Precise Point Positioning Convergence Time Research Articles

Improving GNSS PPP Performance in the South China Under Different Weather Conditions by Using the Weather Research and Forecasting (WRF) Model‐Derived Wet Delay Corrections

AbstractAtmospheric wet delay caused by Precipitable Water Vapor (PWV) significantly impacts the performance of many geodetic surveying systems such as Global Navigation Satellite System (GNSS). In this study, we use wet delay corrections forecast by the Weather Research and Forecasting (WRF) model to enhance GNSS Precise Point Positioning (PPP) during two observation periods with two different weather conditions, that is, period 1: March 01 to 14, 2020 (average PWV: 23.5 kg/m2) and period 2: June 02 to 15, 2020 (flooding weather with average PWV: 55.6 kg/m2), over the South China. PWV data from 277 to 263 GNSS stations are assimilated into WRF model to enhance the WRF water vapor forecasting capability for period 1 and period 2, respectively. Wet delay corrections from two different WRF configurations, that is, WRF no data assimilation and WRF with assimilation of GNSS PWV, are used to augment the PPP. Totally, eight WRF‐enhanced PPP schemes are tested. The results show that WRF‐enhanced PPP schemes generally have a better positioning performance in the up component than traditional PPP. After using WRF wet delay corrections, for static mode, the vertical positioning accuracy is improved by 14.6% and 33.7% for period 1 and period 2, respectively. The corresponding convergence time are reduced by 41.8% and 25.0% for period 1 and period 2, respectively. For kinematic mode, the positioning accuracy improvements in the up component reach 13.8% and 19.0% for period 1 and period 2, respectively. The kinematic PPP convergence time is reduced by up to 8.2% for period 1.

Research on the Real-Time Ambiguity Resolution Algorithm of GPS/Galileo/BDS Based on CNES Real-Time Products

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR.

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.

An open-source software package for Precise Point Positioning: raPPPid

Precise Point Positioning (PPP) has proven to be a powerful GNSS positioning method used for various scientific and commercial applications nowadays. We present a flexible and user-friendly software package named raPPPid suitable for processing single to triple-frequency GNSS observations in various PPP approaches (e.g., ionospheric-free linear combination, uncombined model), available under https://github.com/TUW-VieVS/raPPPid. To tune the PPP procedure, the user can select from many satellite products, models, options, and parameters. This way, the software raPPPid can handle high-to-low quality observation data ranging from geodetic equipment to smartphones. Despite significant improvements, the convergence time of PPP is still a major topic in scientific research. raPPPid is specially designed to reduce the convergence period with diverse implemented approaches, such as PPP-AR or ionospheric pseudo-observations, and to offer the user multiple plots and statistics to analyze this critical period. Typically, raPPPid achieves coordinate convergence times of around 1 min or below with high-quality observations and ambiguity fixing. With smartphone data and a simplified PPP approach, a 2D position accuracy at the one-meter level or below is accomplished after two to three minutes.

Accuracy Analysis of Real-Time Precise Point Positioning—Estimated Precipitable Water Vapor under Different Meteorological Conditions: A Case Study in Hong Kong

Precipitable water vapor (PWV) monitoring with real-time precise point positioning (PPP) is required for the improved early detection of increasingly common extreme weather occurrences. This study takes Hong Kong as the research object. The aim is to explore the accuracy of real-time global navigation satellite system (GNSS) PPP in estimating PWV at low latitudes and under different weather conditions. In this paper, real-time PPP is realized by using observation data from continuously operating reference stations (CORS) in Hong Kong and real-time products from the Centre National d’Etudes Spatiales (CNES). The Tm model calculated using numerical weather prediction (NWP) data converts the zenith tropospheric delay (ZTD) of real-time PPP inversion into PWV and evaluates its accuracy using postprocessing products. The experimental results show that compared with GPS, multi-GNSS can reduce the convergence time of PPP by 29.20% during rainfall periods and by 12.06% during nonrainfall periods. The improvement in positioning accuracy is not obvious, and the positioning accuracy of the two is equivalent. Real-time PPP ZTD experiments show that there are lower average values for bias, standard deviation (STDEV), and root mean square (RMS) during nonrainfall periods than during rainfall periods. Real-time PPP PWV experiments show that there are also lower bias, STDEV, and RMS values during nonrainfall periods than during rainfall periods. The comparative study between rainfall and nonrainfall periods is of great significance for the real-time monitoring and forecasting of water vapor changes.

