Combined Precise Point Positioning Research Articles

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.

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 Assessment of Multi-GNSS PPP Ambiguity Resolution with LEO-Augmentation

The fast motion of low Earth orbit (LEO) satellites provides rapid geometric changes in a short time, which can accelerate the initialization of precise point positioning (PPP). The rapid convergence of ambiguity parameters is conducive to the rapid success of ambiguity fixing. This paper presents the performance of single- and four-system combined PPP Ambiguity Resolution (AR), enhanced with an ambiguity-float solution LEO. Two LEO constellations were designed: L was a typical polar orbit constellation, with a higher number of visible satellites at high latitudes than at low and middle latitudes; and M was designed to compensate for the lack of visible satellites at low and middle latitudes. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because the global navigation satellite systems (GNSSs) were fully operational, the GNSS data were real observation data from the MGEX stations. Based on the daily observation datasets collected at 258 stations in the global MGEX observation network over three days (from January 1 to January 3 2022), in addition to the LEO simulation data, we evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP ambiguity resolution and compared it with LEO-enhanced PPP. The L+M mixed constellation was able to reduce the time to first fix (TTFF) of the four-system combined PPP-AR to 5 min, and four LEO satellites were sufficient to achieve this. L+M mixed constellation was able to redu ce the convergence time of the four-system combined PPP to 2 min. Unlike PPP-AR, PPP required more LEO satellites for augmentation to saturate.

Role of Multi-Constellation GNSS in the Mitigation of the Observation Errors and the Enhancement of the Positioning Accuracy

Using Precise point positioning (PPP) technique can help to reach decimeters accuracy for positioning by using one receiver only. Since it set to track Global Navigation Satellite System (GNSS). Recently BeiDou and Galileo systems have been devolved periodically and increasing the number of working satellites. Addition to those all-global Navigation systems is able to receive triple frequency signals. The effect of using Multi constellation of GNSS and combination of different systems with each other’s need to be investigated. In this paper, four Multi GNSS EXPERIMENT (MGEX) stations with 24 hours observation files and 30 second interval time during a 1 week of averaged data of January 2020 (2134 GPS week) are used to investigate the accuracy of using combined solution of GNSS with 12 cases of study. Data were processed by PPPH program. To investigate the effect of using the different GNSS combinations while using the PPP method, contrast experiments have been tested by mixing dual frequency ionospheric-free PPP models in static mode with G only, GLO only, G + GLO, G+ B, GLO+B, G+GAL, GLO+GAL, GLO+B+GAL, GNSS, G +GAL+B, G+GLO+B and G+GLO+GAL combination cases, where G refers to GPS, GLO refers to GLONASS, GAL refers to Galileo and B refers to BeiDou. The results show that the combined GPS and Galileo observation in PPP solution improves the convergence time and gives the shortest convergence time of the 12 study cases with average value 53 minute and with minimum value 35 minute. By comparing the root mean square error (RMS) values, the combination of G+GL+B had the minimum RMS error in North and East direction with minimum value 1.2 cm, maximum value 1.8 cm and average value1.45 cm. And the combination of GLO+GAL+B had the minimum RMS errors in up directions with average value 2.775 cm and minimum 2.775 cm and maximum 4.5 cm. In conclusion, the results indicate that the combination of different GNSS can give more accurate solution of the PPP. The combined PPP has shown an improvement in the convergence time in the case of using combined of G and GAL observation, while the positioning accuracy after convergence has no shown significant improvement. The result of G+GAL+B give the minimum RMS error in North and East direction and the combination of GLO+GAL+B give the minimum RMS errors in up directions.

GNSS/RNSS Integrated PPP Time Transfer: Performance with Almost Fully Deployed Multiple Constellations and a Priori ISB Constraints Considering Satellite Clock Datums

Currently, the space segment of all the five satellite systems capable of providing precise time transfer services, namely BDS (including BDS-3 and BDS-2), GPS, GLONASS, Galileo, and Quasi-Zenith Satellite System (QZSS), has almost been fully deployed, which will definitely benefit the precise time transfer with satellite-based precise point positioning (PPP) technology. This study focuses on the latest performance of the BDS/GPS/GLONASS/Galileo/QZSS five-system combined PPP time transfer. The time transfer accuracy of the five-system integrated PPP was 0.061 ns, and the frequency stability was 1.24 × 10−13, 2.28 × 10−14, and 8.74 × 10−15 at an average time of 102, 103, and 104 s, respectively, which significantly outperforms the single-system cases. We also verified the outstanding time transfer performance of the five-system integrated PPP at locations with limited sky view. In addition, a method is proposed to mitigate the day-boundary jumps of inter-system bias (ISB) estimates by considering the difference in the satellite clock datums between two adjacent days. After applying a priori ISB constraints, the time transfer accuracy of the five-system integrated PPP can be improved by 37.9–51.6%, and the frequency stability can be improved by 14.8–21.6%, 5.3–7.6% and 20.0–29.6% at the three average times, respectively.

