Precise Point Positioning Research Articles

Algorithms Research and Precision Comparison of Different Frequency Combinations of BDS-3\GPS\Galileo for Precise Point Positioning in Asia-Pacific Region.

With the continuous construction and development of the BeiDou navigation satellite system (BDS), its positioning performance is constantly being improved. In this study, the positioning performance of different frequency combinations of BDS-3/GPS/Galileo in the Asia-Pacific region was investigated. The precision products of Wuhan University and the observation data of nine MGEX stations were selected to compare and analyze the B1I\B1C\B2a\B3I and L1\E1 pseudo-range Standard Point Positioning (SPP) and B1IB2a\B1IB3I\B1CB2a\B1CB3I\B2aB3I\L1L2\E1E5a precise point positioning (PPP) performance, while B1I\B3I\L1 SPP and B1IB3I PPP were investigated using BDS-2 with QZSS supplemented with BDS-3 and GPS. The experimental results showed that the positioning precision of BDS-3/GPS/Galileo SPP was in the order of B1C > E1 > L1 > B1I > B3I > B2a, and it was not significantly improved after BDS-2 and QZSS were added. Moreover, for the PPP of different frequency combinations, the convergence speed was in the order of L1L2 > B1IB3I > E1E5a > B1CB3I > B1CB2a > B1IB2a > B2aB3I. After adding BDS-2, B1IB3I improved by about 11% in static mode and 27% in kinematic mode, which was similar to the L1L2 frequency combination. The positioning precision of different frequency combinations of BDS-3/GPS/Galileo was B1IB3I > B1CB3I > L1L2 > E1E5a > B1B2a > B1CB2a > B2aB3I. In static mode, after adding BDS-2, B1IB3I did not show significant improvement in the plane direction, and showed ~61% improvement in the elevation direction, and ~67% in the three-dimensional (3D) direction. In kinematic mode, after adding BDS-2, B1IB3I was improved by about 16% in the E direction, the N direction did not show significant change, it improved by ~38% in the U direction and by ~70% in the 3D direction. In general, the positioning performance of BDS-3 was slightly better than those of GPS and Galileo in the Asia-Pacific region, and it is believed that with the continuous development of BDS, its positioning performance will surely be improved further.

Properties of multi-GNSS uncalibrated phase delays with considering satellite systems, receiver types, and network scales

The Wide-Lane (WL) and Narrow-Lane (NL) Uncalibrated Phase Delays (UPDs) are the prerequisites in the traditional Precise Point Positioning (PPP) Ambiguity Resolution (AR). As the generation mechanism of various biases becomes more complex, we systematically studied the impact factors of four satellite systems WL and NL UPDs from the perspective of parameter estimation. Approximately 100 stations in a global network are used to generate the UPDs. The results of different satellite systems show that the estimation method, update frequency, and solution mode need to be treated differently. Two regional networks with different receiver types, JAVAD, and Trimble, are also adopted. The results indicate that the receiver-dependent bias has an influence on UPD estimation. Also, the hardware delays can inhibit the satellite-side UPDs if these receiver-specific errors are not fully deployed or even misused. Furthermore, the temporal stability and residual distribution of NL UPDs are significantly enhanced by utilizing a regional network, with the improvements by over 68% and 40%, respectively. It demonstrates that different network scales exhibit the different implication of unmodeled errors, and the unmodeled errors cannot be ignored and must be handled in UPD estimation.

On the role of lidar measurements in speeding up precise point positioning convergence

Global navigation satellite system (GNSS) and light detection and ranging (lidar) are well known to be complementary for vehicle positioning in urban canyons, where GNSS observations are prone to signal blockage and multi-path. As one of the most common carrier-phase-based precise positioning techniques, precise point positioning (PPP) enables single-receiver positioning as it utilizes state-space representation corrections for satellite orbits and clocks and does not require a nearby reference station. Yet PPP suffers from a long positioning convergence time. In this contribution, we propose to reduce the PPP convergence using an observation-level integration of GNSS and lidar. Lidar measurements, in the form of 3D keypoints, are generated by registering online scans to a pre-built high-definition map through deep learning and are then combined with dual-frequency PPP (DF-PPP) observations in an extended Kalman filter implementing the constant-velocity model that captures the vehicle dynamics. We realize real-time PPP (RT-PPP) in this integration using the IGS real-time service products for vehicle positioning. Comprehensive analyses are provided to evaluate different combinations of measurements and PPP corrections in both static and simulated kinematic modes using data captured by multiple receivers. Experimental results show that the integration achieves cm-level accuracy and instantaneous convergence by using redundant measurements. Accordingly, for classical PPP accuracy of 10 cm and convergence within minutes, respectively, lidar input is only required once every 10 s.