Multi-Frequency BDS-3 Real-Time Positioning Performance Assessment Using New PPP-B2b Augmentation Service

A new precise point positioning (PPP)-B2b augmentation service broadcast by the BeiDou Navigation Satellite System (BDS-3) geosynchronous Earth orbit (GEO) satellite can provide real-time and high-precision orbit and clock offset corrections for global navigation satellite system (GNSS) users in China and its surrounding areas. It has great significance and research value for real-time and high-precision positioning applications. First, orbit, clock offset, and differential code bias (DCB) of PPP-B2b products are evaluated. Second, the influence of PPP-B2b service on the enhanced positioning of single-frequency (SF), dual-frequency (DF), and Multi-Frequency (MF) real-time PPP using 30 days of BDS-3 observations is verified. The result shows that the standard deviation (STD) of clock offset and the root mean square (rms) of orbit in the 3-D direction for medium Earth orbit (MEO) satellites are 0.118 ns and 0.286 m, respectively, which is 75.9% and 18.3% higher than that of broadcast ephemeris. The statistical results show that the median positioning accuracy of static SF PPP, DF PPP, and MF PPP is better than 0.20/0.09/0.08 m, and the convergence time is better than 51/10/8 min. The median positioning accuracy of kinematic SF PPP, DF PPP, and MF PPP is better than 0.40/0.12/0.12 m, and the convergence time is better than 145/16/12 min. Using the PPP-B2b products, the positioning accuracy of DF PPP and MF PPP is comparable and close to that of DF PPP using the precise products, while the convergence time of MF PPP is improved by 24.8% and 27.7% over DF PPP in static and kinematic solutions, respectively.

A Tropospheric Zenith Delay Forecasting Model Based on a Long Short-Term Memory Neural Network and Its Impact on Precise Point Positioning

Global navigation satellite system (GNSS) signals are affected by refraction when traveling through the troposphere, which result in tropospheric delay. Generally, the tropospheric delay is estimated as an unknown parameter in GNSS data processing. With the increasing demand for GNSS real-time applications, high-precision tropospheric delay augmentation information is vital to speed up the convergence of PPP. In this research, we estimate the zenith tropospheric delay (ZTD) from 2018 to 2019 by static precise point positioning (PPP) using the fixed position mode; GNSS observations were obtained from the National Geomatics Center of China (NGCC). Firstly, ZTD outliers were detected, and data gaps were interpolated using the K-nearest neighbor algorithm (KNN). Secondly, The ZTD differences between the KNN and periodic model were employed as input datasets to train the long short-term memory (LSTM) neural network. Finally, LSTM forecasted ZTD differences and the ZTD periodic signals were combined to recover the final forecasted ZTD results. In addition, the forecasted ZTD results were applied in static PPP as a prior constraint to reduce PPP convergence time. Numerical results show that the average root-mean-square error (RMSE) of predicting ZTD is about 1 cm. The convergence time of the PPP which was corrected by the LSTM-ZTD predictions is reduced by 13.9, 22.6, and 30.7% in the summer, autumn, and winter, respectively, over GPT2-ZTD corrected PPP and unconstrained conventional PPP for different seasons.

