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European Galileo officially provided global users with the initial high accuracy service (HAS) through Galileo satellites for free on January 24, 2023. The emergence of the Galileo HAS provides the possibility of a globally stable real-time precise point positioning (PPP) time transfer that does not depend on a network. The coverage and service availability (the proportion of epochs that can support PPP solution) of the HAS, accuracy of the satellite orbit and clock offset, and accuracy of HAS time transfer were comprehensively analyzed using real-time and satellite-broadcast HAS data. Twenty-three global time links, including time-keeping laboratories, were established to assess the accuracy of time comparison using the HAS product. The results showed that the average numbers of GPS and Galileo satellites with valid HAS corrections worldwide were 9.44 and 7.95, respectively, and the average service availability of GPS-only and Galileo-only PPP using the HAS product reached 99.9% and 99.6%, respectively, in most areas. Taking post-processing satellite products from GeoForschungZentrum as a reference, the radial errors of the HAS orbit product are concentrated within 5 cm, and the accuracy of the corrected Galileo satellite clock offset was twice that of ephemeris. Further, in the 7200–12295 km-long baselines, the mean standard deviation values of HAS GPS-only, Galileo-only, and GPS/Galileo time comparison result errors were 0.19–0.29 ns, 0.13–0.24 ns, and 0.11–0.21 ns, respectively. In general, HAS time transfer is available globally. [ABSTRACT FROM AUTHOR]

The Galileo high accuracy service (HAS) is a free-of-charge service designed to deliver decimeter-level accuracy in real-time precise point positioning (PPP) applications using global navigation satellite systems (GNSS). With the intention of facilitating the use of HAS corrections with open access tools, we present the open-source library named HASlib and its integration with another open-source library named RTKLIB. HASlib decodes the Reed–Solomon encoded Galileo E6 navigation data pages and outputs the corrections in commonly used formats. This enables the utilization of HAS with conventional GNSS receivers and PPP engines that lack native support for HAS formats. For instance, the outputs from HASlib enable the use of HAS corrections in RTKLIB. In order to validate this integration, we demonstrate that HAS can allow decimeter-level accuracy using only free-of-charge services and tools. We have obtained a 3D root mean square error below 20 cm (1 sigma) after a convergence time of 10–90 min in Finland. This accuracy has overcome classical real-time solutions with broadcast and satellite-based augmentation system (SBAS) data by one order of magnitude. Compared to post-processed multi-GNSS PPP, HAS corrections required longer convergence times, given the real-time nature. Furthermore, our assessment revealed that the longer convergence time, compared to prior literature, was attributed to RTKLIB filtering procedure and geometry deficiencies in high latitudes. Nevertheless, once convergence was attained, a sub-decimeter level of accuracy was observed in both horizontal and vertical components. These findings highlight the effectiveness of Galileo HAS, HASlib, and RTKLIB as powerful tools for providing open-access to real-time PPP solutions. [ABSTRACT FROM AUTHOR]

The high-precision time and frequency transfer method, based on the global navigation satellite system (GNSS) precise point positioning (PPP), has high precision, wide range, and low cost, and the GNSS common-view (CV) can remove all satellite clock errors and partial satellite orbit errors. We conducted a study to select the best satellite and combined PPP and CV to eliminate satellite clock errors, weaken the impact of satellite orbit errors, and unmodeled atmospheric asymmetry in PPP frequency transfer, thus improving the performance of frequency transfer. This study uses conventional dual-frequency ionosphere-free PPP that does not solve for an azimuthal asymmetry in the troposphere. It uses international GNSS service (IGS) products to determine the carrier phase difference between each CV satellite time and the ground clock, for each epoch. Then, the comparison difference is obtained by directly subtracting the carrier phase differences between the CV satellite time and two ground clocks. For each hour, only the satellite that is fully visible at both sites and gives the smallest standard deviation in time comparison of the day between the two ground clocks is selected as the CV satellite. To evaluate the performance of PPP-CV, five stations connected to individual active hydrogen masers are selected to form four links, of which two stations (USN7 and USN8) are common-clock and common-antenna. The results show that the time comparison precision of PPP-CV improves by approximately 12% on average for the three European links compared to PPP with respect to IGS final clock products. For frequency transfer modified Allan deviation (MDEV) over 600,000 s, PPP-CV can reach 2 × 10–16 and 2 × 10–17 for the SPT0-IENG and USN7-USN8 links, respectively. In addition, the frequency transfer stability ranging from 1200 s to 60,000 s of PPP-CV improves by 7% on average compared to PPP, and its short-term stability is also better than that of PPP when the CV satellite does not change. However, the performance of PPP-CV is comparable to PPP when the link length reaches 5991 km and the short-term stability of PPP-CV is slightly worse than PPP when the CV satellite is constantly changing. [ABSTRACT FROM AUTHOR]