Image Mapping Accuracy Evaluation Using UAV with Standalone, Differential (RTK), and PPP GNSS Positioning Techniques in an Abandoned Mine Site.

Global navigation satellite systems (GNSSs) provide a common positioning method that utilizes satellite signals to determine the spatial location of a receiver. However, there are several error factors in standalone GNSS positioning due to instrumental, procedural, and environmental factors that arise during the signal transmission process, and the final positioning error can be up to several meters or greater in length. Thus, real-time kinematic (RTK) correction and post-mission precise point positioning (PPP) processing technologies are proposed to improve accuracy and accomplish precise position measurements. To evaluate the geolocation accuracy of mosaicked UAV images of an abandoned mine site, we compared each orthomosaic image and digital elevation model obtained using standalone GNSS positioning, differential (RTK) GNSS positioning, and post-mission PPP processing techniques. In the three types of error evaluation measure (i.e., relative camera location error, ground control points-based absolute image mapping error, and volumetric difference of mine tailings), we found that the RTK GNSS positioning method obtained the best performance in terms of the relative camera location error and the absolute image mapping error evaluations, and the PPP post-processing correction effectively reduced the error (69.5% of the average total relative camera location error and 59.3% of the average total absolute image mapping error) relative to the standalone GNSS positioning method. Although differential (RTK) GNSS positioning is widely used in positioning applications that require very high accuracy, post-mission PPP processing can also be used in various fields in which it is either not feasible to operate expensive equipment to receive RTK GNSS signals or network RTK services are unavailable.

Method of Development of a New Regional Ionosphere Model (RIM) to Improve Static Single-Frequency Precise Point Positioning (SF-PPP) for Egypt Using Bernese GNSS Software

Due to the lack of coverage of IGS in Africa, especially over North Africa, and the construction revolution of infrastructure in Egypt, a geodetic CORS stations network was established in 2012. These CORS stations are operated by the Egyptian Surveying Authority (Egy. SA) and cover the whole of Egypt. The paper presents a fully developed regional ionosphere model (RIM) depending on the Egyptian CORS stations. The new model and the PPP solution were obtained using Bernese GNSS V. 5.2 software. An observation data series of eight days (DOY 201–208)/2019 was used in this study. Eighteen stations were used to develop the RIM model for each day; fifteen stations were used to validate the new RIM model. A static SF-PPP solution was obtained using the CODE-GIM and RIM models. Comparing the outcomes to the reference network solution, based on the recently developed RIM model, the solution showed a mean error of 0.06 m in the East direction, 0.13 m in the North direction, and 0.21 m in the height direction. In the East, North, and height directions, this solution improves the SF-PPP result achieved by the Global Ionosphere Maps (CODE-GIM) model by 60%, 68%, and 77%, respectively.

Carrier Phase Residual Modeling and Fault Monitoring Using Short-Baseline Double Difference and Machine Learning

Global Navigation Satellite Systems (GNSS) are used to provide accurate position, navigation, and time (PNT) information to users in various sectors of our society including transportation. Augmentation systems such as differential GNSS (DGNSS), real-time kinematics (RTK), and Precise Point Positioning (PPP) improve the GNSS performance, and providing reliable measurements from its reference station is very crucial. To ensure safe and accurate PNT solutions, code and carrier measurements must be monitored for potential faults or a performance degrade. Although there exist numerous methods to model and monitor the measurements, research on the carrier phase measurements is not as extensive as the code measurements. This paper introduces a split of residuals into receiver noise and multipath components to customize their estimation according to their respective statistical properties. This study also proposes a method to use machine learning-based non-linear regression to effectively model and monitor potential faults in the GNSS measurements including the carrier phase. A training dataset is used to model the nominal quantities of GNSS measurement residuals, and inflation factors are applied to over-bound the fault-free residuals. These inflated residuals are coupled with uncertainty factors to compute thresholds for monitoring carrier phase residuals, and the effectiveness of the thresholds is validated with a test dataset by achieving the false alarm rate of 6.61×10−6, slightly lower than the desired level of 10−5.

