Static Precise Point Positioning Research Articles

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.

Analyses of GLONASS and GPS+GLONASS Precise Positioning Performance in Different Latitude Regions

The orbital inclination angle of the GLONASS constellation is about 10° larger than that of GPS, Galileo, and BDS. Theoretically, the higher orbital inclination angle could provide better observation geometry in high latitude regions. A wealth of research has investigated the positioning accuracy of GLONASS and its impact on multi-GNSS, but rarely considered the contribution of the GLONASS constellation’s large orbit inclination angle. The performance of GLONASS in different latitude regions is evaluated in both stand-alone mode and integration with GPS in this paper. The performance of GPS is also presented for comparison. Three international GNSS service (IGS) networks located in high, middle, and low latitudes are selected for the current study. Multi-GNSS data between January 2021 and June 2021 are used for the assessment. The data quality check shows that the GLONASS data integrity is significantly lower than that of GPS. The constellation visibility analysis indicates that GLONASS has a much better elevation distribution than GPS in high latitude regions. Both daily double-difference network solutions and daily static Precise Point Positioning (PPP) solutions are evaluated. The statistical analysis of coordinate estimates indicates that, in high latitude regions, GLONASS has a comparable or even better accuracy than that of GPS, and GPS+GLONASS presents the best estimate accuracy; in middle latitude regions, GPS stand-alone constellation provides the best positioning accuracy; in low latitude regions, GLONASS offers the worst accuracy, but the positioning accuracy of GPS+GLONASS is better than that of GPS. The tropospheric estimates of GLONASS do not present a resemblance regional advantage as coordinate estimates, which is worse than that of GPS in all three networks. The PPP processing with combined GPS and GLONASS observations reduces the convergence time and improves the accuracy of tropospheric estimates in all three networks.

Modelling and Assessment of a New Triple-Frequency IF1213 PPP with BDS/GPS

The currently available triple-frequency signals give rise to new prospects for precise point positioning (PPP). However, they also bring new bias, such as time-varying parts of the phase bias in the hardware of receivers and satellites due to the fact that dual-frequency precise clock products cannot be directly applied to triple-frequency observation. These parameters generate phase-based inter-frequency clock bias (PIFCB), which impacts the PPP. However, the PIFCBs of satellites are not present in all GNSSs. In this paper, various IF1213 PPP models are constructed for these parts, namely, the triple-frequency PIFCB (TF-C) model with PIFCB estimation, the TF inter-frequency bias (IFB) (TF-F) model ignoring the PIFCB, and the TF-PIFCB-IFB (TF-CF) model with one system PIFCB estimation. Additionally, this study compares these IF1213 PPP models with the dual-frequency ionosphere-free (DF) model. We conducted single system static PPP, dual-system static and kinematic PPP experiments based on BDS/GPS observation data. The GPS static PPP experiment demonstrates the reliability of the TF-C model, as well as the non-negligibility of the GPS PIFCB. The BDS static PPP experiment demonstrates the reliability of the TF-F and TF-CF models, and that the influence of the BDS-2 PIFCB can be neglected in BDS. The BDS/GPS PPP experimental results show that the third frequency does not significantly improve the positioning accuracy but shortens the convergence time. The positioning accuracy of TF-C and TF-CF for static PPP is better than 1.0 cm, while that for kinematic PPP is better than 2.0 cm and 4.0 cm in the horizontal and vertical components, respectively. Compared with the DF model, the convergence time of the TF-C and TF-CF models for static PPP is improved by approximately 23.5%/18.1%, 13.6%/9.7%, and 19.8%/12.1%, while that for kinematic PPP is improved by approximately 46.2%/49.6%, 33.5%/32.4%, and 35.1%/36.1% in the E, N and U directions, respectively. For dual-system PPP based on BDS/GPS observations, the TF-C model is recommended.