To analyze the performance of Global Positioning System (GPS) Precise Point Positioning (PPP) Ambiguity Resolution (AR) under various ionospheric scintillation environments, we selected GPS data of ionospheric scintillation monitoring receivers (ISMR) and geodetic receivers from high-latitude and low-latitude regions during 2021–2023. We conducted GPS Kinematic PPP using Canadian Spatial Reference System (CSRS) PPP and used the maximum and average values of σ φ and S 4 as indicators to characterize the intensity of phase scintillation and amplitude scintillation for ISMRs, while the maximum and average values of Rate of Total Electron Content Index (ROTI) to characterize the intensity of ionospheric scintillation for geodetic receivers. We also used ambiguity resolved percentage (ARP) and the 3-Dimensional Root Mean Square (3D RMS) of positioning errors as performance metrics for PPP-AR and PPP. As the maximum and average values of ionospheric scintillation indices increase, the PPP-ARP for high-latitude ISMRs decreases to 90.0 %, and the 3D RMS can reach 0.204 m. During ionospheric quiet conditions, positioning accuracy of GPS PPP can reach the cm-mm level. As the geomagnetic latitude decreases, the scintillation effects on PPP-AR and PPP become more pronounced for high-latitude ISMRs. Compared with high-latitudes, ISMRs located at low-latitudes are more severely affected by scintillation, with PPP-ARP at the station HNLW in China and the station UFBA in Brazil dropping to 80.0 % and 60.0 %, respectively. The 3D RMS can reach 0.288 m and 0.341 m. The results of geodetic receives are consistent with those of ISMRs, with 3D RMS of positioning errors up to 0.240 m and 0.256 m for CYNE and MAL2, respectively, while PPP-ARP drops to 60.4 % and 79.6 %. Additionally, we observed a strong positive correlation between ionospheric scintillation duration and the maximum values of σ φ , S 4 and ROTI. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Multipath is a limiting factor for accurate positioning by global navigation satellite system (GNSS). Different hardware and computational techniques have been proposed for its mitigation. Here a geometrical approach for multipath localization and mitigation is presented: localization is performed by ray-tracing and mitigation by analyzing the residuals of ambiguity resolved precise point positioning. The main advantages of the method are its ability to correct nearly the multipath-affected parts of raw data and its relative independence of observation duration (e.g., more than 1 h). The method is based on a ray-tracing algorithm and is applicable to all GNSS constellations. It is independent of physical properties of reflecting surfaces, receiver/antenna type and observation sampling rate. The methodology was implemented on static real global positioning system (GPS) data acquired during six consecutive days in presence and in absence of a metallic reflecting plate. The analysis was performed on two kinds of data series: observations residuals and epoch-wise coordinates. The overall RMSs of observations residuals were reduced by 55% on average. The RMS of easting, northing, and elevation residual time series resulting from affected observations were 8.1 mm, 13.3 mm, and 23.8 mm, respectively; while they were reduced to 6.9 mm, 9.7 mm, and 22.4 mm after correction (22% improvement in horizontal and a minor improvement in vertical components). [ABSTRACT FROM AUTHOR]

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases. [ABSTRACT FROM AUTHOR]

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

GNSS technology holds significant importance across wide applications, ranging from mapping, surveying, and precise timekeeping to ship navigation. Its operational principle hinges on the accurate measurement of signal travel time, which is crucial for determining the distance between the GNSS satellite and the receiving device. However, the precision of GNSS positioning is often compromised due to various error sources that impact GNSS measurements. Among these sources, atmospheric effects are widely acknowledged as the primary contributors to spatially correlated inaccuracies in GNSS (Global Navigation Satellite System) measurements. The accuracy of zenith tropospheric delay (ZTD) and zenith wet delay (ZWD) prediction using an artificial neural network model was successfully demonstrated in this study. By combining data from GNSS observations and in-situ meteorological measurements, high-resolution water vapour data can be produced for reliable and accurate weather forecasting. The validation of the predictions revealed a mean standard deviation error of 5 mm and 3.6 mm for ZTD and ZWD, respectively. This study emphasizes the significance of estimating tropospheric wet delay in real-time weather forecasting applications.

ABSTRACTThe Global Navigation Satellite System (GNSS) precise point positioning (PPP) from carrier-phase data is influenced by complex elements. The error sources are divided into two categories according to their relation to the signal propagation path. A new GNSS PPP algorithm based on spherical harmonic expansion (PPP-SH) is proposed, which expresses the error adjustments related to the signal propagation path through the spherical harmonic expansion, such as high-order ionosphere delay, zenith wet delay, phase wind-up delay, multipath delay and so on. Carrier-phase data of multiple continuous epochs are used to achieve the sequential sliding PPP solution, and the truncated singular value decomposition and iteration method by correcting characteristic values are used to solve the ill-conditioned equations in the PPP-SH algorithm. The reliable results can be obtained by using dual-frequency ionospheric-free carrier phase data when spherical harmonic expanding to degree 5. The standard deviations of E, N and U are 0.48, 0.43 and 0.27 cm, respectively. The addition of velocity parameters has positive influence on accuracy of positioning. The best positioning results are obtained by using the precise ephemeris and precise clock bias provided by ESA and the standard deviations of E, N and U are 0.41, 0.43 and 0.26 cm, respectively.

