Performance Of Precise Point Positioning Research Articles

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%.

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.

BDS-3 six-frequency precise point positioning: effects of receiver-dependent inter-frequency clock bias and multi-frequency contributions

We find that there is time-varying bias at the receiver in BDS-3 multi-frequency phase observations, which will lead to receiver-dependent inter-frequency clock bias (RIFCB) and damage the rigor of BDS-3 multi-frequency precise point positioning (PPP) model. A unified RIFCB correction method compatible with uncombined and ionospheric-free combined PPP models using any BDS-3 frequencies is proposed. The contributions of multi-frequency integration to BDS-3 static and kinematic PPP performance are evaluated. The results indicate that the RIFCB amplitude can reach 1 dm. If the RIFCB correction is ignored, the phase observation residuals present a systematic bias. RIFCB has potential effects on precise time transfer, ionospheric monitoring, and fractional cycle bias estimation. Experimental results show that the long-term frequency stability of time transfer can be improved by correcting RIFCB. The joint use of all BDS-3 six-frequency signals can significantly shorten the convergence time, and the positioning accuracy can also be slightly improved.

Reconstructed estimation method of the multi-frequency GNSS inter-frequency clock bias

In consideration of contributions from both carrier phase and pseudorange observations during computation, this study introduces a reconstructed method for estimating the multi-frequency global navigation satellite system (GNSS) inter-frequency clock biases (IFCB). Diverging from conventional approaches that separately calculate the time-varying and constant parts of IFCBs using carrier phase and pseudorange observations, the reconstructed method directly utilizes their combination to estimate satellite IFCBs. To validate the efficacy of the presented approach, 7 d observations from 87 International GNSS Service (IGS) stations are analyzed, with a specific focus on triple-frequency GPS, multi-frequency BDS-3, and Galileo IFCBs, aiming to scrutinize their distinctive characteristics. Furthermore, the performances of satellite IFCB estimation are investigated in both precise point positioning (PPP) and single-point positioning (SPP) using 35 IGS stations over 3 d. The results demonstrate that IFCBs of GPS BLOCK IIIA satellites exhibit centimeter-level variations, distinguishing them from BLOCK IIF counterparts. The Galileo IFCBs vary from millimeter to centimeter level, while those of BDS-3 reach a centimeter level. These variations significantly impact GPS PPP convergence performances but have minimal effects on Galileo and BDS-3 PPP. SPP performances are slightly enhanced when the time-varying IFCB part are taken into account. Additionally, we note disparities in the constant parts of satellite IFCBs computed with differential code bias (DCB) products, reconstructed, and pseudorange observation-based methods, particularly for BDS-3 C2I/C6I-C1P/C5P and C2I/C6I-C1P/C6I combinations. The differences of IFCB estimated with different strategies, SPP and PPP performances show that the reconstructed method is better than others, and the IFCB accuracy decreases when computed with satellite DCB products.

Performance evaluation of BDS-3 new B1C/B2a and legacy B1I/B3I signals: Observational quality, POD and PPP

In addition to the BeiDou regional navigation satellite system (BDS-2) backward compatible B1I and B3I signals, the BeiDou global navigation satellite system (BDS-3) also broadcast the B1C and B2a signals for compatibility with other Global Navigation Satellite System (GNSS), and providing satellite-based augmentation service for the International Civil Aviation Organization. Considering that the majority of the existing researches on the BDS-3 precise orbit determination (POD) and precise point positioning (PPP) are based on the B1I/B3I signals, the special attention that systematically comparing the data quality, POD accuracy and PPP performance through B1I/B3I and B1C/B2a signals is aroused in this paper. Signal characteristics of different receivers and antennas for the aforesaid four various signals were analyzed in terms of the carrier-to-noise density ratio (C/N0), pseudorange multipath and observation noise. The B1C signal exhibits the minimum C/N0 values, and the B3I and B2a signals have the smaller pseudorange multipath errors. The smallest pseudorange noise can be observed form the B2a signal, while the root mean squares (RMSs) for carrier phase noise show tiny differences among the four signals. The BDS-3 POD results indicate that the orbit overlapping arc error in three-dimensional (3D) direction is 0.069 and 0.076 m for the B1C/B2a and B1I/B3I, and the standard deviation of the satellite laser ranging validation is 0.041 m for both the two schemes. The clock offset products were evaluated with respect to the precise clock products from Deutsches GeoForschungsZentrum (GFZ), and the standard deviations (STDs) are 0.166 and 0.176 ns for the B1C/B2a and B1I/B3I. Finally, there is no apparent difference in the RMSs for B1C/B2a and B1I/B3I static PPP, while the convergence time that shortened by 31.4 % can be achieved for B1C/B2a. For kinematic PPP, the 3D RMS is 0.043 m and the convergence time is 31.1 min for the B1C/B2a, which is reduced by 14.0 % and 35.2 %, respectively, compared to B1I/B3I.