A Short-Term Forecasting Method of Inter-Frequency Clock Bias for GPS Block IIF Satellites

The time-varying biases within carrier phase observations are integrated into satellite clock offset parameters for precise clock estimation. Consequently, when the precise satellite clock bias is applied to the third frequency observation for precise point positioning (PPP), a new type of inter-frequency clock bias (IFCB) with satellite dependence should be noticed. If the IFCB is estimated together with the receiver coordinates, tropospheric wet delay, ambiguity and other parameters, it will increase the computational burden and lead to more time consumption. In order to solve this problem, the IFCB of GPS Block IIF satellites were estimated using 162 global uniformly distributed Multi-GNSS Experiment (MGEX) stations. By analyzing the time-varying characteristic of each satellite IFCB and combining the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function is proposed. The feasibility of this method was verified through the Student’s t-distribution, comparison with the measured IFCB, the posteriori residual of the third frequency carrier phase and the kinematic/static PPP solutions. The results showed that since the IFCB period was not a complete 24 h, the difference in the IFCBs time series on different days was increasingly significant with the passage of lag time, and the correlation constantly decreased. The peak-to-peak amplitudes of the IFCB difference reached 1.13, 3.44, 6.86 and 11.25 cm when the lag time was 1, 9, 19 and 29 days, respectively. In addition, based on the lag characteristic of final precise ephemerides released by the International GNSS Service (IGS) analysis centers, the prediction accuracy of the IFCB was evaluated with a time lag of 7 days. The root mean square of the posteriori residuals at the third-frequency observation decreased by approximately 51.3% compared to that without considering for IFCB correction. The triple-frequency uncombined PPP in the horizontal and vertical directions improved by approximately 33.2% and 17.2% for the static PPP solutions and 50.2% and 39.7% for the kinematic PPP solutions, respectively. In general, the accuracy and convergence time of the triple-frequency uncombined PPP were equivalently improved when the predicted IFCB and the measured IFCB were used.

Neural network-based ionospheric modeling and predicting—To enhance high accuracy GNSS positioning and navigation

As a highly variable space plasma, the sophisticated monitoring and expression of the ionosphere are critically important for the performance of Global Navigation Satellite System (GNSS). To satisfy the requirement of more precise positioning and navigation, it is necessary to model and predict the ionosphere in a more accurate way. In this paper, the potential advantages of neural networks in ionosphere modeling and predicting are explored. Radial Basis Function Neural Network (RBF-NN) is used for modeling and the Long- and Short-Term Memory Neural Network (LSTM-NN) is used for predicting. Results validate that performance of the RBF-NN is superior to the traditional spherical harmonic and polynomial model. The average root mean square error of one-day modeling residuals by RBF-NN is 1.2951 Total Electron Content Unit (TECU, 1 TECU = 1016 electron/m2), which is reduced by 0.4172 and 0.2710 TECU respectively, compared with the traditional spherical harmonic and polynomial model. The predicting results show that the LSTM-NN has better short-time performance, compared with the finite Fourier series model and the autoregressive integrated moving average model. Finally, one-day predicted products are used as priori constraints for single-frequency static and dynamic precise point positioning (PPP). Positioning results show that constraint effect of the predicted products is equivalent to that of the International GNSS Services (IGS) final products. Compared with the results without ionospheric constraint, the PPP convergence time is obviously reduced, and the positioning performance in the horizontal direction is significantly improved.

Performance Analysis of BDS–5G Combined Precise Point Positioning

Precise point positioning (PPP) technology is one of the core technologies in the field of GNSS high-precision positioning. It is used widely because it can realize centimeter-level positioning in outdoor environments by using only a single receiver. However, its convergence is time-consuming, particularly in urban areas where satellite occlusion is more severe. A combined BeiDou Navigation Satellite System (BDS) and fifth generation mobile communication technology (5G) PPP observation model is proposed, in which the two kinds of observations are combined and solved at the original observation level. The impact of different numbers and geometries of 5G base stations on the convergence time of PPP is analyzed from both static and dynamic perspectives. The results confirm that PPP technology combining BDS and 5G can effectively accelerate convergence while improving the accuracy of positioning.