Abstract The Real-Time Kinematic (RTK) positioning method of the Global Navigation Satellite System (GNSS) has been widely used for landslide monitoring. The stability of its reference station is crucial to obtain accurate and reliable monitoring results. Unstable reference stations due to the geological environment and human activities are difficult to detect and in practical applications often ignored. As a result, it affects the positioning solutions and subsequently the interpretation and detection of landslide motions, which must be addressed in GNSS landslide monitoring. To solve this problem, we propose using the Precise Point Positioning (PPP) technique to analyze the stability of the reference station by verifying its position. The deformations of the monitoring stations are then compensated. First, the reference station coordinates are obtained by the PPP technique and tectonic motion is considered in data processing. The change or breakout of the reference station position is then determined using a cumulative sum control chart method. Finally, each monitoring station’s displacements are compensated according to the displacements of the reference station. According to the results of the Tengqing landslide experiment, the PPP technique can be used in GNSS landslide monitoring to analyze the stability of reference stations. With PPP, millimeter-level accuracy for the coordinates of reference stations is achieved. Compared to the traditional deformation series, the compensated displacement series more reliably reflects the landslide motions. This study will increase the reliability of monitoring results and contribute to implementing GNSS in monitoring landslides.

The accurate measurement of water vapor is essential for research about and the applications of meteorology, climatology, and hydrology. Based on the BeiDou PPP-B2b service, real-time precipitable water vapor (PWV) can be retrieved with the precise point positioning (PPP) software (XTW-PPP version 0.0). The experiment was conducted in Beijing in January 2023. Three solutions were designed with PPP using the BeiDou system only, the GPS system only, and the BeiDou-GPS combined solution. Real-time PWVs for the three solutions were validated with the ERA5 reanalysis data. Between the PWV values from the single BeiDou and ERA5, there was a bias of 0.7 mm and an RMSE of 1.8 mm. For the GPS case, the bias was 0.73 mm and the RMSE was 1.97 mm. The biases were less than 1 mm and RMSEs were less than 2 mm. Both the BeiDou and the GPS processing performed very well. But little improvement was found for the BeiDou-GPS combined solution, compared with the BeiDou system-only and the GPS system-only solution. This may be due to the poor handling of two different kinds of errors for the GPS and the BeiDou systems in our PPP software. A better PWV estimation with the two systems is to estimate PWV with a single system at the first step and then obtain the optimization by Bayesian model averaging.

Ambiguity resolution (AR) can markedly enhance the precision of precise point positioning (PPP) and accelerate the convergence process. The decoupled clock model represents a pivotal approach for ambiguity resolution, yet current research on this topic is largely confined to GPS. Consequently, in this study, we extend the investigation of the decoupled clock model to multi-GNSS. Firstly, based on the conventional model, we derive the multi-GNSS decoupled clock estimation model and the precise point positioning with ambiguity resolution (PPP-AR) model. Secondly, we provide a detailed explanation of the estimation process for the multi-GNSS decoupled clock estimation. To validate the efficacy of the proposed model, we conduct multi-GNSS decoupled clock estimation and PPP-AR experiments using six days of observation data. The results demonstrate that the decoupled clocks of GPS, Galileo, and BDS-3 can all achieve high accuracy, thus fully meeting the requirement of ambiguity resolution. In terms of positioning performance, the joint three systems have higher positioning accuracy, reaching 3.10 cm and 6.13 cm in horizontal and vertical directions, respectively. Furthermore, the convergence time (CT) and time to first fix (TTFF) are shortened, to 23.13 min and 13.65 min, respectively. The experimental findings indicate that the proposed multi-GNSS decoupled clock model exhibits high precision and rapid positioning service capabilities.

This study aims to investigate the comparative performance of PPP technique in evaluating the precision of three distinct geoid models and to quantify the contribution of GLONASS constellation to GPS as well as the effect of observation length. We use recently and concurrently measured GNSS and levelling data crossing rough topography with steep geoid slope in Türkiye. The RMSE statistics about the mean of the geometric minus gravimetric geoid heights reveal that at least 4-hours of static data should be collected regardless of the constellation. We find out encouraging results with 8-hours of GPS + GLONASS solutions having RSME values of 3.0, 5.0 and 21.5 cm in validating national, globally combined and satellite-only geoid models, respectively. The multi-GNSS PPP processing with a relatively long observation period yields comparable results to relative positioning though the latter still performs slightly better. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) technology has emerged as a powerful tool for unraveling Earth's dynamic nature, offering continuous and precise monitoring of geodetic positions with global coverage. This study quantifies the noise magnitude and velocity uncertainty estimates using GNSS-derived coordinate time series data from 31 IGS global stations. It assessed the relationship between the noise level and the uncertainties related to the derived velocities and systematically evaluated the influence of different coordinate solution time spans, satellite orbit/clock products, and GNSS constellation on the noise level and velocity uncertainties. The result gives insights into GNSS velocity estimation, noise characteristics, and the influence of ambiguity resolution. The results suggested that resolving ambiguities and using specific GNSS constellation satellite orbits and clocks solutions enhances the precision of velocity estimates and reduces noise magnitude. The noise levels are observed to be consistently above --0.7 in 5-year solution sets and below --0.8 in 8-year solution sets. There is an average of 30 and 42% reduction in velocity uncertainties due to 3 year increment in solution span using JPL and ESA orbits, respectively. GPS-only solution set appeared to be favorable for high-precision GNSS-based geodynamic applications with increased favourability when the ambiguities are resolved. The identified noise model, GGM+WN, demonstrated the most appropriate noise model in most cases which is not out of place to have been used in quantifying the noise magnitude and velocity uncertainties in this study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Decimeter-level positioning accuracy is the premise for most ocean applications, such as ocean development and ocean engineering construction. Although the existing real-time precise point positioning method can achieve economical decimeter to centimeter-level positioning accuracy based on Global Beidou Short Message Communication, they can only broadcast limited satellites for regional users. This is because the above method maintains minimum resolution of real-time precise satellite orbit and clock corrections using a single-card GBSMC. We proposed an ocean decimeter-level real-time BDS PPP method based on dual-card GBSMC to implement global positioning service. First, the encoding ranges of real-time precise satellite orbit and clock corrections were redefined to reduce occupied digits based on 2-month data. Second, the resolution adjustment strategy for real-time precise satellite orbit and clock corrections at the service-end was proposed to broadcast 24 global BDS-3 Middle Earth Orbit (MEO) satellites based on dual-card GBSMC device. Last, aiming at the frequency limitation of GBSMC, the real-time correction method at the user-end was employed due to the change of equivalent distance within 1 min at the centimeter-level. The proposed method was verified by six static stations around the world, and the average positioning accuracy was 0.089 m and 0.103 m in the horizontal and vertical directions, respectively. Meanwhile, compared with the original SSR scheme, the proposed method had a longer convergence time. Furthermore, the real-time kinematic ocean multi-users experiment with reference to XP service of Kongsberg DPS 132 receiver was carried out. The results showed that the positioning accuracy was 0.132 m and 0.217 m in the horizontal and vertical directions after converged. [ABSTRACT FROM AUTHOR]

