a reference to conduct single-difference observations. Usually, the satellite with the highest elevation is selected as the reference satellite, however, once this satellite has a cycle slip or signal interference, its ambiguity will be reinitialized, resulting in the calculated wide-lane and narrow-lane ambiguities are not accurate enough, which further affects all the ambiguities fixed rates and positioning accuracies. In this contribution, we propose a multi-indicators comprehensive evaluation method of the global navigation satellite system (GNSS) based on entropy weight-grey correlation analysis for reference satellite selection of PPP-AR. The comprehensive evaluation includes the observations index selection, the index normalization, the calculation of index entropy weight and the grey correlation analysis. According to the new method, the quality ranking of satellite observations for each epoch can be obtained, and the observation value with the highest ranking is used as the reference satellite during the PPP-AR. One-week observations from 243 multi-GNSS experiment stations are selected to conduct GPS-only, Galileo-only and BDS-3-only kinematic PPP-AR, and the reference satellite selection method using the highest-elevation and the proposed method is applied, respectively. The results show that the PPP performance for the new method can be improved in the positioning accuracies, convergence time and ambiguity fixed rates. The positioning accuracies of three-dimensional directions can be improved by about 5.54%, 8.81% and 6.02% for GPS, BDS-3 and Galileo, respectively. The average improvements of convergence time in the east, north and up directions are 4.67%, 2% and 4% for GPS, BDS-3 and Galileo, respectively. The ambiguity fixed rates are improved by 7.31%, 6.89% and 1.45% for GPS, BDS-3 and Galileo between the 80%-100% range, respectively.

A method to assess the quality of GNSS satellite phase bias products

As part of the International GNSS Service (IGS), several analysis centers provide GPS and Galileo satellite phase bias products to support precise point positioning with ambiguity resolution (PPP-AR). Due to the high correlation with satellite orbits and clock offsets, it is difficult to assess directly the precision of satellite phase bias products. Once outliers exist in satellite phase biases, PPP-AR results are no longer reliable and the combination of satellite phase bias products from IGS analysis centers also gets difficult. In this contribution, we propose a method independent of ground measurements to detect outliers in satellite phase biases by computing the total Difference of satellite Orbits, Clock offsets and narrow-lane Biases at the midnight epoch between two consecutive days. Results over 180 days show that about 0.2, 1.1, 2.0 and 0.1% of the total DOCB values for GPS satellites exceed 0.15 narrow-lane cycles for CODE final, CODE rapid, CNES/CLS final and WUHN rapid satellite products, respectively, while the same outlier-ratios for Galileo satellites are 0.1, 0.9, 0.4 and 0.1%, respectively. As an important contribution to the orbit, clock and bias combination task, we check the consistency of satellite phase bias products between two analysis centers before and after removing these detected outliers from individual analysis centers. It is convincing that the number of large differences of satellite phase biases between two analysis centers is notably reduced.

Estimation of BDS-2/3 phase observable-specific signal bias aided by double-differenced model: an exploration of fast BDS-2/3 real-time PPP

GNSS phase observable-specific signal bias (OSB) corrections are essential for widespread application of precise point positioning with ambiguity resolution (PPP-AR) or PPP-RTK. However, subject to the orbital error effects, conventional undifferenced (UD) model-derived BeiDou System (BDS) real-time (RT) OSB products are usually unsatisfactory. In this study, a novel OSB-generating method assisted by the double-differenced (DD) model is proposed. The reliable integer UD ambiguities are obtained by converting DD ambiguities with given ambiguity datums, by which the RT orbit error effects on ambiguity fixing can be reduced during the OSB extraction and PPP-AR process. Validated using data from two regional sparse GNSS reference networks in Shaanxi, China, and Europe, results show that the proposed method-derived OSB products can improve RT PPP-AR performance effectively. In the Shaanxi network, the narrow-lane ambiguity residuals for BDS-3 within ± 0.25 cycles are improved by 23.1% and 33.2% compared to those using the UD model and Centre National d’Etudes Spatiales (CNES)-derived OSB products, respectively, and the corresponding values are 15.2% and 43.1% in the European network. A centimeter- or even millimeter-level positioning accuracy can be achieved for BDS PPP using the poposed OSB products in both networks. In the kinematic PPP-AR test within the Shanxi network, the mean RMS of the BDS-2/3 fixed solutions in the east, north, and up directions is 0.9, 0.7, and 2.3 cm, with a decrease of 57.1%, 53.3%, and 46.5% compared to that using OSB derived by UD model. The median Time-To-First-Fix (TTFF) is also shortened from 23.8 to 7.5 min.