BDS-3/GPS/Galileo OSB Estimation and PPP-AR Positioning Analysis of Different Positioning Models

With the completion of the BeiDou Global Navigation Satellite System (BDS-3), the multi-system precise point positioning ambiguity resolution (PPP-AR) has been realized. The satellite phase fractional cycle bias (FCB) is a key to the PPP-AR. Compared to the combined ionosphere-free (IF) model, the undifferenced and uncombined (UDUC) model retains all the information from the observations and can be easily extended to arbitrary frequencies. However, the FCB is difficult to apply directly to the UDUC model. An observable-specific signal bias (OSB) can interact directly with the original observations, providing complete flexibility for PPP-AR for multi-frequency multi-GNSS. In this study, the OSB product generation for the GPS (G), Galileo (E), and BDS-3 (C) systems is performed using 117 globally distributed multi-GNSS experiment (MGEX) stations, and their performances are evaluated. Then, the PPP-AR comparison and analysis of the two positioning models of the UDUC and IF are conducted. The results show that the stability of OSB products of the three systems is better than 0.05 ns. For the precise point positioning (PPP) ambiguity fixed solution, with comparable positioning accuracy and convergence time to the products of both the Wuhan University (WUM) and the Centre National d’Etudes Spatials (CNES) institutions, an average fixed-ambiguity rate is over 90%. Compared to the PPP float solution, the PPP-AR has the most significant improvement in positioning accuracy in the E-direction. The average improvements in the positioning accuracy under the IF and UDUC models in the static and kinematic modes are higher than 45% and 40%, respectively. The convergence times of the IF and UDUC models are improved on average by 48% and 60% in the static mode and by 40% and 55% in the kinematic mode, respectively. Among the IF and UDUC positioning models, the former has slightly better positioning accuracy and convergence time than the latter for the PPP float solution. However, both models have comparable positioning accuracy and convergence time after the PPP-AR. The GCE multi-system combination is superior to other system combinations. The average convergence time for the static PPP fixed solution is 8.5 min, and the average convergence time for the kinematic PPP fixed solution is 16.4 min.

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.

Performance of Multi-GNSS in the Asia-Pacific Region: Signal Quality, Broadcast Ephemeris and Precise Point Positioning (PPP)

Since BeiDou Navigation Satellite System (BDS) and Japan’s Quasi-Zenith Satellite System (QZSS) have more visible satellites in the Asia-Pacific region, and navigation satellites of Global Positioning System (GPS), Galileo satellite navigation system (Galileo), and GLONASS satellite navigation system (GLONASS) are uniformly distributed globally, the service level of multi-mode Global Navigation Satellite System (GNSS) in the Asia-Pacific region should represent the best service capability. Based on the observation data of 10 Multi-GNSS Experiment (MGEX) stations, broadcast ephemeris and precision ephemeris from 13 to 19 October 2021, this paper comprehensively evaluated the service capability of multi-GNSS in the Asia-Pacific region from three aspects of observation data quality, broadcast ephemeris performance, and precision positioning level. The results show that: (1) the carrier-to-noise-density ratio (C/N0) quality of the GPS and Galileo is the best, followed by BDS and GLONASS, and QZSS is the worst. GPS, BDS-2, GLONASS, and QZSS pseudorange multipath values range from 0 to 0.6 m, while Galileo system and BDS-3 pseudorange multipath values range from 0 to 0.8 m. (2) In terms of broadcast ephemeris accuracy, BDS-3 broadcast ephemeris has the best orbit, and the three-dimensional (3D) Root Mean Square (RMS) is 0.21 m; BDS-2 was the worst, with a 3D RMS of 1.99 m. The broadcast ephemeris orbits of GPS, Galileo, QZSS, and GLONASS have 3D RMS of 0.60 m, 0.62 m, 0.83 m, and 1.27 m, respectively. For broadcast ephemeris clock offset: Galileo has the best performance, 0.61 ns, GLONASS is the worst, standard deviation (STD) is 3.10 ns, GPS, QZSS, BDS-3 and BDS-2 are 0.65 ns, 0.75 ns, and 1.72 ns, respectively. For signal-in-space ranging errors (SISRE), the SISRE results of GPS and Galileo systems are the best, fluctuating in the range of 0 m–2 m, followed by QZSS, BDS-3, Galileo, and BDS-2. (3) GPS, BDS, GLONASS, Galileo, GPS/QZSS, and BDS/QZSS were used for positioning experiments. In static PPP, the convergence time and positioning accuracy of GPS show the best performance. The positioning accuracy of GPS/QZSS and BDS/QZSS is improved compared with that of GPS and BDS. In terms of kinematic PPP, the convergence time and positioning accuracy of GPS/QZSS and BDS/QZSS are improved compared with that of GPS and BDS. In addition to GLONASS and Galileo systems, the other combinations outperformed 3 cm, 3 cm, and 5 cm in the east, north, and up directions.