LEO augmentation systems are attracting worldwide attention. However, their performance in real-world environments has not yet been reported, although several systems have already launched experimental satellites, such as the CENTISPACE™ system developed by Beijing Future Navigation Tech Co., Ltd. By using real observations from two experimental CENTISPACE™ satellites recorded by a regional network, we present the results of LEO-enhanced precise point positioning (PPP) performance. Based on a proposed three-step approach for LEO orbit determination and time synchronization, a framework for LEO augmentation data processing is established and validated. Two stations are selected for LEO augmentation evaluation, and static PPP is performed by combining the LEO augmentation observations with different GNSS systems, including GPS, BDS-3, and Galileo. The static PPP precision shows a few improvements attributed to LEO observations; the positioning errors with one, two, and three GNSS systems are 6.1, 4.6, and 4.6 cm, respectively, while they are reduced to 5.2, 3.9, and 3.8 cm by adding the LEO satellites, respectively, revealing improvements of 13.9, 16.4, and 18.8%, respectively. Moreover, PPP convergence is significantly enhanced. The average convergence times with one, two, and three GNSS systems are 32.7, 17.9, and 14.2 min, respectively, which are reduced to 16.7, 8.9, and 5.7 min, respectively, by adding LEO observations. This indicates that the convergence time is significantly shortened by approximately 53% with the augmentations from only two LEO satellites. Such results show the potential of LEO augmentation, and larger improvements can be expected with more LEO satellites to be deployed in the future. [ABSTRACT FROM AUTHOR]

The flex power technology of satellite navigation systems can improve the anti-jamming ability of navigation signals, but the flex power technology may have many effects in navigation and positioning. In this paper, the effects of the BeiDou Navigation Satellite System (BDS) flex power on differential code biases (DCBs) estimation and precise point positioning (PPP) convergence were researched. First, the variation characteristics of the carrier-to-noise density ratio and daily DCB products during BDS flex power active periods were analyzed. Then, the influence of BDS flex power on DCB estimation was examined by different DCB estimation strategies. Finally, the convergence performance of PPP algorithms using different DCB corrections during BDS flex power active periods was investigated. Results show the B3I signals of the BDS-2 Geostationary Orbit (GEO), Medium Earth Orbit (MEO), and Inclined Geosynchronous Orbit (IGSO) satellites have the capability of flex power. The BDS observation data during flex power events that occurred on DOY 029 in 2021 were analyzed. Estimates derived from reference satellite constraint indicate that the DCB of the satellites without flex power activated did not change, whereas the DCB of the IGSO satellites with flex power activated increased by 10–15 ns. When the flex power was activated at part of the DOY 029, 2021, the correction of daily DCB products resulted in the extension of BDS PPP convergence time for most stations within the flex power coverage area, regardless of whether the flex power was activated; however, the convergence time of PPP was unaffected if the station was outside the flex power coverage area. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Although deformations are mostly insignificant, they can be catastrophic when accumulated to certain amounts. Precise point positioning (PPP) can work with one receiver, preventing problems caused by the base station constrain upon employment of current methods such as real-time kinematics (RTK). However, current methods employing PPP focus on high-frequency monitoring such as earthquake or geological calamity monitoring, and these methods are not suitable for structures. Thus, this study proposes a new method for the deformation monitoring of structures via PPP. First, we obtained the coordinate sequence of structures via static PPP when setting the interval. Then, we transformed the coordinates to the same coordinate system with the same basis. Finally, we decomposed the sequences via empirical mode decomposition (EMD) to obtain a low-frequency part, which is the deformation of the target structure. The result of the monitoring experimentation on IGS stations shows that the monitoring index, S d , of the sequence under different intervals using this method could be 1–2 mm on average in the directions of E, N, and U, which is much better than the original monitoring sequence. Alongside that, it prevented a fall in accuracy when the interval decreased. Therefore, all results proved the feasibility and validity of the method. [ABSTRACT FROM AUTHOR]