Analysis of the effect of the 2021 Semeru eruption on water vapor content and atmospheric particles using GNSS and remote sensing

Mount Semeru, an active volcano in East Java, Indonesia, erupted on December 4, 2021, following extreme rainfall that caused an avalanche of hot pyroclastic flows and lava. The tropospheric conditions and dominant particle components in the atmosphere can be monitored using Global Navigation Satellite System (GNSS) technology and remote sensing satellites. GNSS signal propagation delay in Precise Point Positioning (PPP) processing can be used to determine Zenith Tropospheric Delay (ZTD) and Precipitable Water Vapor (PWV) variables so that atmospheric conditions can be generated. In addition, by using remote sensing satellite data, it is possible to obtain rainfall data with high temporal resolution as well as the dominant particle and gas content values during eruptions. During the eruption period, the high value of PWV was dominated by the high intensity of precipitation during the rainy season. High rainfall before the eruption caused activity inside the mountain to increase, which occurred in avalanche type eruption. Apart from that, the atmosphere around Semeru was also dominated by SO2 content, which spreaded for tens of kilometers. SO2 content began to be detected significantly by remote sensing sensors on December 7, 2021. In this study, deformation and atmospheric monitoring were also carried out using low-cost GNSS at the Semeru Monitoring Station on September 9–15, 2022. The results of the ZTD and ZWD values show the dominance of the wet component, which is directly proportional to rainfall activity in this period.

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.

TECX-TCN: Prediction of ionospheric total electron content at different latitudes in China based on XGBoost algorithm and temporal convolution network

The correction of ionospheric delay error through the estimation of ionospheric total electron content (TEC) parameters is very important for the accuracy and rapid convergence of precise point positioning (PPP), especially for single frequency PPP position and double frequency undifferenced and uncombined PPP models. This paper studies the prediction method of ionospheric TEC by analyzing various influencing factors. Firstly, considering the influence of latitude, the TEC values of different observation stations in China at middle and low latitudes are used for research. Secondly, due to the influence of solar storms, the years with and without solar storms are selected for comparative study. At the same time, the moving average value of TEC and the lag value of each solar and geomagnetic index are also added. Because the influence of each feature on ionospheric TEC is not clear, the importance score of each feature is obtained according to the EXtreme Gradient Boosting (XGBoost) algorithm to establish a reasonable feature combination. Then, the temporal convolution network (TCN) is used to train according to data of the collected solar cycle and predict data for the next year. Through experiments, the prediction model with feature selection can obtain higher prediction accuracy, the error reaches ∼2TECU at middle latitude region and ∼3 TECU at low latitude region. Finally, compared with other algorithms, our ionospheric TEC prediction algorithm based on XGBoost and TCN (TECX-TCN) significantly has better performance. When the solar activity is low, its RMSE can reach ∼2.5TECU, the correlation coefficient can reach ∼0.9, and even in the low latitude area with high solar activity, its RMSE can reach ∼5TECU, the correlation coefficient can reach ∼0.85.

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning, the ideal estimator in the least-squares (LS) can be obtained only by using the suitable stochastic model. This study investigates the role of variance component estimation (VCE) in the LS method for Precise Point Positioning (PPP). This estimation is performed by considering the ionospheric-free (IF) functional model for code and the phase observation of Global Positioning System (GPS). The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes: a) antenna type, b) receiver type, c) the tropospheric effect, and d) the ionosphere effect. The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model. This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions. Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE. The position error difference for the east-west, north-south, and height components was 1.5 cm, 4 mm, and 1.8 cm, respectively. Therefore, weight estimation with LS-VCE can provide more appropriate results. Eventually, the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight. According to the results, the LS-VCE has a higher convergence rate than the nominal weight. The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11, 13, 12, and 9 min, respectively.