Performance analysis of familiar elevation-dependent stochastic models with error variance compensation and posteriori unit weight in GPS/BDS precise point positioning

With global networking of BeiDou Navigation Satellite System (BDS) in July 2020, multi-constellation Precise Point Positioning (PPP) with Global Positioning System (GPS) and BDS has become a more accurate global positioning technique. In multi-constellation PPP, a suitable stochastic model can accurately describe observation noises of different satellites to help estimate accurate positioning parameters. To balance the unit weight between GPS and BDS, the posteriori unit weight is adopted between GPS and BDS constellation by using least-squares variance component estimator (LS-VCE). Under the error variance compensation and posteriori unit weight, the positioning performances of stochastic models using four familiar elevation-dependent functions are compared in terms of obtaining small positioning error and convergence with the GPS and BDS constellations. The positioning experiments were conducted to verify the positioning performances of different elevation dependent stochastic models in multi-constellation PPP with GPS and BDS at 55 stations over an 8 day period. The results show that all stochastic models have the similar positioning accuracy and precision, the differences are sub-millimeter level. But compared with second-best stochastic models, the mean convergence time reduces by more than 4.2% and the convergence stability increases by more than 10.0% in the stochastic model using the exponential function. While its mean convergence time reduces by 10.0% and its convergence stability increases by 29.1%, compared with the worst stochastic model. The stochastic model using exponential function is the most suitable under the error variance compensation and posteriori unit weight in static PPP with GPS and BDS, compared with the other familiar elevation dependent stochastic models.

An optimal indoor trust-region PPP algorithm with constrain of homologous array pseudolite

Homologous array pseudolite with simple time synchronization technique can provide high-precision larger-area indoor location service with outdoor GNSS receiver, but this architecture is born with several drawbacks, such as poor geometry, larger linearization error and multi-path error caused by signal reflection, and indoor positioning with this homologous array pseudolite can easily lead to potential divergence. Besides, fluctuation of time-delay, error of phase center and potential multipath error break integer propriety of carrier phase ambiguity and can’t be ignored for indoor PPP (Precise Point Positioning). Under these constrictions, optimal ambiguity-float indoor PPP algorithm with trust region is proposed, and performance of this optimal algorithm with the modified Levenberg-Marquardt technique, which is designed to avoid potential divergence particularly for poor geometry, is assessed with simulation and observation filed experiment. Meanwhile, the domain factor affecting performance of PPP and mechanism of accumulative error when moving are analyzed. The experimental result reveals that: unavoidable inaccuracy of position of pseudolite transmitting antenna can cause larger error of carrier phase bias that can be larger than 0.105 cycles, and it along with fluctuation of hardware group delay and multi-path error will cause position error that can be larger than 0.12 for most cases, the indoor static and kinematic PPP can obtain a few centimeter and smooth trace respectively, and the accuracy of indoor positioning based on this optimal algorithm can be better than 0.1668 m even at the corner of experiment area with poor geometry. Still there is particular circumstance that accuracy of this algorithm can be larger than 0.5741 m due to serious accumulative error with less satellite available when moving, the mechanism for it is analyzed with relationship between error of position and measurement error and depicted as follows: when some satellites with cycle slip occurs, the accuracy of position determined will reduce greatly due to less satellite available particularly with indoor homologous array pseudolite. Afterwards, the error of the position determined will lead to error of carrier phase ambiguity biases, which will cause large biases of subsequent position determined.