Approaching the peak year of the 25th solar activity cycle, the frequency of strong geomagnetic storms is gradually increasing, which seriously affects the navigation and positioning performance of GNSS. Based on the globally distributed GNSS station data and FORMOSAT-7/COSMIC-2 occultation data, this paper explores for the first time the effects of the G4-class geomagnetic storm that occurred on 23–24 April 2023 on the global ionosphere, especially the ionospheric equatorial anomalies and F-layer perturbations. It reveals the precise point positioning (PPP) accuracy degradation during a geomagnetic storm. The results show that the ionospheric rate of total electron content index (ROTI) and near high latitude GNSS phase scintillations index have varying levels of perturbation during geomagnetic storms, with the maximum ROTI and phase scintillations index exceeding 0.5 TECU/min and 0.8, respectively. The equatorial ionization anomaly (EIA) shows an enhanced state (positive ionospheric storms) during geomagnetic storms, and the cause of this phenomenon is most likely the equatorward neutral wind. The variation of the S4 index of the FORMOSAT-7/COSMIC-2 satellite reveals the uplift of the F-layer during geomagnetic storms. During geomagnetic storms, the PPP accuracy degrades most seriously at high latitudes, the maximum MAE exceeds 2.3 m, and the RMS in the three-dimensional (3D) direction exceeds 2.0 m. These investigations can provide case support for space weather and GNSS studies of the impact of geomagnetic storms during peak solar activity years. [ABSTRACT FROM AUTHOR]

The aim of the new generation of Global Geodetic Observing System is a millimeter-level accuracy in positioning, with a crucial role to be played by Global Navigation Satellites Systems (GNSS) in the Precise Point Positioning (PPP) mode. This is of course because GNSS constellations and receivers provide an efficient stand-alone technique with a homogeneous performance over large areas (positions, navigation and meteorology) when used in conjunction with the PPP mode, with also an ever-increasing data flow and different satellite line-of-sights. The requirement of accuracies reaching the millimeter or sub-millimeter implies a knowledge at this level of each line in the GNSS-PPP error budget, including, but not restricted to: clock biases, troposphere and ionosphere delays, multipath and ground deformations. In this review study, we consider this millimeter-/submillimeter level GNSS-PPP error budget, and possible mitigations and improvements in the frame of the existing global constellations: GPS, Galileo, GLONASS and BDS, in view of augmented constellations and/or Low Earth Orbit constellations, which will be available in the near future. We also pay a special attention to systematic biases that can/could exist between constellations. [ABSTRACT FROM AUTHOR]

The precise point positioning (PPP) technique generally takes tens of minutes to converge, severely limiting its use. This longer convergence time is mainly due to the slower variation of satellite geometry in space and the stronger correlation of unknown parameters to be estimated. Fortunately, the lower orbit altitude of Low Earth Orbit (LEO) satellites contributes to the fast variation of the satellites' spatial geometry. In addition, high-precision atmospheric delay information has become readily available, which can help decrease unknown parameters' correlation. This study proposes a double-augmentation PPP approach with accelerated convergence by tightly integrating the LEO/atmosphere-augmented information. The GNSS observations in both mid-latitude and low-latitude areas, and simulated LEO observations under a Walker/polar mixed constellation, are used to validate the double-augmentation PPP approach. Test results in both areas indicate that the double-augmentation PPP can converge within 0.8 min, improving the convergence time by over 73%, and over 83% compared to the LEO-only augmented PPP and atmosphere-only augmented PPP. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) is an important alternative to real-time kinematic (RTK) positioning for deformation monitoring. Global Navigation Satellite System (GNSS) multi-frequency and multi-system integration can benefit PPP dynamic deformation monitoring due to increased measurement redundancy and facilitated ambiguity resolution (AR). This study investigates the performance of GNSS multi-frequency uncombined (UC) PPP-AR with GPS triple-frequency, BDS-3 triple-frequency, and Galileo five-frequency signals for monitoring high-rate vibrations based on 20-Hz observations from a shaking table. The GNSS multi-frequency UC fractional cycle bias (FCB) estimation method and PPP-AR method are developed. The results of vibration tests indicate that the displacement monitoring accuracy of GPS/BDS-3/Galileo multi-frequency PPP-AR solution is 5.3–8.4 mm. BDS-3 dual-frequency PPP-AR, BDS-3 triple-frequency PPP-AR, and GPS/BDS-3/Galileo multi-frequency PPP-AR solutions improve the accuracy by 8%, 17%, and 46% over the BDS-3 dual-frequency float solutions, respectively. GNSS multi-frequency UC PPP-AR can accurately identify the vibration frequency and amplitude, but the PPP-derived displacement is nosier than that of RTK. [ABSTRACT FROM AUTHOR]