An extended inter-system biases model for multi-GNSS precise point positioning

The inter-system bias (ISB) is an important parameter in multi-GNSS precise point positioning (PPP). However, on the one hand, the generation mechanism and error components of ISB are not clear. On the other hand, it is unclear whether the ISB parameter should be added to the BDS-2/BDS-3 combined PPP. First, in order to solve these problems, an extended ISB mathematical model is proposed, which unifies the common errors between receiver and satellite, and extends the original ISB model. Second, to demonstrate the correctness of the new model, the components of the new ISB model are verified, and then it is used to explain whether the ISB parameter should be added to BDS-2/BDS-3 combined PPP. Furthermore, 41 stations from the MGEX network and precise products from COD (Center for Orbit Determination in Europe), GBM (Deutsches GeoForschungsZentrum) and WUM (Wuhan University) are used to calculate and analyze the multi-GNSS PPP and ISB during day of year (DOY) 307–365, 2020. Finally, we propose to use a different estimation method of ISB with different precise products to improve the positioning accuracy and shorten the convergence time. The experimental results show that: (1) ISB parameter is composed of five parts: time system error, receiver hardware delay, signal distortion biases (SDB), MGEX-realized (multi-GNSS experiment) time scale and other unmodeled deviations. (2) Due to different receiver hardware delay, SDB and MGEX-realized time scale between BDS-2 and BDS-3, it is necessary to add an ISB parameter in BDS-2/BDS-3 PPP. (3) In multi-GNSS PPP, if the ISB changes greatly but the traditional constant method is used to estimate the ISB parameter, the impact on single station PPP coordinates can reach decimeters. The statistical results demonstrate that the RMS of GBM(CON(Constant)) in East (E), North (N) and Up (U) directions are 2.34 cm, 0.60 cm, and 1.59 cm, respectively, while the RMS of GBM(RWK(Random walk)) decreased by 59.8 %, 13.3 %, and 18.2 %, respectively.

Evaluating the Performance of Two Inter-Frequency Code Bias (IFCB) Models in Combined Precise Point Positioning (PPP)

The main purpose of this article is to evaluate the comprehensive performance of two inter-frequency code bias (IFCB) models using undifferenced and uncombined observations. These two IFCB models estimate IFCB parameters for each GLONASS satellite (EG model) and IFCB parameters using a quadratic function of frequency channels K (K = −7…6) (QF model). The data sampled in 30 s from 140 stations of the IGS network on 1–7 September 2021, are used for this study. We analyze all the combinations, including the GLONASS data, from the perspective of positioning accuracy, convergence time, and data utilization. The results show that the positioning accuracy of these two IFCB models for the same combination is comparable in three directions in both static and kinematic modes under long-term observation; the positioning accuracies of each IFCB model for all the combinations are almost the same in three directions in static mode, and the positioning accuracy of the combinations including the GPS data in three directions is better than that of the combinations not including the GPS data for kinematic mode. For some combinations, such as GLONSS-only and GPS/GLONASS, the convergence time of the EG model is better than that of the QF model, but the improvement rate does not exceed 22%. However, for other combinations, such as GLONASS/BDS and GLONASS/BDS/GALILEO, the convergence time of the QF model is better than that of the EG model, and the improvement rate in some directions is more than 50%. For the combinations including GPS data, the data utilization of the EG and QF models are almost the same for both static and kinematic modes; however, for combinations without GPS data, the data utilization of the QF model is better than that of the EG model. For these two IFCB models (EG and QF models), all combinations can achieve the set accuracy thresholds in three directions, but the EG model has more parameters to estimate than the QF model. From the perspectives of positioning accuracy, solution convergence time, data utilization, and the number of estimated parameters for each IFCB model, we suggest that the IFCB should be estimated using the QF model when performing combined PPP for different combinations.