An Analysis of Satellite Multichannel Differential Code Bias for BeiDou SPP and PPP

Differential code bias (DCB) of satellite is an error that cannot be ignored in precise positioning, timing, ionospheric modeling, satellite clock correction, and ambiguity resolution. The completion of the third generation of BeiDou Navigation Satellite System (BDS-3) has extended DCB to multichannel code bias observations and observable-specific signal bias (OSB). In this paper, the DCB and OSB products provided by the Chinese Academy of Sciences (CAS) are analyzed and compared. The DCB parameters for the BDS satellites are applied in both single- and dual-frequency single point positioning (SPP), and the results are intensively investigated. Based on the satellite DCB parameters of the BDS, the performance of precise point positioning (PPP) with different frequency combinations is also analyzed in terms of positioning accuracy and convergence time. The standard deviations (STDs) of DCBs at each signal pair fluctuate from 0.2 ns to 1.5 ns. The DCBs of BDS-2 are slightly more stable than those of BDS-3. The mean values and STDs of C2I and C7I OSBs for BDS-2 are at the same level and are numerically smaller than their counterparts for the C6I OSBs. The mean OSBs for each signal of the BDS-3, excluding C2I, fluctuate between 12.35 ns and 12.94 ns, and the STD fluctuates between 2.11 ns and 3.10 ns. The DCBs and OSBs of the BDS-3 of the IGSO satellites are more stable than those of the MEO satellites. The corrections for TGD and DCB are able to improve the accuracy of single-frequency SPP by 44.09% and 44.07%, respectively, and improve the accuracy of dual-frequency SPP by 6.44% and 12.85%, respectively. The most significant improvements from DCB correction are seen in single-frequency positioning with B1I and dual-frequency positioning with B2a+B3I. DCB correction can improve the horizontal and three-dimensional positioning accuracy of the dual-frequency PPP of different ionosphere-free combinations by 13.53% and 13.84% on average, respectively, although the convergence is slowed.

BDS-3/BDS-2 FCB estimation considering different influencing factors and precise point positioning with ambiguity resolution

Since the full system deployment of BDS-3 in July 2020, it has provided stable and reliable positioning, navigation and timing (PNT) services for users around the world. It is an urgent task to explore the potential performance of precise point positioning (PPP) based on the full constellation of BDS-2/BDS-3. This research presented the global satellite visibility of BDS-2/BDS-3, analyzed the stability and accuracy of BDS-2 and BDS-3 rubidium clocks and hydrogen clocks, jointly estimated the BDS-2 and BDS-3 fractional cycle biases (FCB) and evaluated the PPP performance with ambiguity resolution (AR). Due to the fact that International GNSS Service (IGS) precise products have a great impact on narrow-lane (NL) FCB estimation, the FCB obtained by using the precise products from CODE (Center for Orbit Determination in Europe) and GBM (Deutsches GeoForschungsZentrum) in two different analysis centers and the FCB obtained by using GBM precise products with different calculation strategies are analyzed. In addition, the experimental data from Multi-GNSS Experiment (MGEX), EUREF (EPN) and Germany (GPN) observation networks are used to evaluate the influence of orbital errors on BDS FCB estimation. For wide-lane (WL) FCB, MGEX WL FCB has the highest accuracy, followed by EPN and GPN. On the contrary, for NL FCB, MGEX NL FCB has the worst accuracy, followed by EPN, and GPN is the best. Eventually, numerous experiment results showed that compared with the static float solution, the PPP fixed solutions in East (E), North (N) and Up (U) directions are improved by 32.9%, 27.7%, 13.8% for BDS-3 and 10.0%, 7.5%, 3.8% for BDS-2/BDS-3. Compared with the kinematic float solution, the PPP fixed solutions in E, N and U directions are improved by 27.9%, 23.4%, 16.6% for BDS-3 and 15.9%, 8.9%, 5.3% for BDS-2/BDS-3.