Sequential Generation of Multi-GNSS Multi-Frequency PPP-RTK Products and Their Performance Using the EUREF Permanent GNSS Network

In the classic Precise Point Positioning (PPP) approach, observations of Global Navigation Satellite Systems (GNSS) are processed at the network level to generate satellite clocks and positions. This information can be used to enable accurate point positioning for a single GNSS receiver. In the PPP Real-Time Kinematic (PPP-RTK) approach, satellite phase biases are considered as well, enabling ambiguity resolution at the network and user levels. In this research, 30 s multi-frequency raw GPS, Galileo, and BDS-2/3 observations are processed at the network and user levels in a sequential Kalman filter. PPP-RTK enabling products are generated for up to five frequencies, and ambiguity resolution is performed at the network and user levels using a flexible ambiguity reparameterization approach, comparable to wide- and narrow-laning, which has shown to yield a significantly improved single epoch coordinate solution when multi-frequency observations are available. Different assumptions regarding the time stability of receiver and satellite phase biases have been made and compared. The availability of a precise user coordinate solution when multi-frequency and dual-frequency observations are processed is assessed and compared. A precise ambiguity-fixed solution is available in three epochs or fewer in 77% of all cases with an average of 24 visible satellites for static and kinematic receivers when multi-frequency observations are processed. When only dual-frequency observations are considered, a fixed solution is available in seven epochs or fewer in 71% of all cases. The fastest fixed solution was found in two epochs with multi-frequency observations and in six epochs with dual-frequency observations. Estimating a reference phase clock did not lead to an improvement in the coordinate solution. The findings indicate that a fixed solution can potentially be found faster than often suggested, with potential for further improvement when more satellites or regional atmospheric corrections are considered.

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.

A PPP-RTK APPROACH TO MASS-MARKET APPLICATIONS

Abstract. PPP-RTK has been widely investigated to take the advantages of both real-time kinematic (RTK) and precise point positioning (PPP) techniques. Prior to PPP-RTK, the conventional RTK based on the use of a single base station, on the one hand, has been extended to work within a regional network of multiple base stations, known as network RTK (NRTK). The RTK and NRTK enable fast ambiguity resolution over a short baseline or a local region. PPP, on the other hand, eliminates the need to establish any local network like NRTK, which is able to work in a single receiver mode but it suffers long convergence time in ambiguity resolution. PPP-RTK therefore can provide fast ambiguity resolution capability like RTK and NRTK. Current PPP-RTK techniques however still face challenges in supporting mass-market applications such as mobile devices and autonomous vehicles. Although PPP-RTK system (a combination of RTK and PPP technologies) can help expand the coverage of RTK and speed up the ambiguity resolution in PPP, the deployment and maintenance of a dense network of permanent base stations and a central data processing infrastructure for generation of SSR corrections increases not only the system cost but also the system complexity. This is particularly an obstacle for mass-market applications. In this paper, a new RTK approach is described. First it is based on a single base station state-space-representation (SSR) correction generation strategy to support fast ambiguity resolved PPP. Further it presents a new peer-to-peer propagation strategy to form a real-time dynamically generated network of base stations to support mass-market application users with unbounded coverage. As a result, the new approach eliminates the need to deploy and maintain a dense network of permanent base stations and central data processing infrastructure as required in a conventional PP-RTK system.

Crustal displacement in Vietnam using CORS data during 2018 - 2021

Continuously Operation Reference Stations (CORS) networks provide surveying, mapping, and positioning services and play a crucial role in determining crustal displacement. This study processed the continuous Global Navigation Satellite System (GNSS) data collected from 55 CORS stations in the TAST’s CORS in Vietnam to determine the crustal displacement in Vietnam from 2018 to 2021. The processing was performed using online Precise Point Positioning (PPP) services and the displacement model to estimate the velocity of the position time series. The result showed that the horizontal velocity field of all CORS stations is uniform in magnitude and direction, ranging from 25.3 to 42.6 mm/year with accuracy from ±0.1 to ±1.0 mm/year in the south-east direction in the International Terrestrial Reference Frame 2014 (ITRF2014). This study confirms the stability and accuracy of GNSS data from the TAST’s CORS network for crustal displacement analysis.

LEO navigation augmentation constellation design and precise point positioning performance analysis based on BDS-3

Low Earth orbit (LEO) satellites have high signal strength and faster geometry changes over short periods, offering unique advantages in navigation augmentation. Integrating LEO satellites into the navigation system can help augment the performance of the global satellite navigation system and break the dilemma of the existing navigation system with limited services in challenging environments. Constellation design is the key before establishing a complete LEO navigation augmentation platform. Therefore, in this study, two LEO navigation augmentation constellations, Polar/Walker (S1) and Walker/Walker (S2) with different inclinations, are designed and optimized using the non-dominated sorting genetic algorithm III (NSGA-III). The global average geometric dilution of precision (GDOP) of BDS-3 is reduced from 1.56 to 0.92 and 0.95, and the average visible satellite number is improved from 11.74 to 27.83 and 25.72 with the navigation augmentation of the optimized constellations. To further validate the navigation augmentation effect of two LEO constellations on BDS-3 precision point positioning (PPP), nine stations at different latitudes were selected for LEO augmented BDS-3 PPP simulation experiments. The results show that after adding S1 and S2 constellations to BDS-3, respectively, the convergence times of the nine stations are reduced by 35.5%∼96.5% and 43.7%∼96.2%, and the positioning accuracy is improved by 5.7%∼71.9% and 24.2%∼69.5%, respectively. Overall, each S1 and S2 constellations can significantly improve the global service performance and PPP performance of BDS-3.