BeiDou intra-system bias using different precise orbit and clock products

An intra-system bias (ISB) is a necessary parameter in the BeiDou Navigation Satellite System (BDS)-2 and BDS-3 integrated precise point positioning (PPP); however, its influence in BDS-2/BDS-3 combined processing remains unclear. This paper investigates the ISB effects on the combined PPP using different precise orbit and clock products. Considering an increasing number of BDS products, a comprehensive evaluation of the products is undertaken before validating with PPP tests. Results indicate that BDS-2 Wuhan University (WUM) orbital differences outweigh Centre National d’Etudes Spatiales (CNT), Shanghai Observatory (SHA), and Information and Analysis Center (IAC) orbits. Moreover, BDS-3 constellation registers better clock performance than BDS-2 using any MGEX product. Furthermore, introducing the ISB into the combined processing of BDS-2 and BDS-3 improves both the positioning performance and convergence time for all products. The best improvement in positioning performance is achieved when Deutsches GeoForschungsZentrum (GBM) product is employed. Finally, it is found that considering the ISB in the PPP model affects the code more than the phase observations.

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.

Application of Multi-System Combination Precise Point Positioning in Landslide Monitoring

To verify the positioning performance and reliability of multi-system combination Precise Point Positioning in landslide monitoring, we carried out a multi-system combination Precise Point Positioning calculation experiment on the monitoring data of a single landslide disaster area in Fujian Province. The coordinates of the monitoring points obtained by a continuously operating reference station and the monitoring station for static relative positioning were used as reference values. The GPS system was used as the standard system and the combined PPP solution mode of G/R/C, G/R/E and G/R/E/C was used to obtain the surface displacement of the landslide area. The research showed that multi-system combination PPP converges to the centimeter level in about 30 min. The average value of internal accordant precision was more than 1 mm after convergence, and that of the external accordant precision was more than 5 cm, which meets the centimeter-level accuracy requirements in rapid landslide deformation monitoring.

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.

Modeling and performance assessment of BDS-2/BDS-3 triple-frequency ionosphere-free and uncombined precise point positioning

The global BeiDou Navigation Satellite System (BDS-3) and regional system (BDS-2) are transmitting signals on three or more frequencies, which brings more choices and practical potentials. To deeply integrate and fully utilize the BDS-2 and BDS-3 signals, this research is dedicated to the modeling and assessment of BDS-2/BDS-3 combined triple-frequency precise point positioning (PPP). Using ionosphere-free (IF) or uncombined (UC) observables, the three BDS-2/BDS-3 combined triple-frequency PPP models, named IF1213, IF123 and UC123 are developed. Particularly, new biases such as time delay bias (TDB) and inter-frequency bias (IFB) as well as the parameterizations are addressed. One-month observations from 16 Multi-GNSS Experiment (MGEX) stations located in and around the Asia-Pacific region are utilized to validate and compare the models. The results indicate that the three BDS-2/BDS-3 combined triple-frequency PPP models have the comparable performance and the third frequency makes a marginal contribution to positioning and tropospheric delay retrieval. The TDB should be carefully considered in BDS-2/BDS-3 combined PPP, especially for the IF123 model due to the larger absolute values of TDB. Meanwhile, the IFB derived from receiver uncalibrated code delay difference shows good stability in both short-term (intra-day) and long-term (inter-day) periods. In addition, demonstrated by triple-frequency PPP tests with one-month data from 47 global MGEX stations, the BDS-2/BDS-3 combined constellation allows for significantly improved convergence performance and positioning accuracy over the BDS-2-only constellation. The BDS-3 system has the ability to provide the precise positioning accuracy of 12.1/9.8/15.8 mm on a global scale after the convergence time of 23.0/13.2/24.7 min in east/north/up components.