Design optimisation of low earth orbit constellation based on BeiDou Satellite Navigation System precise point positioning

The use of low earth orbit (LEO) satellites to enhance the performance of global navigation satellite system navigation and positioning services has become a popular research topic. In this study, NSGA-III optimisation algorithm was used to design two hybrid configurations of 177 and 186 LEO constellations for enhancing the BeiDou Satellite Navigation System (BDS). Under the enhanced effect of optimisation constellation, the global average geometric dilution of precision (GDOP) of BDS was reduced to 0.8 ± 0.1, and the maximum GDOP was reduced from 2.4 to less than 1.1 (54.2% reduction). In order to verify the contribution of the two constellations to the convergence time and positioning accuracy of BDS precise point positioning (PPP), a LEO enhanced BDS PPP simulation experiment was carried out using International GNSS Service data from five stations. The results show that after 10 min of static positioning, both LEO constellations improved the positioning accuracy of BDS from the decimetre level to less than 5 cm. The maximum improvement for 177 and 186 LEO was 95.0% and 96.9%, respectively. Additionally, the convergence time for 177 and 186 LEO reduced to less than 3.5 and 3 min, and the maximum improvement was 93.5% and 95.2%, respectively. Overall, both constellations can improve the positioning accuracy and convergence time of BDS PPP.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

The performance of precise point positioning (PPP) has been significantly improved thanks to the continuous improvements in satellite orbit, clock, and ambiguity resolution (AR) technologies, but the convergence speed remains a limiting factor in real-time PPP applications. To improve the PPP precision and convergence time, tropospheric delays from a regional network can be modeled to provide precise correction for users. We focus on the precise modeling of zenith wet delay (ZWD) over a wide area with large altitude variations for improving PPP-AR. By exploiting the water vapor exponential vertical decrease, we develop a modified optimal fitting coefficients (MOFC) model based on the traditional optimal fitting coefficients (OFC) model. The proposed MOFC model provides a precision better than 1.5 cm under sparse inter-station distances over the Europe region, with a significant improvement of 70% for high-altitude stations compared to the OFC model. The MOFC model with different densities of reference stations is further evaluated in GPS and Galileo kinematic PPP-AR solutions. Compared to the PPP-AR solutions without tropospheric delay augmentation, the positioning precision of those with 100-km inter-station spacing MOFC and OFC is improved by 25.7% and 17.8%, respectively, and the corresponding time to first fix (TTFF) is improved by 36.9% and 33.0% in the high-altitude areas. On the other hand, the OFC model only slightly improves the TTFF and positioning accuracy when using the 200 km inter-station spacing modeling and even degrades the positioning for high-altitude stations, whereas using the MOFC model, the PPP-AR solutions always improve. Moreover, the positioning precision improvement of MOFC compared with OFC is about 22.1%, 21.7%, and 25.7% for the Galileo-only, GPS-only, and GPS + Galileo PPP-AR solutions, respectively.

On Enhanced PPP with Single Difference Between-Satellite Ionospheric Constraints

<h3>Abstract</h3> Applications of precise point positioning (PPP) are limited by PPP’s long convergence time. One effective way to shorten the convergence time is to apply ionospheric constraints because of the external ionospheric information. The conventional way to do this is to apply high precision but biased ionospheric corrections. The limitations of the method are that all ionospheric constraints must be derived from the same set of reference stations to have the same data. An approach based on single differences between satellite ionospheric constraints (SDBS-IONO) is developed to address the data issue due to having no common satellite visibility. The proposed method is more flexible and scalable in terms of adding ionospheric constraints. Based on a network of about 130 stations, we validated the proposed SDBS-ION method and compared it to the conventional method. Our results confirm that the ionospheric constraints enhance the PPP convergence time significantly depending on the accuracy of ionospheric constraints. Finally, we discuss crucial factors regarding how long and accurate the effectiveness of ionospheric constraints are in reducing PPP convergence time.