GALILEO HAS – FIRST PERFORMANCE TESTS DURING ITS INITIAL PHASE OF OPERATION

Galileo High Accuracy Service (HAS) became available in January 2023. As declared, in its final operational capability, it should be able to provide to users the Precise Point Positioning (PPP) at horizontal accuracy level better than 20 cm in real-time with 95% confidence globally. At the moment Galileo HAS works in its initial phase of operation with some limitations regarding its availability, convergence time and accuracy but gives the chance to observe the performance of positioning tool at the accuracy level which was available before by using differential measurement only. Galileo HAS PPP, free of charge and based only on satellite signals delivered by nominal Galileo constellation is unique in its kind between various GNSS positioning modes. This article presents the results of first, preliminary tests on Galileo HAS performance conducted in July 2023 in Gdynia, Poland. The field tests were conducted with Galileo HAS capable receiver in static conditions and focused on the verification the declared service performance in the real positioning scenarios. Additionally, the Galileo HAS PPP performance was compared with the simultaneous performance of other GNSS positioning methods such as EGNOS, DGPS, dual frequency GPS+Galileo or dual frequency GPS and dual frequency Galileo. This first experiences with Galileo HAS positioning should show all potential users what performance level can be achieved with this new, unique in its kind GNSS positioning method at the present state of its implementation.

BDS/GPS/Galileo Precise Point Positioning Performance Analysis of Android Smartphones Based on Real-Time Stream Data

Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products in some older smart devices are applied in current studies. The performances of precise point positioning (PPP) with the smartphone using real-time products and newly smartphones are still unrevealed, which is more valuable for real-time applications. This study investigates the observation data quality and multi-GNSS real-time PPP performance using recent smartphones. Firstly, the observed carrier-to-noise density ratio (C/N0), number of satellites and position dilution of precision (PDOP) of GNSS observations are evaluated. The results demonstrate that the C/N0 received by Huawei Mate40 is better than that of the Huawei P40 for GPS, BDS, QZSS and Galileo systems, while the GLONASS is poorer, and the PDOP of the Huawei P40 is slightly better than that of Mate40. Additionally, a comprehensive analysis of real-time precise orbit and clock offset products performance is conducted. The experiment result expresses that the orbit and clock offset performance of GPS and Galileo is better than that of BDS-3 and GLONASS, and BDS-2 is the worst. Finally, single- and dual-frequency multi-GNSS combined PPP experiments using observations received from smartphones and real-time products are conducted; the results indicate that the real-time static PPP using a smartphone can achieve decimeter-level positioning accuracy, and kinematic PPP can achieve meter-level positioning accuracy after convergence.

Performance analysis of four PPP service software under different intensity geomagnetic storms

Currently, many precise point positioning (PPP) services provide through software or online websites for GNSS positioning studies and applications. Various PPP service software has different positioning performances due to their respective algorithms and versions. In addition, the positioning accuracy and reliability of PPP services lack systematic evaluation, especially in the case of geomagnetic storms. This study presents the PPP performance analysis of the common GNSS PPP software as CSRS-PPP (https://www.geod.nrcan.gc.ca/), APPS (https://apps.gdgps.net/), Net_Diff (http://center.shao.ac.cn/shao_gnss_ac/), and GAMP (https://www.ngs.noaa.gov/gps-toolbox/GAMP) under different geomagnetic storm intensities. The PPP experiments involve data from 916, 885, and 676 GPS stations data on 17 March 2015 (severe), 26 August 2018 (strong), and 15 January 2022 (moderate), respectively. The results showed that the positioning performance of the four PPP software is different in the magnetic storm environment. We found that during geomagnetic storms, the CSRS-PPP software has the highest positioning accuracy and reliability, while the APPS software shows the worst positioning performance. The performance of Net_Diff and GAMP during geomagnetic storms are comparable but are better than that of APPS. Statistical results indicate that the average values of 3D RMS of CSRS-PPP, APPS, Net_Diff, and GAMP under severe storm are 0.14 m, 0.60 m, 0.40 m, and 0.33 m, under strong storm are 0.18 m, 0.65 m, 0.27 m, and 0.33 m, and under moderate storm are 0.25 m, 1.66 m, 0.26 m, and 0.34 m, respectively. The main reason why the CSRS-PPP has the best positioning accuracy under different intensity storms is that it uses the ambiguity-fixed PPP solution, while the other three software use float solution.