Models and performance of SBAS and PPP of BDS

Satellite Based Augmentation System (SBAS) is one of the services provided by the BeiDou Navigation Satellite System (BDS). It broadcasts four types of differential corrections to improve user application performance. These corrections include the State Space Representation (SSR) based satellite orbit/clock corrections and ionospheric grid corrections, and the Observation Space Representation (OSR) based partition comprehensive corrections. The algorithms generating these SBAS corrections are not introduced in previous researches, and the user SBAS positioning performance with the contribution of BDS-3 has not been evaluated. In this paper, we present the BDS SBAS algorithms for these differential corrections in detail. Four types of Precise Point Positioning (PPP) function models for BDS Dual-Frequency (DF) and Single-Frequency (SF) users using the OSR and SSR parameters are also proposed. One week of data in 2020 is collected at 20 reference stations including the observations of both BeiDou-2 Navigation Satellite System (BDS-2) and BeiDou-3 Navigation Satellite System (BDS-3) satellites, and the PPP under various scenarios are performed using all the datasets and the BDS SBAS broadcast corrections. The results show that the performance of BDS-2/BDS-3 combination is superior to that of BDS-2 only constellation. The positioning errors in Root Mean Square (RMS) for the static DF PPP are better than 8 cm/15 cm in horizontal/vertical directions, while for the static SF PPP are 11 cm/24 cm. In the scenarios of simulated kinematic PPP, three Dimension (3D) positioning errors can reach 0.5 m in less than 10 min for the DF PPP and 30 min for the SF PPP, and the RMSs of the DF and SF PPP are better than 17 cm/21 cm and 20 cm/32 cm in horizontal/vertical directions. In a real-time single- and dual-frequency kinematic positioning test, the positioning errors of all three components can reach 0.5 m within 30 min, and the positioning accuracy after solution convergence in the N, E and U directions is better than 0.3 m.

Assessment of tropospheric modeling on PPP-AR performances under brazilian atmospheric condition

In the Global Navigation Satellite System (GNSS), ambiguity resolution (AR) can shorten observation time and increase the positioning quality. The correct tropospheric modeling is intrinsically related to the ability to perform AR. Here, we assessed the influence of different tropospheric correction alternatives on AR for static Precise Point Positioning (PPP) in Brazilian territory. Our goal was to provide directions to users when choosing a suitable tropospheric model for application in PPP-AR under Brazilian atmospheric conditions. Thus, this study was carried out using well-known models such as the Saastamoinen model and the Zenith Tropospheric Delay (ZTD) Estimation and Numerical Weather Prediction (NWP) model from CPTEC/INPE. Six GNSS stations from the Brazilian Network for Continuous Monitoring (RBMC) (BRAZ, UFPR, RNNA, POVE, SMAR, and SAGA) were selected. Different GNSS processing setups were considered for GNSS data registered at selected stations during summer and winter. The assessment was based on a statistical analysis of positioning accuracy during one-hour sessions. The results indicated that such as the ZTD Estimation, the NWP model provides an accuracy of a few centimeters. On the other hand, the Saastamoinen model provided decimeter level accuracy, thus it is not the recommended choice for PPP-AR in the experimental conditions.

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.

Pass-by-Pass Ambiguity Resolution in Single GPS Receiver PPP Using Observations for Two Sequential Days: An Exploratory Study

“Pass-by-pass” or “track-to-track” ambiguity resolution removes Global Navigation Satellite System (GNSS) satellite hardware delays between adjacent undifferenced (UD) ambiguities, which is often applied in precise orbit determination (POD) for Low Earth Orbit (LEO) satellites to improve the accuracy of orbits. In this study, we carried out an exploratory study to use the “pass-by-pass” ambiguity resolution by differencing the undifferenced ambiguity candidates for two adjacent passes in sidereal days for a single Global Positioning System (GPS) receiver static Precise Point Positioning (PPP). Using the GPS observations from 132 globally distributed reference stations of International GPS Service (IGS), we find that 99.08% wide-lane (WL) and 97.83% narrow-lane (NL) double-difference ambiguities formed by the “pass-by-pass” method for all stations can be fixed to their nearest integers within absolute fractional residuals of 0.2 cycles. These proportions are higher than the corresponding values of network solution with multiple receivers with 97.39% and 91.20%, respectively. About 97% to 98% of ambiguities can be fixed finally on average. The comparison of the estimated station coordinates with the IGS weekly solutions reveals that the Root Mean Square (RMS) in East and North directions are 2-4 mm and is about 6 mm in the Up direction. For hourly data, it is found that the mean positioning accuracy improvement can achieve to about 10% after ambiguity resolution. From a dam deformation monitoring application, it shows that the fixing rate of WL and NL ambiguity can be closed to 100% and higher than 90%, respectively. The time series generated by PPP are also in agreement with the short baseline solutions.

Performance Evaluation of Precise Point Positioning for BeiDou-3 B1c/B2a Signals in the Global Range.