The Real-Time Kinematic (RTK) positioning method of the Global Navigation Satellite System (GNSS) has been widely used for landslide monitoring. The stability of its reference station is crucial to obtain accurate and reliable monitoring results. Unstable reference stations due to the geological environment and human activities are difficult to detect and in practical applications often ignored. As a result, it affects the positioning solutions and subsequently the interpretation and detection of landslide motions, which must be addressed in GNSS landslide monitoring. To solve this problem, we propose using the Precise Point Positioning (PPP) technique to analyze the stability of the reference station by verifying its position. The deformations of the monitoring stations are then compensated. First, the reference station coordinates are obtained by the PPP technique and tectonic motion is considered in data processing. The change or breakout of the reference station position is then determined using a cumulative sum control chart method. Finally, each monitoring station's displacements are compensated according to the displacements of the reference station. According to the results of the Tengqing landslide experiment, the PPP technique can be used in GNSS landslide monitoring to analyze the stability of reference stations. With PPP, millimeter-level accuracy for the coordinates of reference stations is achieved. Compared to the traditional deformation series, the compensated displacement series more reliably reflects the landslide motions. This study will increase the reliability of monitoring results and contribute to implementing GNSS in monitoring landslides. [ABSTRACT FROM AUTHOR]

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

The antenna phase center correction is an important error source in GNSS precise positioning. The discussion on the difference of antenna phase center model based on different reference frames and its influence on post-static positioning position parameter estimation is helpful to obtain the consistent positioning results of the reference frame and improve the positioning reliability. Firstly, the difference of satellite/ground antenna phase center correction was analyzed under different reference frames, and then the IGS core station with uniform global distribution was selected; the estimated position difference caused by satellite/ground antenna phase center correction based on different reference frames was calculated and analyzed. The results show that the site difference caused by phase center correction under different reference frames is millimetre in plane direction and centimetre in elevation direction, and the average value of site difference is 7.1 mm; the influence of satellite antenna phase center correction on the estimated position of stations under different reference frames is greater than that of ground antenna phase center correction, the influence of the same type of antenna on different stations is basically the same. [ABSTRACT FROM AUTHOR]

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.

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.

Abstract In order to facilitate high-precision and real-time Precise Point Positioning (PPP), the International GNSS (Global Navigation Satellite System) Service (IGS), BDS-3 (BeiDou-3 Navigation Satellite System), and Galileo navigation satellite system (Galileo) have provided real-time satellite clock correction, which is updated at a high-frequency. However, the frequent updates pose the challenges of increasing the computational burden and compromising the timeliness of these correction parameters. To address this issue, an improved Real-Time Service (RTS) method is developed using an extrapolation algorithm and a linear model. The results indicate that a 1 h arc length of the satellite clock correction series is optimal for fitting a linear model of the RTS. With this approach, the 1 h extrapolation results for BDS-3 and Galileo are superior to 0.09 ns. Moreover, when these model coefficients are transmitted and updated at the intervals of 1, 2, 5, and 10 min, the corresponding PPP can converge at the centimeter-level. It is evident that these improved RTS methods outperform the current approach with high-frequency interval transmission, as they effectively mitigate the challenges associated with maintaining the timeliness of correction parameters.

BeiDou navigation satellite system with global coverage (BDS-3) has been fully operational since July 2020, currently providing the positioning, navigation and timing service together with regional BDS-2. In addition to the legacy signals of B1I and B3I, the BDS-3 also transmits several new signals such as BIC, B2a and B2b, which brings new opportunities for rapid ambiguity resolution (AR) of BDS precise point positioning (PPP). In this contribution, a multi-frequency (MF) rapid PPP-AR method with regional network augmentation was proposed. Firstly, BDS five-frequency observations were introduced into uncombined double-differenced models to retrieve regional augmentation corrections at the server. Thereafter, a cascade PPP-AR strategy using extra-wide-lane, wide-lane and narrow-lane ambiguity was employed at the user. Once ambiguities were fixed to integers, the phase correction accuracy could reach about 3 cm on average overall BDS frequencies in the network with inter-station distances of 100–200 km. Subsequently, the statistical results of seven-day simulated kinematic experiments showed that over 99% of epochs on average realized PPP-AR. Correspondingly, the positioning accuracy of the MF fixed solution reached 1.8, 1.9, 4.7 cm in the east, north and up components, respectively, improving by 5–15% compared with the dual-frequency scheme. Moreover, several vehicle-borne experiments under different urban scenarios were also conducted. Under an open-sky or a relatively open highway scene, the BDS-MF scheme similarly exhibited good performance, and over 98% of epochs achieved rapid PPP-AR with a positioning accuracy better than 3 cm. More encouragingly, for this BDS-challenged experiment with an average satellite number of 8.6, although only 72.06% of epochs were available due to serious signal blockages caused by overpass, tunnels or tall buildings, the horizontal positioning accuracy could still remain 7 cm on average.

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube’s performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime.

Global Navigation Satellite System (GNSS) signals experience delays when passing through the atmosphere due to the presence of free electrons in the ionosphere and air density in the non-ionized part of the atmosphere, known as the troposphere. The Precise Point Positioning (PPP) technique demonstrates highly accurate positioning along with Zenith Tropospheric Delay (ZTD) estimation. ZTD estimation is valuable for various applications including climate modelling and determining atmospheric water vapor. Current GNSS network resolutions are not completely sufficient for the scale of a few kilometres that regional climate and weather models are increasingly adopting. The Centipede-RTK network is a low-cost option for increasing the spatial resolution of tropospheric monitoring. This study is motivated by the question of whether low-cost GNSS networks can provide a viable alternative without compromising data quality or precision. This study compares the performance of the low-cost Centipede-RTK network in calculating the Zenith Tropospheric Delay (ZTD) to that of the existing EUREF Permanent Network (EPN), using two alternative software packages, RTKLIB demo5 version and CSRS-PPP version 3, to ensure robustness and software independence in the findings. This investigation indicated that the ZTD estimations from both networks are almost identical when processed by the CSRS-PPP software, with the highest mean difference being less than 3.5 cm, confirming that networks such as Centipede-RTK could be a reliable option for dense precise atmospheric monitoring. Furthermore, this study revealed that the Centipede-RTK network, when processed using CSRS-PPP, provides ZTD estimations that are very similar and consistent with the EUREF ZTD product values. These findings suggest that low-cost GNSS networks like Centipede-RTK are viable for enhancing network density, thus improving the spatial resolution of tropospheric monitoring and potentially enriching climate modelling and weather prediction capabilities, paving the way for broader application and research in GNSS meteorology.