Evaluation and Analysis of the Accuracy of Open-Source Software and Online Services for PPP Processing in Static Mode

It has been proven that precise point positioning (PPP) is a well-established technique to obtain high-precision positioning in the order between centimeters and millimeters. In this context, different studies have been carried out to evaluate the performance of PPP in static mode as a possible alternative to the relative method. However, only a few studies have evaluated the performance of a large number of different open-source software programs and have focused extensively on online free PPP services. Therefore, in this paper, a comprehensive comparison of processing in static mode between different open-source software and the online free PPP services is developed. For the evaluation, different GNSS observation files collected at 45 International GNSS Service (IGS) stations distributed worldwide were processed in static PPP mode. Within this frame of reference, ten open-source PPP software and five online free PPP services were studied. The results from the processing strategy demonstrate that it is possible to obtain precision in the order of millimeters with both open-source software and online PPP services. In addition, online PPP services experienced better performance than some other specialized PPP software. In summary, the results show that the daily solutions for the E (East), N (North), and U (Up) components estimated by the ten open-source software and by the five online free PPP services can reach millimeter precision for some stations. Among the open-source software, the PRIDE-PPPAR presented the best performance with a Root Mean Square Error (RMSE) of 5.52, 5.40, and 6.79 mm in the E, N, and U components, respectively. Alternatively, in the case of the online free PPP services, the APPS and CSRS-PPP produced the most accurate results, with RMSE values less than 12 mm for the three components. Finally, the open-source software and online free PPP services experienced similar positioning performance in the horizontal and vertical components, demonstrating that both can be implemented in static mode without compromising the accuracy of the measurement.

An ERA5 tropospheric parameters-augmented approach for improving GNSS precise point positioning

Precise Point Positioning (PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring. As atmospheric reanalysis data products' accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay (ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts (ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System (GNSS) PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service (IGS) stations for 2016–2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm, respectively. Further, GNSS observations for one week in each of the four seasons (spring: DOY 92–98; summer: DOY 199–205; autumn: DOY 275–281; and winter: DOY 22–28) from 34 multi-GNSS experiments (MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes (without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern (E) and Northern (N) directions, while the average convergence time over four weeks in the vertical (U) direction improved by 53.3% and 52.7%, respectively (in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively. Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

Assessing the Performance of Precise Point Positioning (PPP) with the Fully Serviceable Multi-GNSS Constellations: GPS, BDS-3, and Galileo

Nowadays, both BDS-3 and Galileo can provide global positioning and navigation services. This contribution carried out a comprehensive analysis and validation of positioning performance in terms of positioning accuracy (RMS) and convergence time, which are derived from BDS-3 and Galileo precise point positioning (PPP) solutions at a global scale. Meanwhile, the comparison with GPS was demonstrated. The performance and geographical distribution of RMS and convergence time for each satellite system were analyzed. GPS outperforms the other two systems on a global scale. Galileo and BDS-3, on the other hand, only perform moderately well in certain latitude zones. The combination of dual systems related to each single system is analyzed. For the dual-system combinations, the combination of systems presents a definite advantage over Galileo and BDS-3, and this advantage is more pronounced for the kinematic PPP. For GPS, the combination with Galileo and BDS-3 has little improvement in positioning performance. For the dual-system combination based on Galileo and BDS-3, the RMS and convergence time can be improved by 50% compared with the single system. The influence of single-system kinematic PPP selection for precise products from different MGEX analysis centers on positioning performance was studied. Among the five precise products, grg products have the best positioning performance for GPS, while cod products have the best positioning performance for Galileo and BDS-3. The difference in RMS and convergence time between 2 cm and 15 min can be caused by different precise product selections.