Performance of kinematic GPS PPP AR under different ionospheric scintillation conditions

To analyze the performance of Global Positioning System (GPS) Precise Point Positioning (PPP) Ambiguity Resolution (AR) under various ionospheric scintillation environments, we selected GPS data of ionospheric scintillation monitoring receivers (ISMR) and geodetic receivers from high-latitude and low-latitude regions during 2021–2023. We conducted GPS Kinematic PPP using Canadian Spatial Reference System (CSRS) PPP and used the maximum and average values of σφ and S4 as indicators to characterize the intensity of phase scintillation and amplitude scintillation for ISMRs, while the maximum and average values of Rate of Total Electron Content Index (ROTI) to characterize the intensity of ionospheric scintillation for geodetic receivers. We also used ambiguity resolved percentage (ARP) and the 3-Dimensional Root Mean Square (3D RMS) of positioning errors as performance metrics for PPP-AR and PPP. As the maximum and average values of ionospheric scintillation indices increase, the PPP-ARP for high-latitude ISMRs decreases to 90.0 %, and the 3D RMS can reach 0.204 m. During ionospheric quiet conditions, positioning accuracy of GPS PPP can reach the cm-mm level. As the geomagnetic latitude decreases, the scintillation effects on PPP-AR and PPP become more pronounced for high-latitude ISMRs. Compared with high-latitudes, ISMRs located at low-latitudes are more severely affected by scintillation, with PPP-ARP at the station HNLW in China and the station UFBA in Brazil dropping to 80.0 % and 60.0 %, respectively. The 3D RMS can reach 0.288 m and 0.341 m. The results of geodetic receives are consistent with those of ISMRs, with 3D RMS of positioning errors up to 0.240 m and 0.256 m for CYNE and MAL2, respectively, while PPP-ARP drops to 60.4 % and 79.6 %. Additionally, we observed a strong positive correlation between ionospheric scintillation duration and the maximum values of σφ, S4 and ROTI.

Uncalibrated phase delay estimation and ambiguity resolution for BDS-3 six-frequency uncombined PPP with legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases.

Precise position determination of USV based on the IF combination and un-combined PPP ambiguity resolution model

Unmanned surface vehicles (USVs) are becoming increasingly important for ocean operations and monitoring, but their precise positioning remains challenging. Real-time kinematic (RTK) technology, commonly used for cm-level positioning in cities, is unsuitable for USVs because it requires nearby reference stations. To address this, we present the uncombined precise point positioning ambiguity resolution (UC PPP-AR) solution, where wide-lane (WL) and narrow-lane (NL) uncalibrated phase bias (UPD) products estimated by the ionosphere-free (IF) PPP model are used. To evaluate the performance of the proposed model, we conducted kinematic USV tests. The results show that the proposed model could shorten the convergence time and achieve cm-level positioning accuracy, with horizontal accuracy better than 2 cm and vertical accuracy better than 5 cm, which is better than that of IF PPP-AR. These results demonstrate the feasibility of the UC PPP-AR technique for USV precise positioning. However, IF PPP-AR may be a better choice if computational consumption time (CCT) is a concern.

Advancing Precise Orbit Determination and Precise Point Positioning of BDS-3 Satellites from B1IB3I to B1CB2a: Comparison and Analysis

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time.