With the construction and development of the BeiDou navigation satellite system (BDS), the precise point positioning (PPP) performance of the BDS is worthy of research. In this study, observational data from 17 stations around the world across 20 days are used to comprehensively evaluate the PPP performance of BDS B1c/B2a signals. For greater understanding, the results are also compared with the Global Positioning System (GPS) and BDS PPP performance of different signals and system combinations. The evaluation found root mean square (RMS) values of the static PPP in the north (N), east (E), and upward (U) components, based on the B1c/B2a frequency of BDS-3, to be 6.9 mm, 4.7 mm, and 26.6 mm, respectively. Similar to the static positioning, the RMS values of kinematic PPP in the three directions of N, E, and U are 2.6 cm, 6.0 cm, and 8.5 cm, respectively. Besides this, the static PPP of BDS-3 (B1cB2a) and BDS-2 + BDS-3 (B1IB3I) have obvious system bias. Compared with static PPP, kinematic PPP is more sensitive to the number of satellites, and the coordinate accuracy in three dimensions can be increased by 27% with the combination of GPS (L1L2) and BDS. Compared with BDS-2+BDS-3 (B1IB3I), the convergence time of BDS-3 (B1CB2a) performs better in both static and kinematic modes. The antenna model does not show a significant difference in terms of the effect of the convergence speed, though the number of satellites observed has a certain influence on the convergence time.

Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution Using Products from Different Analysis Centers

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence time and a high-precision solution for PPP technology and PPP AR products are critical to implement PPP AR. Nowadays, various institutions provide PPP AR products in different forms with different strategies, which allow to enable PPP AR for Global Positioning System (GPS) and Galileo or BeiDou Navigation System (BDS). To give a full evaluation of PPP AR performance with various products, this work comprehensively investigates the positioning performance of GPS-only and multi-GNSS (Global Navigation Satellite System) combination PPP AR with the precise products from CNES, SGG, CODE, and PRIDE Lab using our in-house software. The positioning performance in terms of positioning accuracy, convergence time and fixing rate (FR) as well as time to first fix (TTFF), was assessed by static and kinematic PPP AR models. For GPS-only, combined GPS and Galileo PPP AR with different products, the positioning performances were all comparable with each other. Concretely, the static positioning errors can be reduced by 21.0% (to 0.46 cm), 52.5% (to 0.45 cm), 10.0% (to 1.33 cm) and 21.7% (to 0.33 cm), 47.4% (to 0.34 cm), 9.5% (to 1.16 cm) for GPS-only and GE combination in north, east, up component, respectively, while the reductions are 20.8% (to 1.13 cm), 42.9% (to 1.15 cm), 19.9% (to 3.4 cm) and 20.4% (to 0.72 cm), 44.1% (to 0.66 cm), 10.1% (to 2.44 cm) for kinematic PPP AR. Overall, the positioning performance with CODE products was superior to the others. Furthermore, multi-GNSS observations had significant improvements in PPP performance with float solutions and the TTFF as well as the FR of GPS PPP AR could be improved by adding observations from other GNSS. Additionally, we have released the source code for multi-GNSS PPP AR, anyone can freely access the code and example data from GitHub.

Estimating the Fractional Cycle Biases for GPS Triple-Frequency Precise Point Positioning with Ambiguity Resolution Based on IGS Ultra-Rapid Predicted Orbits

We investigate the estimation of the fractional cycle biases (FCBs) for GPS triple-frequency uncombined precise point positioning (PPP) with ambiguity resolution (AR) based on the IGS ultra-rapid predicted (IGU) orbits. The impact of the IGU orbit errors on the performance of GPS triple-frequency PPP AR is also assessed. The extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) FCBs are generated with the single difference (SD) between satellites model using the global reference stations based on the IGU orbits. For comparison purposes, the EWL, WL and NL FCBs based on the IGS final precise (IGF) orbits are estimated. Each of the EWL, WL and NL FCBs based on IGF and IGU orbits are converted to the uncombined FCBs to implement the static and kinematic triple-frequency PPP AR. Due to the short wavelengths of NL ambiguities, the IGU orbit errors significantly impact the precision and stability of NL FCBs. An average STD of 0.033 cycles is achieved for the NL FCBs based on IGF orbits, while the value of the NL FCBs based on IGU orbits is 0.133 cycles. In contrast, the EWL and WL FCBs generated based on IGU orbits have comparable precision and stability to those generated based on IGF orbits. The use of IGU orbits results in an increased time-to-first-fix (TTFF) and lower fixing rates compared to the use of IGF orbits. Average TTFFs of 23.3 min (static) and 31.1 min (kinematic) and fixing rates of 98.1% (static) and 97.4% (kinematic) are achieved for the triple-frequency PPP AR based on IGF orbits. The average TTFFs increase to 27.0 min (static) and 37.9 min (kinematic) with fixing rates of 97.0% (static) and 96.3% (kinematic) based on the IGU orbits. The convergence times and positioning accuracy of PPP and PPP AR based on IGU orbits are slightly worse than those based on IGF orbits. Additionally, limited by the number of satellites transmitting three frequency signals, the introduction of the third frequency, L5, has a marginal impact on the performance of PPP and PPP AR. The GPS triple-frequency PPP AR performance is expected to improve with the deployment of new-generation satellites capable of transmitting the L5 signal.