BDS pseudorange biases handling: Simultaneous estimation, daily magnitude and analytical comparison of the BDS PPP models

With the completed establishment of the Beidou global navigation satellite system (BDS-3), the BDS constellation is qualified for the global positioning, navigation and timing (PNT) services. The simultaneous observed B1I/B3I signals of the BDS-2 and BDS-3 satellites facilitate the BDS-2/BDS-3 joint precise point positioning (PPP) solution. For reasons related to the modulation modes, signal property, receiver front end design, precise satellite clock products arising from the different analysis centers and so on, BDS pseudorange biases are absorbed by the pseudorange measurements, including the pseudorange bias variation, signal distortion bias (SDB) and time delay bias (TDB). The large magnitude of the BDS pseudorange biases will degrade the BDS PPP performance. Herein, the simultaneous estimation of the BDS pseudorange biases are applied in BDS PPP and totally six pseudorange biases processing strategies are presented. The magnitudes of the existed BDS SDB and TDB are analyzed. The statistics showed that the BDS PPP performance in term of the convergence time and positioning accuracy can be remarkably improved by considering the BDS pseudorange biases. By comparing the BDS PPP performance in different scenarios, we recommend three processing schemes that are reducing weight of the BDS-2 pseudorange observations, estimating the BDS TDB as constant and neglecting the SDB, and estimating the BDS SDB as the constant per satellite. The analytical results can facilitate the optimal BDS PPP performance.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Investigating the Impacts of Ionospheric Irregularities on Precise Point Positioning Over China and Its Mechanism

AbstractThe impacts of ionospheric irregularities on precise point positioning (PPP) have been commonly noticed in the field of the ionosphere and the precise application of the Global Navigation Satellite System. But few attentions have been paid to how ionospheric irregularities deteriorate the performance of PPP. Aiming at exploring the mechanism of degradation of PPP solutions during the period of ionospheric irregularities, this paper investigates the impacts of ionospheric irregularities on the performance of kinematic PPP. The experiment uses GPS observation data sampled at the 30‐s interval over China on the days of 2014, 2015, and 2017 covering some active space weather, for example, solar and geomagnetic activities. The results show that the ionospheric irregularities caused increased positioning errors (decimeter‐ to meter‐level), enlarged phase residuals (decimeter‐level), and increased the number of detected cycle slips in PPP processing in low latitude regions of China. By proposing a novel strategy that compares the number of detected cycle slips from 30 s‐sampling interval data and 1s‐sampling interval data at the same station in an “aligned” mode, we present direct evidence of the existence of the falsely detected cycle slips in 30 s‐sampling interval data by the traditional cycle‐slip detection threshold in PPP processing. We reveal that the unnecessary and frequent reinitialization of ambiguity induced by the falsely detected cycle slips is dominantly responsible for the degradation of kinematic PPP solutions during the period of ionospheric irregularities. Our findings pointed out the direction for the improvement of kinematic PPP performance in the environment of ionospheric irregularities.

Improving the performance of GNSS precise point positioning by developed robust adaptive Kalman filter

Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) is a great precision positioning method based on GNSS. PPP based on multi-constellation GNSS uses the extended Kalman filter (EKF). Inappropriately, the measurement outliers and the system's dynamic model might produce mistakes in the positioning accuracy acquired using this method. An adaptive robust Kalman filter (RKF) was recently developed in order to alleviate these errors. In addition, the preceding variance is sometimes used to determine the weights of different categories of observations, which has an effect on PPP performance. A novel developed robust adaptive filtering (DRKF) has been developed to provide better placement results. For the equivalent weight matrix to be generated, an equivalent weight model that is statistically robust by the chi-square test for classification is constructed in this technique. According to prior Kalman filter models employing International GNSS Service (IGS) final clock and orbit products, the performance of GNSS PPP using the DRKF is confirmed in contrast to those produced using the current model. DRKF surpasses traditional robust adaptive filters in terms of positioning accuracy, convergence time, and PPP sturdiness according to the results of this study. In comparison to RKF, DRKF improves the positioning solution by 201 mm with 119.10 %, 77 mm with 164.86 %, and 160 mm with 211.74 % in the east, north, and up (ENZ) directions, respectively. It is recommended to use the newly developed robust adaptive Kalman filter in kinematic mode, especially in urban areas, due to the noticeable improvement in position accuracy.