Comparison Analysis on the Accuracy of Galileo PPP Using Different Frequency Combinations in Europe

The Galileo constellations are characterized by transmitting GNSS signals on multi-frequencies, which can benefit the robustness and accuracy of the solutions. However, the dual-frequency E1/E5a combinations are generally used for precise point positioning (PPP). In this paper, the performance of Galileo static and kinematic PPP using different dual- and multi-frequency combinations are assessed using observations from the European region. Overall, the accuracy of daily PPP achieved by the dual-frequency GPS, Galileo, and BDS is better than 5 mm in the horizontal direction and better than 10 mm in the vertical direction. Though the number of observed Galileo satellites is less than GPS, the horizontal accuracy can reach 1.6 mm/2.3 mm/5.7 mm on North/East/Up component, which is improved by 59.0% and 12.3% compared to the GPS in the north and up direction. Then, the accuracy of Galileo static PPP is analyzed using different dual- and multi-frequency combinations. Results indicate that the Galileo E1/E5b PPP can degrade the accuracy due to the inter-frequency clock biases between the E1/E5a and E1/E5b combinations. Best accuracy can be achieved for the triple- and four-frequency PPP, which is 4.8 mm in the up direction. The hourly accuracy for the static PPP can reach 5.6 mm/9.2 mm/12.6 mm in the north/east/up direction using the GPS/Galileo/GLONASS/BDS combinations. Finally, a positioning convergence ratio (PCR) indicator, which represents the accuracy of PPP over a period, is used to analyze the convergence time of kinematic PPP. Results indicated that the multi-frequency Galileo observations contribute minorly to the convergence of kinematic PPP. However, Galileo shows the best convergence performance for the single GNSS positioning, and the GPS/Galileo combined PPP achieved the best performance for the PPP using different GNSS combinations.

LEO Enhanced Global Navigation Satellite System (LeGNSS): progress, opportunities, and challenges

ABSTRACT With the completion of Chinese BeiDou Navigation Satellite System (BDS), the world has begun to enjoy the Positioning, Navigation, and Timing (PNT) services of four Global Navigation Satellite Systems (GNSS). In order to improve the GNSS performance and expand its applications, Low Earth Orbit (LEO) Enhanced Global Navigation Satellite System (LeGNSS) is being vigorously advocated. Combined with high-, medium-, and low- earth orbit satellites, it can improve GNSS performance in terms of orbit determination, Precise Point Positioning (PPP) convergence time, etc. This paper comprehensively reviews the current status of LeGNSS, focusing on analyzing its advantages and challenges for precise orbit and clock determination, PPP convergence, earth rotation parameter estimation, and global ionosphere modeling. Thanks to the fast geometric change brought by LEO satellites, LeGNSS is expected to fundamentally solve the problem of the long convergence time of PPP without any augmentation. The convergence time can be shortened within 1 minute if appropriate LEO constellations are deployed. However, there are still some issues to overcome, such as the optimization of LEO constellation as well as the real time LEO precise orbit and clock determination.

Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model

Precise Point Positioning (PPP), as a global precise positioning technique, suffers from relatively long convergence times, hindering its ability to be the default precise positioning technique. Reducing the PPP convergence time is a must to reach global precise positions, and doing so in a few minutes to seconds can be achieved thanks to the additional frequencies that are being broadcast by the modernized GNSS constellations. Due to discrepancies in the number of signals broadcast by each satellite/constellation, it is necessary to have a model that can process a mix of signals, depending on availability, and perform ambiguity resolution (AR), a technique that proved necessary for rapid convergence. This manuscript does so by expanding the uncombined Decoupled Clock Model to process and fix ambiguities on up to three frequencies depending on availability for GPS, Galileo, and BeiDou. GLONASS is included as well, without carrier-phase ambiguity fixing. Results show the possibility of consistent quasi-instantaneous global precise positioning through an assessment of the algorithm on a network of global stations, as the 67th percentile solution converges below 10 cm horizontal error within 2 min, compared to 8 min with a triple-frequency solution, showing the importance of having a flexible PPP-AR model frequency-wise. In terms of individual datasets, 14% of datasets converge instantaneously when mixing dual- and triple-frequency measurements, compared to just 0.1% in that of dual-frequency mode without ambiguity resolution. Two kinematic car datasets were also processed, and it was shown that instantaneous centimetre-level positioning with a moving receiver is possible. These results are promising as they only rely on ultra-rapid global satellite products, allowing for instantaneous real-time precise positioning without the need for any local infrastructure or prior knowledge of the receiver’s environment.