Characterization of Inter-System Biases in GPS + BDS Precise Point Positioning

With the combination of multi-GNSS data, the precise-point positioning (PPP) technique can improve its accuracy, availability and reliability: Inter-system bias (ISB) is the non-negligible parameter in multi-GNSS PPP. To further enhance the performance of multi-GNSS PPP, it is crucial to analyze the characterization of inter system biases (ISBs) and model them properly. In this contribution, we comprehensively investigate the characterization of ISBs between global positioning system (GPS) and BeiDou navigation satellite system (BDS) in different situations. (1) We estimate ISB by using different precise products from the Center for Orbit Determination (CODE), Deutsches GeoForschungsZentrum (GFZ) and Wuhan University (WHU). The results indicate that the one-day estimates of ISB are stable when using CODE and WHU products, whereas the estimates based on GFZ products vary remarkably. As for the three-day time series of ISB, a sudden jump exists between two adjacent days, which is due to the change of satellite clock datum; (2) We investigate the ISB characterization affected by the ambient environments of the receivers. The result shows that the ISBs estimated from receivers (and antennas) with same type are still inconsistent, which indicates that the ambient environment, probably the temperature, influences the ISB characterization as well, since the receivers are in different areas; (3) We analyze the ISB characterization affected by receiver and antenna type with the same ambient environment. To ensure the same ambient environment, the ultra-short baselines were applied to investigate the ISB characterization affected by the receiver and antenna type. With the insights into ISB characterizations, we carry out combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The results suggest that the random walk process outperforms in most cases, since it strengthens the model to some extend and, at the same time, considers the variation of ISBs.

Investigation of real-time kinematic multi-GNSS precise point positioning with the CNES products

The performance of precise point positioning (PPP) is easily affected by the observation environment, satellite number, spatial geometry and the accuracy of the external data products being used. In this study, we formulate the mathematical model of multi-GNSS PPP and assess the performance of dual- and triple-frequency PPP modes using the real-time products from the Centre National d’Etudes Spatiales (CNES). For real-time dual-frequency PPP performance, the results show that, no significant differences can be observed from different combined PPP modes at a low cut-off angle (e.g. 10°). With the increase of the elevation cut-off angle, the multi-GNSS PPP shows a better performance in the convergence speed and positioning accuracy, especially in the early stage of convergence. Of all six PPP modes, the convergence time of GPS/BDS/GLONASS/GALILEO PPP is the shortest one under the elevation cut-off angle of 30°. Compared with GPS-only, the convergence time is reduced by 47.6% when converging to 0.2 m, and by 30.4% when converging to 0.1 m. For the position accuracy, under the elevation cut-off angle of 30°, 80.4% of positioning biases are within 0–10 cm in horizontal direction, and 91.0% within 0–20 cm in vertical direction for the GPS/BDS/GLONASS/GALILEO combined PPP. In addition, the convergence performance of triple-frequency PPP is improved by at least 36.4% in two schemes compared with dual-frequency PPP. The accuracy also be improved, with a mean RMS of about 2.9, 3.2 and 6.0 cm in East, North and Up directions.

GPS\u2009+\u2009Galileo\u2009+\u2009BeiDou precise point positioning with triple-frequency ambiguity resolution

Along with the rapid development of GNSS, not only BeiDou, but also Galileo, and the newly launched GPS satellites can provide signals on three frequencies at present. To fully take advantage of the multi-frequency multi-system GNSS observations on precise point positioning (PPP) technology, this study aims to implement the triple-frequency ambiguity resolution (AR) for GPS, Galileo, and BeiDou-2 combined PPP using the raw observation model. The processing of inter-frequency clock bias (IFCB) estimation and correction in the context of triple-frequency PPP AR has been addressed, with which the triple-frequency uncalibrated phase delay (UPD) estimation is realized for real GPS observations for the first time. In addition, the GPS extra-wide-line UPD quality is significantly improved with the IFCB correction. Because of not being contaminated by the IFCB, the raw UPD estimation method is directly employed for Galileo which currently has 24 satellites in operation. An interesting phenomenon is found that all Galileo satellites except E24 have a zero extra-wide-lane UPD value. With the multi-GNSS observations provided by MGEX covering 15 days, the positioning solutions of GPS + Galileo + BeiDou triple-frequency PPP AR have been conducted and analyzed. The triple-frequency kinematic GNSS PPP AR can achieve an averaged 3D positioning error of 2.2 cm, and an averaged convergence time of 10.8 min. The average convergence time can be reduced by triple-frequency GNSS PPP AR by 15.6% compared with dual-frequency GNSS PPP AR, respectively. However, the additional third frequency has only a marginal contribution to positioning accuracy after convergence.

