Shengfeng Gu

Rapid PPP ambiguity resolution using GPS+GLONASS observations

Integer ambiguity resolution (IAR) in precise point positioning (PPP) using GPS observations has been well studied. The main challenge remaining is that the first ambiguity fixing takes about 30 min. This paper presents improvements made using GPS+GLONASS observations, especially improvements in the initial fixing time and correct fixing rate compared with GPS-only solutions. As a result of the frequency division multiple access strategy of GLONASS, there are two obstacles to GLONASS PPP-IAR: first and most importantly, there is distinct code inter-frequency bias (IFB) between satellites, and second, simultaneously observed satellites have different wavelengths. To overcome the problem resulting from GLONASS code IFB, we used a network of homogeneous receivers for GLONASS wide-lane fractional cycle bias (FCB) estimation and wide-lane ambiguity resolution. The integer satellite clock of the GPS and GLONASS was then estimated with the wide-lane FCB products. The effect of the different wavelengths on FCB estimation and PPP-IAR is discussed in detail. We used a 21-day data set of 67 stations, where data from 26 stations were processed to generate satellite wide-lane FCBs and integer clocks and the other 41 stations were selected as users to perform PPP-IAR. We found that GLONASS FCB estimates are qualitatively similar to GPS FCB estimates. Generally, 98.8% of a posteriori residuals of wide-lane ambiguities are within

National BDS Augmentation Service System (NBASS) of China: Progress and Assessment

\pm 0.25

The Impact of Non-nominal Yaw Attitudes of GPS Satellites on Kinematic PPP Solutions and their Mitigation Strategies

±0.25 cycles for GPS, and 96.6% for GLONASS. Meanwhile, 94.5 and 94.4% of narrow-lane residuals are within 0.1 cycles for GPS and GLONASS, respectively. For a critical value of 2.0, the correct fixing rate for kinematic PPP is only 75.2% for GPS alone and as large as 98.8% for GPS+GLONASS. The fixing percentage for GPS alone is only 11.70 and 46.80% within 5 and 10 min, respectively, and improves to 73.71 and 95.83% when adding GLONASS. Adding GLONASS thus improves the fixing percentage significantly for a short time span. We also used global ionosphere maps (GIMs) to assist the wide-lane carrier-phase combination to directly fix the wide-lane ambiguity. Employing this method, the effect of the code IFB is eliminated and numerical results show that GLONASS FCB estimation can be performed across heterogeneous receivers. However, because of the relatively low accuracy of GIMs, the fixing percentage of GIM-aided GPS+GLONASS PPP ambiguity resolution is very low. We expect better GIM accuracy to enable rapid GPS+GLONASS PPP-IAR with heterogeneous receivers.

Assessing the Performance of GPS Precise Point Positioning Under Different Geomagnetic Storm Conditions during Solar Cycle 24

Modernized GPS and GLONASS, together with new GNSS systems, BeiDou and Galileo, offer code and phase ranging signals in three or more carriers. Traditionally, dual-frequency code and/or phase GPS measurements are linearly combined to eliminate effects of ionosphere delays in various positioning and analysis. This typical treatment method has imitations in processing signals at three or more frequencies from more than one system and can be hardly adapted itself to cope with the booming of various receivers with a broad variety of singles. In this contribution, a generalized-positioning model that the navigation system independent and the carrier number unrelated is promoted, which is suitable for both single- and multi-sites data processing. For the synchronization of different signals, uncalibrated signal delays (USD) are more generally defined to compensate the signal specific offsets in code and phase signals respectively. In addition, the ionospheric delays are included in the parameterization with an elaborate consideration. Based on the analysis of the algebraic structures, this generalized-positioning model is further refined with a set of proper constrains to regularize the datum deficiency of the observation equation system. With this new model, uncalibrated signal delays (USD) and ionospheric delays are derived for both GPS and BeiDou with a large dada set. Numerical results demonstrate that, with a limited number of stations, the uncalibrated code delays (UCD) are determinate to a precision of about 0.1 ns for GPS and 0.4 ns for BeiDou signals, while the uncalibrated phase delays (UPD) for L1 and L2 are generated with 37 stations evenly distributed in China for GPS with a consistency of about 0.3 cycle. Extra experiments concerning the performance of this novel model in point positioning with mixed-frequencies of mixed-constellations is analyzed, in which the USD parameters are fixed with our generated values. The results are evaluated in terms of both positioning accuracy and convergence time.