Analyzing the contributions of multi-GNSS and INS to the PPP-AR outage re-fixing

GNSS observation outage occurs inevitably in various situations, e.g., automobile driving in urban environments. Although the ambiguity resolution (AR) significantly shortens the initialization time of precise point positioning (PPP), frequent re-initialization of PPP AR may be needed due to outages. The inertial navigation system (INS) can be used for acquiring highly accurate position information during GNSS outages. In the previous studies, the GPS PPP/INS with the ambiguity resolution model is proposed, and the experimental results confirm that the INS could facilitate the re-fixing of the interrupted GNSS ambiguity. Multiple GNSS can also be used to shorten the PPP convergence time. We compare the contribution of multi-GNSS and the INS to the ambiguity re-fixing during GNSS outage. Results show that the multi-GNSS, e.g., Galileo, GLONASS and BDS, without ambiguity resolution has little contribution to the re-fixing of GPS ambiguity in PPP/INS, while INS can provide highly accurate positioning results during the GNSS outages. The higher the accuracy of the predicted INS positioning, the lower the contribution of multi-GNSS to the re-fixing of the ambiguity in the PPP/INS. The finding is verified by a theoretical analysis, carborne experiment and shipborne experiment. Experiment results show that the re-fixing time is 43 s for GPS PPP and MEMS-grade INS coupled system in GNSS outage of 1 s. The re-fixing time of GPS is slightly changed when adding the multi-GNSS, e.g., Galileo, GLONASS and BDS, without the ambiguity resolution. However, by performing ambiguity resolution to the added GNSS system, the re-fixing time of PPP/INS is significantly reduced from 43 to 4 s. The reason is that, although the multi-GNSS provides little improvement on the accuracy of the ambiguity, it enlarges the number of the ambiguity parameter. The possibility of ambiguity resolution is increased due to the large candidate set of the ambiguity, which reduces re-fixing time.

Assessment and Analysis of the Four-Satellite QZSS Precise Point Positioning and the Integrated Data Processing With GPS

The Quasi-Zenith Satellite System (QZSS), which serves Japan and its surrounding areas, is a regional navigation satellite system developed by Japan Aerospace Exploration Agency. The system is now in a four-satellite constellation with preliminary standalone navigation and positioning capabilities. In this paper, the performance of QZSS-only precise point positioning (PPP) in both static and kinematic modes is initially evaluated using the datasets spanning 11 days from 11 tracking stations in Asia-Pacific regions and the final precise orbit and clock products from the analysis centers GFZ and WUM. For completeness, the GPS/QZSS integrated data processing with GFZ and WUM final products as well as the L6E real-time orbit and clock corrections is also analyzed. The results indicate that the static positioning accuracy of QZSS-only PPP is approximately 4, 2 and 15 cm in the east, north and up directions, respectively, and the static convergence time of QZSS-only PPP with WUM and GFZ products can be 75.2, 44.3 and 45.6 min, and 153.5, 201.6 and 162.8 min in the three directions, respectively. As for the QZSS-only kinematic PPP solutions, the re-convergence repeatedly occurs due to limited available satellites. To achieve more reliable solutions, the inter-system bias parameter in GPS/QZSS PPP processing is recommended to be estimated as random walk process or white noise process. The improvement of post-processed GPS/QZSS PPP over GPS-only case is marginal on position accuracies, but can be several minutes on convergence time. Compared with post-processed GPS/QZSS PPP, the real-time one achieves worse position accuracies but comparable convergence time.