Studying the Fixing Rate of GPS PPP Ambiguity Resolution Under Different Geomagnetic Storm Intensities

AbstractGlobal Positioning System (GPS) Precise Point Positioning (PPP) with correct fixing ambiguity resolution (AR) can reach cm‐mm level positioning accuracy. However, this accuracy can be degraded by the geomagnetic storm effects. To comprehensively investigate the ambiguity resolved percentage (ARP) of GPS kinematic PPP, referred to as PPP‐ARP, under different intensities of geomagnetic storms, based on the Natural Resources Canada's Canadian Spatial Reference System (CSRS) PPP, this study for the first time gives the correlation between the PPP‐ARP and storm intensity using 67 storms occurred in the past 5 years of 2018–2022. Experimental results indicate that the PPP‐ARP decreases gradually as the increase of geomagnetic storm intensity. Under quiet and low geomagnetic conditions (Dstmin > −50 nT), the PPP‐ARP of global GNSS stations can achieve more than 96%, while these during strong storms (Dstmin ≤ −100 nT) are generally lower than 90.0%, especially for the PPP‐ARP of some stations located at low latitudes which are lower than 40.0%. The mechanism of PPP‐ARP decrease under geomagnetic storms is mainly due to the cycle slips and even loss of lock of GNSS signals caused by the storms induced ionospheric disturbances and scintillations. In addition, different from many previous studies, we found that the CSRS‐PPP with AR can achieve good positioning accuracy (3D RMS <0.2 m) even under strong geomagnetic storms.

Research on the performance of the PPP-AR technique under different FCB product services

Researchers and manufacturers use the Precise Point Positioning (PPP) technique. After the phase biases of the satellites are resolved from GNSS networks, they are broadcast to users as Fractional Cycle Bias (FCB). In this study, FCB products provided by WUHAN, CODE, CNES and JAXA services were downloaded and PPP Ambiguity Resolution solutions were realised by Net_Diff software. For ten days in 2022, 24-hour observations were collected from 40 International GNSS Service stations. As a result, it has been observed that WUHAN and CODE services provided the ±1 cm or ±5 cm accuracy level by converging in short-term observations.

Assessing the Performance of Multipath Mitigation for Multi-GNSS Precise Point Positioning Ambiguity Resolution

Real-time GNSS PPP is commonly used for high-precision positioning, but its utility is constrained by factors that necessitate extended convergence periods for a dependable accuracy. Multipath, as an unmodeled error, significantly curtails PPP performance in time-constrained scenarios. Approximately 31 consecutive days of multi-GNSS data from the satellite positioning service of the German national survey (SAPOS) network were collected to evaluate the effectiveness of multipath correction for real-time PPP ambiguity resolution (AR). Using principal component analysis (PCA) to extract the common-mode error (CME) from observation residuals prior to multipath modeling, a multipath hemispherical map (MHM) and sidereal filtering (SF) approach were employed to alleviate the effects of multipath and assess the efficacy of multipath correction in real-time PPP-AR. The average RMS reductions of the carrier-phase and pseudorange residual of multi-GNSS were 25.5% and 20.1% with MHM 0.5, while being 24.4% and 18.3% using SF. With MHM 0.5 correction, the TTFF reductions were approximately 7.0%, 17.7%, 37.5%, and 23.7% for G/GE/GC/GEC kinematic PPP-AR, respectively; and the convergence times for G/GE/GC PPP-AR were reduced to 18.2, 11.7, and 8.6 min, while GEC achieved an average convergence time of 7.1 min; a remarkable improvement compared to the multipath-uncorrected result (18 min). Moreover, 80% of the stations achieved convergence within 10 min, while 40% achieved convergence within 5 min. The kinematic positioning accuracy for the GEC solution improved from 0.97, 0.88, and 2.07 cm, to 0.94, 0.70, and 1.72 cm. In the static results, the TTFF shortened by 30.1%, 19.1%, and 20.1% for G/GE/GC, and the GEC decreased from 10.5 to 9.7 min; the average convergence time for G/GE/GC shortened to 13.0, 10.0, and 11.3 min, and for GEC shortened from 12.5 to 8.3 min. For the GPS-only solution, 78.3% of stations achieved convergence within 15 min. Similarly, for the GE scheme, the convergence time was primarily concentrated within 10 min, and for GC and GEC, with the application of enhanced multipath error correction, some of the stations even achieved convergence of PPP-AR within 5 min. The static positioning accuracy for GEC PPP was 0.50, 0.30, and 0.71 cm for the east, north, and up components.