Assessment of multi-GNSS precise orbit and clock products from different analysis centers based on precise point positioning

Performance of 24h static Precise Point Positioning (PPP) solutions based on multi-GNSS precise satellite orbit and clock products from four analysis centers and seven various constellation combinations was studied to evaluate their quality and characteristics. Data from ten European and four Chinese GNSS stations and 152 days long period from year 2020 were processed. Obtained coordinates were firstly compared with those provided by IGS final weekly combined solution. In Europe, the best agreement with this reference product was reached by solutions including Galileo signals, namely by a combination of GPS+GLONASS+Galileo systems with a mean RMS of 11 mm. This situation was different in China where inclusion of Galileo always led to worse results and the best agreement was achieved by a combination of GPS+GLONASS systems. Although product provided by German Research Center for Geosciences (GFZ) could be selected as the best performing over Europe and product by Center for Orbit Determination in Europe (CODE) over China, differences between individual precise products were mostly at a minimal level. Secondly, coordinates repeatability over the processed period was computed in order to assess the positioning stability. In this regard, the lowest values in both horizontal and vertical direction were reached by GPS+GLONASS solutions. From the perspective of precise products, the repeatability results were dependent on the selected constellation where mainly a specific behavior of product from Wuhan University (WUM) for Galileo system was observed.

Inter-satellite link augmented BeiDou-3 orbit determination for precise point positioning

Precise Point Positioning (PPP) requires precise products, including high-accuracy satellite orbit and clock parameters. It is impossible to obtain an orbit solution that is sufficiently accurate for PPP services with a regional tracking network; therefore, satellite orbits are usually estimated by a global tracking network with a large number of ground stations. However, it is expensive to build globally distributed stations. Fortunately, BeiDou-3 satellites carry an Inter-Satellite Link (ISL) payload, which can track the whole arc of the BeiDou-3 satellites and enhance the orbit determination accuracy with regional ground stations. In this contribution, a novel orbit determination strategy for BeiDou-3 PPP is proposed, in which the BeiDou-3 satellite orbits are enhanced by the ISL. First, the generation of precise satellite products is demonstrated in detail. In addition, the products are assessed by Satellite Laser Ranging (SLR) residuals and overlap comparisons. Moreover, the products are used for receivers in mainland China to carry out the static and kinematic modes to research the PPP performance of BeiDou-3′s 3IGSO/24MEO constellation. The SLR validations of the satellite orbits demonstrate an accuracy better than 0.1 m in the radial component, and the orbit overlap comparisons show accuracies of 0.016 m in the radial component, 0.088 m in the along-track component and 0.087 m in the cross-track component. The Standard Deviation (STD) in the differences in overlapping arcs for the estimated satellite clocks is approximately 0.10 ns. The static PPP results demonstrate that the error in both the horizontal and vertical components is smaller than 10 cm after 30 minutes of convergence. After 24 hours of convergence, the errors are 0.70 cm, 0.63 cm and 1.99 cm for the north, east and up components, respectively. The kinematic PPP experiment illustrates that the Root Mean Square (RMS) position errors in the north, east and up components are approximately 3.23 cm, 5.27 cm and 8.64 cm, respectively, after convergence. The obtainable positioning and convergence performances are comparable to those using products generated by global tracking networks.

Performance Evaluation of Triple-Frequency GPS/Galileo Techniques for Precise Static and Kinematic Applications.