The Effect of BDS-3 Time Group Delay and Differential Code Bias Corrections on Positioning

The timing group delay parameter (TGD) or differential code bias parameter (DCB) is an important factor that affects the performance of GNSS basic services; therefore, TGD and DCB must be taken seriously. Moreover, the TGD parameter is modulated in the navigation message, taking into account the impact of TGD on the performance of the basic service. International GNSS Monitoring and Assessment System (iGMAS) provides the broadcast ephemeris with TGD parameter and the Chinese Academy of Science (CAS) provides DCB products. In this paper, the current available BDS-3 TGD and DCB parameters are firstly described in detail, and the relationship of TGD and DCB for BDS-3 is figured out. Then, correction models of BDS-3 TGD and DCB in standard point positioning (SPP) or precise point positioning (PPP) are given, which can be applied in various situations. For the effects of TGD and DCB in the SPP and PPP solution processes, all the signals from BDS-3 were researched, and the validity of TGD and DCB has been further verified. The experimental results show that the accuracy of B1I, B1C and B2a single-frequency SPP with TGD or DCB correction was improved by approximately 12–60%. TGD will not be considered for B3I single-frequency, because the broadcast satellite clock offset is based on the B3I as the reference signal. The positioning accuracy of B1I/B3I and B1C/B2a dual-frequency SPP showed that the improvement range for horizontal components is 60.2% to 74.4%, and the vertical components improved by about 50% after the modification of TGD and DCB. In addition, most of the uncorrected code biases are mostly absorbed into the receiver clock bias and other parameters for PPP, resulting in longer convergence time. The convergence time can be max increased by up to 50% when the DCB parameters are corrected. Consequently, the positioning accuracy can reach the centimeter level after convergence, but it is critical for PPP convergence time and receiver clock bias that the TGD and DCB correction be considered seriously.

Performance evaluation of GIMs released by different IGS ionosphere associate analysis centers in ionospheric constrained single-frequency precise point positioning

Single-frequency precise point positioning (PPP) is widely used with the advantage of cost-efficient, while its further development and application are limited by the difficulty of ionospheric delay correction and the long-time convergence, especially for real-time positioning. And the development of high-accuracy ionospheric models plays an important role for the correction of ionospheric delay in single-frequency PPP. In this paper, the final and rapid global ionospheric map (GIM) products released by Chinese Academy of Science (CAS), Center for Orbit Determination in Europe (CODE), European Space Agency (ESA), Jet Propulsion Laboratory (JPL), Universitat Politècnica de Catalunya (UPC), Wuhan University (WHU) and International GNSS Service (IGS) were used as external constraints in static, simulation kinematic and kinematic single-frequency PPP respectively. The performance and practicality of each product were analyzed by using IGS station observation data (September 2017 and January 2018, with different ionospheric activity levels) and a kinematic experiment. The results indicate that GIM products may improve convergence time in most areas of middle and high latitudes of the globe. However, the improvement of convergence time of some regions in low latitudes or near the equator with dense and uniform distributed IGS stations show even better performance than the regions in middle and high latitudes. Comparing with standard PPP (S-PPP), the convergence time of static PPP is reduced about 14–42% and 13–29% with GIM final and rapid products respectively. In simulation kinematic PPP, the convergence time improves 10–43% and 12–25% for final and rapid products respectively. In the kinematic positioning, the addition of external ionospheric constraints may speed up the convergence in the early stage of positioning and improve the accuracy to a certain extent. Among all GIM products, the final products show better performance than that of the rapid products obviously. The GIM products from CAS and CODE and UQRG from UPC express the best performance are recommended to process ionospheric delay in the high-accuracy positioning.