A method for undifferenced and uncombined PPP ambiguity resolution based on IF FCB

The integer characteristics of the undifferenced ambiguity can be recovered after the correction of fractional cycle biases (FCB), which can significantly shorten the initialization time of precise point positioning (PPP). In the former work, the ambiguity resolution model of the client end needs to be consistent with the FCB products server. However, the client may face the problem that inconsistent FCB products are provided and cannot be used to fix the ambiguity. We propose a new method for client of undifferenced and uncombined PPP ambiguity resolution based on FCB product of ionosphere-free combination PPP model. The hardware delay in server of ionosphere-free combination FCB (IF FCB) and undifferenced and uncombined FCB (L1L2 FCB) are deduced in detail. Constructing the narrow-lane ambiguity by using the raw ambiguity and the wide-lane ambiguity, the FCB product of the ionosphere-free combination PPP model is used to fix the ambiguity step by step. A globally distributed network consisting of about 118 MGEX stations is selected as the server end. Two types of FCB products, i.e., IF FCB and L1L2 FCB, are generated. 50 additional MGEX stations in global are selected as client end for performance assessment. The experimental results show that the new method for client of UU PPP model based on the IF FCB products has a comparable performance with the traditional method based on L1L2 FCB products, which improves the utilization of FCB products.

BDS/GPS/LEO triple-frequency uncombined precise point positioning and its performance in harsh environments

Precise point positioning (PPP) usually takes a few tens of minutes to achieve centimeter-level positioning accuracy, and reliable ambiguity resolution also requires a relatively long observation time. In addition, the time required will be longer in harsh environments such as urban and canyons. These problems limit the application of PPP. Currently, low earth orbit (LEO) enhanced Global Navigation Satellite System (GNSS) can increase the number of visible satellites and optimize observation structure, which is expected to improve the positioning performance of GNSS-only PPP under complex conditions. In this paper, the performance of LEO/GNSS combined PPP in harsh environments is evaluated initially. First, triple-frequency uncombined PPP model is developed. Then, a LEO constellation consisting of 180 polar-orbiting satellites is designed, and BDS-3 and current GPS constellation are also simulated for subsequent analysis. Besides, the corresponding observation simulation is also carried out. In order to better analyze the performance of LEO enhanced GNSS PPP in harsh environments, six sets of contrast experiments are designed. Both PPP float solution and fixed solution are processed. In term of float solution, it usually takes about 30 min for BDS-only to converge into 5 cm, while the BDS/LEO combination only takes about 10 min in extremely harsh environments. Compared with BDS-only, the accuracy of float solution of BDS/GPS, BDS/LEO, BDS/GPS/LEO combined PPP is improved by 42.44%, 73.77%, and 77.43%, respectively. In term of fixed solution, compared BDS-only, the average time to first fix (TTFF) of BDS/GPS, BDS/LEO, BDS/GPS/LEO combination can be shortened from 20.0 min to 10.3 min, 4.8 min and 4.0 min respectively. The fix rate of epochs increases from 83.8% to 91.6%. 96.1% and 96.7% in harsh environments, respectively. Compared with the float solution, the positioning accuracy of fixed solution in N, E, and U directions increases by 3.6%, 4.6%, and 3.2%, respectively.

Assessing the contribution of Galileo to GPS+GLONASS PPP: Towards full operational capability

By the end of 2018, the Galileo constellation consisted of four in-orbit validation (IOV) satellites and 22 full operational capability (FOC) satellites. Except for GPS and GLONASS, the FOC of Galileo has not been reached. In 2018, four Galileo FOC satellites were launched. With these launches, most of the Galileo FOC has been reached. In this paper, the latest contribution of the Galileo constellation to GPS+GLONASS combined Multi-GNSS precise point positioning (PPP) solutions is analyzed in terms of static/kinematic accuracy and convergence time. Three different elevation cut-off angles (5°,-15°,-30°) are chosen to simulate the ideal and restricted satellite visibilities. A two-month period and a one-week period in 2019 are chosen for conducting static and kinematic PPP, respectively, using the data of 20 Multi-GNSS Experiment (MGEX) stations. Non-overlapping sessions of 24, 12, 6, 3, 1, and 0.5 h within two months are processed for static PPP to analyze the effect of the Galileo contribution to static PPP for each observation length and cut-off angle. GipsyX scientific software developed by NASA’s Jet Propulsion Laboratory (JPL) is used for PPP processes. The statistical results show that the contribution of Galileo generally becomes higher as the observing sessions become shorter, but no significant correlation between the contribution of Galileo and observing session is found for each station. The largest horizontal and vertical accuracy improvements of Galileo are observed as 8 mm/11 mm (47%/61%) and 23 mm/30 mm (20%/48%) for static and kinematic PPP, respectively. The accuracy degradation is observed more in the vertical component for some stations when adding Galileo to GPS+GLONASS combined static and kinematic PPP. The Galileo contributions to minimum, maximum, and mean convergence times are also computed for both static and kinematic PPP. The largest improvement show that mean horizontal and vertical convergence times are shortened by 24 min/24 min (52%/45%) and 61 min/23 min (89%/62%) for static and kinematic PPP, respectively. The results also show that outliers can be reduced significantly for most of the stations by adding Galileo to the GPS+GLONASS combined PPP for short observation sessions.