The objective of this research was to develop new precise point positioning (PPP) processing models using triple-frequency GPS/Galileo observations. Different triple-frequency PPP models were developed including undifferenced, between-satellite single-difference (BSSD) and semi-decoupled PPP models. Additionally, a dual-frequency ionosphere-free undifferenced PPP model was developed. The performance of our developed PPP models was evaluated for both static and kinematic applications. To validate the proposed PPP models for static applications, triple-frequency GPS/Galileo observations spanning three successive days from eight globally distributed reference stations were acquired. Then, the observations were processed using the four static PPP solutions. It is found that the 3D positioning accuracy of the triple-frequency semi-decoupled, BSSD and undifferenced PPP models is enhanced after 10 min by about 50, 41 and 29%, respectively, compared with the dual-frequency undifferenced PPP model. After 20 min of processing, improvements in the 3D positioning accuracy by 40, 31 and 21% are obtained for the triple-frequency semi-decoupled, BSSD and undifferenced PPP models, respectively, with respect to the dual-frequency PPP model. The 3D positioning accuracy is also improved after 60 min, compared with the dual-frequency solution, by 40, 40 and 35% for the triple-frequency semi-decoupled, BSSD and undifferenced PPP solutions, respectively. For kinematic application validation, a vehicle trajectory was carried out. The collected triple-frequency GPS/Galileo observations were processed using the four kinematic PPP solutions. It is shown that the triple-frequency semi-decupled, BSSD and undifferenced PPP solutions enhance the 3D positioning accuracy by 31, 23 and 10%, respectively, in comparison with the dual-frequency undifferenced PPP solutions.

An Investigation of Precise Orbit and Clock Products for BDS-3 from Different Analysis Centers.

A quality evaluation of precise products for BDS-3 constellations is presented for the first time in this contribution. Then, the tropospheric delay retrieval and positioning performance of BDS-3 precise point positioning (PPP) solutions using the precise products (gbm, wum, iac, sha, cnt) with observations from 24 stations from DOY 280 to 317 in 2020 was comprehensively investigated. The orbit comparisons present consistencies of 0.09–0.22 m for the C19–C37 satellites and of 0.5–1.2 m for the C38–C46 satellites among the final products. The standard deviation (STD) values of the clock differences of iac showed the best agreement with those of gbm, followed by wum, sha. The clock differences performance of cnt was the worst. For BDS-3 PPP solutions with five Analysis centers (ACs) products, the median convergence times of static PPP mode incorporating the gbm, wum, iac, sha, and cnt products were 31.0, 33.5, 34.5, 37.8, and 72.0 min, respectively; the median convergence times of kinematic PPP model incorporating the same products were 40.5, 41.0, 50.5, 55.0, and 94.0 min, respectively. The positioning accuracies in the static and kinematic modes were approximately 1–4 cm, 2–6 cm in the horizontal and vertical components, respectively. With the final products in kinematic mode, the performance of PPP with real-time products (cnt) is poorer than all PPP with final products. The median of ZTD accuracies of the five products gbm, wum, iac, sha, and cnt were 7.84, 7.58, 7.04, 7.19, and 10.1 mm, respectively, and the accuracy differences were very small among five AC products (gbm, wum, iac, sha).

Preliminary analysis of the quality and positioning performance of BDS-3 global interoperable signal B1C&B2a

BeiDou-3 Navigation Satellite System (BDS-3) satellites are equipped with the new generation GNSS signals B1C and B2a, which support the interoperability with GPS and Galileo systems. In this study, the pseudo-range multipath error and carrier phase observation noise of the BDS-3 B1C and B2a signals were evaluated based on zero baseline measurements from the day of year (DOY) 113 to 116, 2020. Further, the precision and performance of the single point positioning (SPP) and precise point positioning (PPP) are assessed at 9 stations. This assessment manifests that the standard deviations (STDs) of the pseudo-range multipath error are about 0.09 ~ 0.22 m, while STDs of the carrier phase observation noise are about 0.075 mm. For the single-frequency SPP, its positioning precision is about 2.03 ~ 4.85 m and 3.29 ~ 10.73 m at the 99.99% confidence level in horizontal and vertical directions, respectively, while the dual-frequency SPP precision is about 1.92 ~ 8.02 m and 4.81 ~ 12.77 m in horizontal and vertical directions, respectively. For the daily static PPP, the convergence time is about 20 ~ 30 min, while the daily positioning precision can reach 1.38 ~ 4.42 cm and -1.31 ~ 4.34 cm in horizontal and vertical directions, respectively. In general, the quality and the SPP and PPP performance of the BDS-3 B1C&B2a signals are comparable to the GPS and Galileo.