The Global Navigation Satellite System (GNSS) can be utilized for long-distance and high-precision time transmission. With the ongoing development of low Earth orbit (LEO) satellites and the rapidly changing geometric relationships between them, the convergence rate of ambiguity parameters in Precise Point Positioning (PPP) algorithms has increased, enabling fast and reliable time transfer. In this paper, GPS is used as an experimental case, the LEO satellite constellation is designed, and simulated LEO observation data are generated. Then, using the GPS observation data provided by IGS, a LEO-enhanced PPP model is established. The LEO-augmented PPP model is employed to facilitate faster and more reliable high-precision time transfer. The application of the LEO-augmented PPP model to time transfer is examined and discussed through experimental examples. These examples show multiple types of time transfer links, and the experimental outcomes are uniform. GPS + LEO is compared with exclusive GPS time transfer schemes. The clock offset of the time transfer link for the GPS + LEO scheme converges more swiftly, meaning that the time required for the clock offset to reach a stable level is the briefest. In this paper, standard deviation is employed to assess stability, and Allan deviation is utilized to assess frequency stability. The results show that the clock offset stability and frequency stability achieved by the GPS + LEO scheme are superior within the convergence time range. Controlled experiments with different numbers of satellites for LEO enhancement indicate that time transfer performance can be improved by increasing the number of satellites. As a result, augmenting GPS tracking data with LEO observations enhances the time transfer service compared to GPS alone.

The 2014 North Aegean Sea earthquake was a strong (Mw 6.9) event that caused significant crustal deformations. In the present study we investigate the long-term impact of the earthquake on the kinematics of the North Aegean Trough (NAT). For this purpose, we analyzed GPS observations collected from May 2010 to April 2022 at five permanent GPS reference stations. Two of these stations are located close to the epicenter(s) on the Islands of Lemnos and Samothrace. We processed the data using the Precise Point Positioning (PPP) technique. The analysis of the obtained coordinate time-series revealed a post-seismic deformation (PSD) period lasting for more than two years leading to cumulative 2D post-seismic displacement of 22 mm and 27 mm for Samothrace and Lemnos, respectively. The magnitudes of these post-seismic slip vectors correspond to 23% and 49% of the co-seismic vectors at Samothrace and Lemnos, respectively. The long-term analysis showed that after the end of the PSD period the stations are characterized by stable velocities that are noticeably different compared to the velocities prior to the event. We observed a change in the velocity in the order of 2 mm/yr for both Samothrace and Lemnos. It is the first time that PSD and velocity changes have been reported for the 2014 North Aegean Sea earthquake shedding light on the characteristics and the impact of this important earthquake on the kinematics of NAT.

Precise Point Positioning (PPP) with Integer Ambiguity Resolution (IAR) is an effective way of improving the overall performance of the PPP technique both in terms of convergence time and accuracy. Even though PPP-IAR has seen a tremendous development in the last two decades, there is still room for improvement. Specifically, the search stage of candidate carrier phase ambiguities is characterized as an NP-hard problem that requires a long processing time, leading to limitation in the reliability of the identified optimal solution. A field that would have an impact on the search process of carrier phase ambiguities, and is addressed conceptually in this paper, is Artificial Intelligence (AI). [ABSTRACT FROM AUTHOR]

The Galileo High-Accuracy Service (HAS) is providing free Precise Point Positioning (PPP) corrections for Galileo and GPS satellites through the E6b signal and the internet. Currently, HAS should provide a horizontal and vertical 95% accuracy below 20 centimetres and 40 centimetres, respectively. To assess the accuracy of the current HAS corrections, software has been developed to receive, decode and use HAS corrections. HAS corrections were acquired in the Munich area (Germany) during two sessions in November 2022 and April 2023. The decoder was validated by comparing recorded corrections to data from the Galileo High Accuracy Reference Algorithm and User Terminal (HAUT). Then, the availability and quality of HAS corrections were analysed. The use of orbit and clock corrections significantly improves the broadcast product accuracy; for instance, the Galileo orbit RMS error decreases up to 43% and the GPS RMS up to 80%. The code bias accuracy is at sub-nanosecond level. Finally, to validate the use of HAS corrections, PPP positioning has been achieved. For the used station network, we reached a 95% horizontal and vertical accuracy of 19 cm and 34 cm, respectively, for the kinematic and bi-constellation positioning matching with targeted HAS performances. [ABSTRACT FROM AUTHOR]