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.

A Dynamic Continuous Constrained Phase Factor Graph Optimization Method for GNSS Kinematic Precise Point Positioning

Carrier phase measurements play a more critical role in achieving precise positioning for lower noise and insensitivity to multipath error over code (pseudorange) measurements. Real-time kinematic (RTK) is the most used precise positioning technique. However, the application costs are increased due to the demands for differential base stations. The undifferenced precise point positioning (PPP) does not require differential station assistance but is typically for static use. This paper proposes a dynamic continuous constrained phase (DCCP) method based on factor graph optimization for kinematic positioning without differential stations, even in the presence of cycle slips. The precise velocity estimated via integral doppler and the time correlation of phase ambiguity are regarded as the probability constraints in the factor graph. A real-world experiment was carried out to verify the feasibility of the DCCP method. Experimental results show that the proposed method had a better performance than the kinematic PPP method and window carrier phase (WCP) optimization method with 0.034m standard deviation and 1.338m mean error. It is our hope that this approach provides new insight into the study of other time-correlated state estimation problems.

Performance analysis of BDS-3 vehicle-/ship-/air-borne kinematic SPP/PPP/RTK

This paper comprehensively analyzes the kinematic positioning performance of the third-generation BeiDou Navigation Satellite System (BDS-3) in car-borne, ship-borne, and air-borne scenes. Specifically, this work collects three types kinematic data, i.e., car-borne, ship-borne, and air-borne in three scenes including a real experimental scene, a simulated urban canyon or forest-covered scene, and a simulated regional interference or covered scene. Based on these datasets, the kinematic positioning performance of the BDS-3 interoperable signals of B1C and B2a is systematically analyzed and compared with GPS. The results demonstrate that the BDS-3 has slightly more visible satellites than GPS in the Asia-Pacific test area, and the positioning performance indexes for the B1C and B2a new signals are comparable to GPS in terms of the single point positioning (SPP), precise point positioning (PPP), and real-time kinematic (RTK) positioning.

A methodology for long-term offshore structural health monitoring using stand-alone GNSS: case study in the Gulf of Mexico

This article presents a robust methodology for long-term offshore structural health monitoring (SHM) using the Global Navigation Satellite Systems (GNSS). The methodology relies on recently developed regional reference frames and single-receiver phase-ambiguity-fixed Precise Point Positioning techniques. The stable Gulf of Mexico Reference Frame 2020 (GOM20) provides a robust and consistent reference system for long-term offshore SHM in the Gulf of Mexico (GOM). Continuous GNSS observations (DEV1, 2010–2020) on a fixed platform in the Eugene Island 330 oil field are used to illustrate the methodology. The platform was installed in 1982 in 82-m water about 130 km away from the Mississippi Delta coastline. The major monitoring items include horizontal movements, seafloor subsidence, structure submergence, and seasonal oscillations. The stand-alone GNSS monitoring achieves 3- to 4-mm root-mean-square accuracy in the horizontal direction and 7 mm in the vertical direction for daily positions in the GOM region. According to this study, the GNSS antenna (DEV1) has moved 6 cm toward the northeast with respect to GOM20 since 2010; the ongoing structure submergence rate in the Eugene Island 330 oil field area is approximately 15 mm/year, a combination of seafloor subsidence (12 mm/year) and sea-level rise (2.6 mm/year) with respect to GOM20. The submergence in the future 40 years (2021–2060) would be greater than 0.6 m, likely between 0.8 and 1.0 m, but is unlikely to exceed 1.3 m. The peak-to-trough amplitudes of the seasonal movements at the top of the platform are below 5 mm in all three directions, comparable with the seasonal movements recorded by onshore GNSS in the Louisiana coastal region. The methodology introduced in this article can be applied to SHM in other offshore regions where stable regional reference frames are available.