GPS and BDS combined PPP model with inter-system differenced observations

This study proposes a combined precise point positioning (PPP) model, called the inter-system differenced PPP model, in which it formed the satellite-differenced observation between different satellite systems. Compared with the traditional combined PPP model, the inter-system differenced PPP model has the following characteristics: (1) The satellite difference between various systems can eliminate the receiver clock bias parameter, it enhances the strength of the PPP model. (2) Inter-satellite differences can eliminate some common model errors and reduce the impact of observation errors. (3) The system time difference can be calculated directly to provide the basis for time offset monitoring. In order to verify the positioning results of the inter-system differenced model, static PPP and dynamic PPP experiments were carried out to test the positioning accuracy and convergence time, and the results were compared with those of the traditional combination PPP model. In addition, the offset characteristics introduced by the inter-system differenced model were analysed, and the optimal estimation strategy was determined by dynamic PPP tests. Preliminary results are as follows: (1) For inter-system differenced static PPP, the convergence time of stations is less than 20 min. The standard deviation (STD) of the position bias for the East (E), North (N), and Up (U) components are better than 2.5 cm, 1.0 cm and 3.0 cm, respectively, and the corresponding root mean square deviation (RMS) are better than 3.0 cm, 1.5 cm and 6.0 cm, respectively. Compared with the traditional combined PPP model, the average convergence time of the inter-system differenced model is nearly the same, but its overall positioning accuracy is better. (2) For the inter-system differenced dynamic PPP model, the convergence time of stations is better than 30 min. The STD of the position bias for the E, N, and U components is better than 3.0 cm, 2.0 cm and 4.5 cm respectively, and the RMS is better than 4.0 cm, 2.5 cm and 7.0 cm respectively. Compared with the traditional combined PPP model, the convergence of the inter-system differenced model is slightly better, and the positioning accuracy does not differ significantly. Moreover, the inter-system differenced model is much better than the traditional model when fewer satellites are available. (3) The offset between GPS and BDS corresponding with the precise products of GFZ is related to the type of receiver, and the daily standard of offset is less than 0.5 ns. In addition, we determined optimum process noise of the offset parameter to be a 10-3/3(m2/s) random walk after comparing several options.

Mitigation of Unmodeled Error to Improve the Accuracy of Multi-GNSS PPP for Crustal Deformation Monitoring

High-rate multi-constellation global navigation satellite system (GNSS) precise point positioning (PPP) has been recognized as an efficient and reliable technique for large earthquake monitoring. However, the displacements derived from PPP are often overwhelmed by the centimeter-level noise, therefore they are usually unable to detect slight deformations which could provide new findings for geophysics. In this paper, Global Positioning System (GPS), GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS), and BeiDou navigation satellite system (BDS) data collected during the 2017 Mw 6.5 Jiuzhaigou earthquake were used to further exploit the capability of BDS-only and multi-GNSS PPP in deformation monitoring by applying sidereal filtering (SF) in the observation domain. The equation that unifies the residuals for the uncombined and undifferenced (UCUD) PPP solution on different frequencies was derived, which could greatly reduce the complexity of data processing. An unanticipated long-term periodic error term of up to ± 3 cm was found in the phase residuals associated with BDS satellites in geostationary Earth orbit (GEO), which is not due to multipath originated from the ground but is in fact satellite dependent. The period of this error is mainly longer than 2000 s and cannot be alleviated by using multi-GNSS. Compared with solutions without sidereal filtering, the application of the SF approach dramatically improves the positioning precision with respect to the weekly averaged positioning solution, by 75.2%, 42.8%, and 56.7% to 2.00, 2.23, and 5.58 cm in the case of BDS-only PPP in the east, north, and up components, respectively, and 71.2%, 27.7%, and 37.9% to 1.25, 0.81, and 3.79 cm in the case of GPS/GLONASS/BDS combined PPP, respectively. The GPS/GLONASS/BDS combined solutions augmented by the SF successfully suppress the GNSS noise, which contributes to the detection of the true seismic signal and is beneficial to the pre- and post-seismic signal analysis.