An improved ionosphere interpolation algorithm for network RTK in low-latitude regions

Abstract: In this contribution, the processing strategies of real-time BeiDou System (BDS) precise orbits, clocks, and ionospheric corrections in the National BDS Augmentation Service System (NBASS) are briefly introduced. The Root Mean Square (RMS) of BDS predicted orbits are better than 10 cm in radial and cross-track components, and the accuracy of the BDS real-time clock is better than 0.5 ns for Inclined Geosynchronous Orbit (IGSO) and Mid Earth Orbit (MEO) satellites. The accuracy of BDS Geostationary Earth Orbit (GEO) orbits and clocks are worse than the IGSO and MEO satellites due to its poor geometry conditions. The real-time ionospheric correction is evaluated by cross-validation, and the average accuracy in the vertical direction is about 4 TECU. With these real-time corrections, the overall single and dual-frequency kinematic precise point positioning (PPP) performance in China are evaluated in terms of positioning accuracy at the 95% confidence level and convergence time. The BDS PPP positioning accuracy shows significant regional characteristics due to the geometry distribution of BDS satellites and the accuracy of ionospheric model in different regions. The BDS dual-frequency PPP positioning accuracy in high-latitude and western fringe region is about 0.5 m and 1.0 m in the horizontal and vertical component, respectively, while the horizontal accuracy is better than 0.2 m and the vertical accuracy is better than 0.3 m in the midlands. The convergence time of the BDS PPP is much longer than the GPS PPP and it needs more than 60 min to achieve the accuracy better than 10 cm in both horizontal and vertical directions for dual-frequency PPP. Similar with dual-frequency PPP, the positioning accuracy of the BDS single-frequency PPP in the fringe region is worse than other regions. The positioning in the midlands can achieve 0.5 m in horizontal component and 1.0 m in the vertical component. In addition, when GPS and BDS are combined, the positioning performance of both single-frequency and dual-frequency PPP can be greatly improved.

Analysis of regionally enhanced GPS orbit and clock solutions and contribution to improvement of real-time precise point positioning

During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.

Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models

The yaw attitudes of Global Positioning System (GPS) satellites are critical to both satellite antenna phase centres and the phase wind-up corrections. However, the nominal yaw attitude of GPS satellites can barely be maintained during eclipse seasons. Thus, several yaw attitude models have been developed by the International GNSS Service Analysis Centres (IGS ACs) to avoid positioning degradation caused by non-nominal yaw attitudes. Based on the analysis of the strategy of each AC, the modelled yaw attitude is compared with the nominal one, and the residuals of Precise Point Positioning (PPP) are investigated to evaluate the influence of non-nominal attitudes with over one year of observable data collected from 15 IGS stations. The results suggest that non-nominal attitudes of BLOCK II/IIA satellites have the largest impact of about 20–30 cm, and their positioning accuracy can be improved by 20%−30% with the corresponding yaw attitude model. Similar results have also been demonstrated with BLOCK IIR and BLOCK IIF satellites. Furthermore, compared with the strategy of directly deleting the data for the eclipsing seasons, PPP with the yaw-attitude model achieves better results by about 30% when the satellite geometry is relatively poor.

An improved approach to model ionospheric delays for single-frequency Precise Point Positioning

The geomagnetic storm, which is an abnormal space weather phenomenon, can sometimes severely affect GPS signal propagation, thereby impacting the performance of GPS precise point positioning (PPP). However, the investigation of GPS PPP accuracy over the global scale under different geomagnetic storm conditions is very limited. This paper for the first time presents the performance of GPS dual-frequency (DF) and single-frequency (SF) PPP under moderate, intense, and super storms conditions during solar cycle 24 using a large data set collected from about 500 international GNSS services (IGS) stations. The global root mean square (RMS) maps of GPS PPP results show that stations with degraded performance are mainly distributed at high-latitude, and the degradation level generally depends on the storm intensity. The three-dimensional (3D) RMS of GPS DF PPP for high-latitude during moderate, intense, and super storms are 0.393 m, 0.680 m and 1.051 m, respectively, with respect to only 0.163 m on quiet day. RMS errors of mid- and low-latitudes show less dependence on the storm intensities, with values less than 0.320 m, compared to 0.153 m on quiet day. Compared with DF PPP, the performance of GPS SF PPP is inferior regardless of quiet or disturbed conditions. The degraded performance of GPS positioning during geomagnetic storms is attributed to the increased ionospheric disturbances, which have been confirmed by our global rate of TEC index (ROTI) maps. Ionospheric disturbances not only lead to the deteriorated ionospheric correction but also to the frequent cycle-slip occurrence. Statistical results show that, compared with that on quiet day, the increased cycle-slip occurrence are 13.04%, 56.52%, and 69.57% under moderate, intense, and super storms conditions, respectively.