Satellite Clock Batch Estimation Accuracy Analysis and Its Impacts on PPP

The ultra-rapid satellite clock product based on the satellite clock batch estimation is commonly used for high-precision and reliable precise point positioning (PPP) services. In order to clarify the effect of different ranging errors on the satellite clock batch estimation accuracy, the source of the satellite clock bias induced by the batch observation model is classified into the initial clock bias (ICB) and time-dependent bias (TDB). In addition to the effect of the ICB and TDB, the analytic relationship between the observation redundancy and the satellite clock batch estimation accuracy are derived and verified. The suitable number of stations is suggested to be 40 for the satellite clock batch estimation to achieve the counterbalance between the efficiency and saturable accuracy. For the PPP based on the batch-estimated satellite clock, the impacts of the ICB and TDB on PPP are clarified. The satellite clock batch estimation and PPP experiments are carried out to investigate the impacts of the ICB and TDB on the satellite clock batch estimation accuracy and the PPP performance. The ICB causes a significant bias for the batch-estimated satellite clock. The TDB is impacted by the assimilation ability of the batch-estimated satellite clock to the satellite orbit error. The convergence time and the positioning accuracy after the convergence of PPP are primarily affected by the ICB and TDB, respectively.

A resilient adjustment method to weigh pseudorange observation in precise point positioning

The accurate weighting of pseudorange observations is important to improve the convergence time and positioning quality of Precise Point Positioning (PPP). Currently, the weight of a pseudorange observation is mainly determined with empirical stochastic models. However, in a complex environment, due to the inability to adapt for the dynamic changes of the user environment, the empirical stochastic models usually cannot reflect the real error level of pseudorange observations. To address this problem, a resilient adjustment method to weigh pseudorange observations is proposed, which constructs the real-time estimation and inflation model for the variance of pseudorange multipath error and measurement noise to replace the empirical stochastic model to determine the weights of pseudorange observations. A set of static and dynamic Global Positioning System (GPS) test data are used to verify the effectiveness of the proposed method. The test results indicate that the proposed real-time estimation model can provide a better representation of the pseudorange accuracy, and the positioning performance of PPP using the real-time estimation model is better than that with the empirical stochastic model. Compared with the optimal empirical stochastic model, the positioning accuracy of PPP with the real-time estimation model is improved by at least 20%, and the convergence time is reduced by at least 50%.

An improved method for real-time PPP timing and time transfer with broadcast ephemerides

Due to the problem of network communication, it is difficult to ensure the reliability of real-time precise point positioning (PPP) timing/time transfer with real-time precise products. With the continued reduction in the signal-in-space range error, the performance and feasibility of GPS and Galileo PPP timing/time transfer with broadcast ephemeris were analyzed for the first time in real time. Then, we present a smoothing method and time-series decomposition method to reduce the noise and the interpolation error for GPS and Galileo PPP timing\ ime transfer with broadcast ephemeris in real time. The results show that GPS or Galileo PPP timing with broadcast ephemeris can achieve a 4 × 1 × 10−14 level at 15 360 s in the current state. The accuracy is about (0.46–0.81) ns and (0.44–0.61) ns for GPS and Galileo PPP time transfer. The frequency stability is at about 7.0 × 1 × 10−14 and 5.0 × 1 × 10−14 levels at 15 360 s for GPS and Galileo PPP. It is important to note that by applying our approach, the maximum improvement in frequency stability for GPS and Galileo PPP timing/time transfer is up to 99%. Furthermore, the average accuracy of GPS or Galileo PPP time transfer can achieve approximately 0.3 ns, which is an improvement of up to 67.3% compared to the traditional method.