The Galileo High-Accuracy Service (HAS) was declared operational (initial service) in January 2023 after an intense testing phase aimed at assessing its service performance through the transmission of live HAS corrections. The HAS performance at high latitudes is evaluated by analyzing data collected at the Polish Polar Station located in Hornsund, in the Norwegian Svalbard archipelago. At such a location, the reception conditions can be affected by poor satellite geometries and ionospheric scintillation may degrade the signal quality. In this respect, data affected by scintillation events were identified and used for the performance analysis. The assessment is carried out by comparing the HAS corrections with the International GNSS Service (IGS) precise products. Moreover, the retrieved HAS corrections are used to assess the Precise Point Positioning (PPP) performance. [ABSTRACT FROM AUTHOR]

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time. [ABSTRACT FROM AUTHOR]

In this study, a precise single-receiver differential code bias (DCB) estimation method using the precise point positioning (PPP) model is presented. The first step is to extract the high-precision ionospheric observations, including DCBs, based on the PPP model. Then, the satellite DCBs are corrected using International GNSS Service (IGS) products. Lastly, the algorithm for the minimization of the standard deviation of vertical total electron content (VTECmstd) is employed to determine the value of receiver DCB. To check the method, GNSS data from more than 200 IGS stations around the globe on four days with various geomagnetic and solar activity circumstances are processed. The receiver DCBs are compared to those obtained using previous carried-to-code level (CCL) models. The experimental results show that, compared to the CCL model, the values of VTECmstd for most stations are significantly reduced, the mean number of stations with negative ionospheric measurements is reduced by 40% after correcting the receiver DCBs, and the mean error of estimated receiver DCBs is reduced by approximately 0.6 ns using the PPP model. These results suggest that this method can provide more high-precision receiver DCB estimation. [ABSTRACT FROM AUTHOR]

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future. [ABSTRACT FROM AUTHOR]

The 2014 North Aegean Sea earthquake was a strong (Mw 6.9) event that caused significant crustal deformations. In the present study we investigate the long-term impact of the earthquake on the kinematics of the North Aegean Trough (NAT). For this purpose, we analyzed GPS observations collected from May 2010 to April 2022 at five permanent GPS reference stations. Two of these stations are located close to the epicenter(s) on the Islands of Lemnos and Samothrace. We processed the data using the Precise Point Positioning (PPP) technique. The analysis of the obtained coordinate time-series revealed a post-seismic deformation (PSD) period lasting for more than two years leading to cumulative 2D post-seismic displacement of 22 mm and 27 mm for Samothrace and Lemnos, respectively. The magnitudes of these post-seismic slip vectors correspond to 23% and 49% of the co-seismic vectors at Samothrace and Lemnos, respectively. The long-term analysis showed that after the end of the PSD period the stations are characterized by stable velocities that are noticeably different compared to the velocities prior to the event. We observed a change in the velocity in the order of 2 mm/yr for both Samothrace and Lemnos. It is the first time that PSD and velocity changes have been reported for the 2014 North Aegean Sea earthquake shedding light on the characteristics and the impact of this important earthquake on the kinematics of NAT. [ABSTRACT FROM AUTHOR]

The moving horizon estimation (MHE) always plays an important estimation role in low-cost devices. We introduced the MHE into the precise point positioning (PPP). However, the dimension of the state-space vector is constant in the conventional MHE, it limits applications of the MHE algorithm in PPP where the number of estimated parameters is varied, such as the number of integer ambiguity and ionosphere varying with satellites. We presented a state-space-varied moving horizon estimation (SSV-MHE) algorithm for PPP. Meanwhile, the Cramer-Rao Lower Bound (CRLB) is derived to analyze the convergence of SSV-MHE. Finally, the real-time PPP field experiments are conducted to verify the performance of SSV-MHE in different environments by using the devices with low-cost antenna and chipset, such as the receiver Ublox C099 and smartphone Huawei Nova 8 pro. The results show that the mean convergence time of the SSV-MHE algorithm is approximate to that of the Extended Kalman Filter (EKF) algorithm. As to the mean accuracy, there is a 9.8% increase, while to the mean precision, the increase, which is relatively larger, is 28.7%. Although the field test results show a similar convergence time of the two algorithms, the positioning performance, in terms of accuracy and precision, almost always has a commendable improvement for the SSV-MHE algorithm, especially in a poor environment. This indicates that the SSV-MHE algorithm can make positioning results of PPP accurate and stable when a low-cost receiver encounters a harsh environment. [ABSTRACT FROM AUTHOR]

Over the last decade, chip-scale atomic clocks (CSACs) have emerged as stable time and frequency references with small size, weight, and power (SWaP). While the short-term stability of these devices clearly outperforms other oscillators with similar power consumption, their stability over longer time intervals is notably limited by frequency noise. Such long-term deviations can effectively be compensated by disciplining the clock with respect to a stable time and frequency reference such as Coordinated Universal Time (UTC) or a time scale based on GNSS observations. In view of the limited accuracy of GPS pseudorange observations and broadcast ephemerides, the performance of GNSS-disciplined atomic clocks is commonly limited to the few-nanosecond level. For further improvement, this study combines the use of carrier phase-based precise-point-positioning (PPP) techniques and high-performance broadcast ephemerides to discipline the phase of a CSAC with respect to GNSS broadcast time. Making use of a dual-frequency, dual-constellation GPS/Galileo receiver, a sub-nanosecond time interval error with respect to a national UTC timing laboratory is demonstrated over time intervals from 1 s to several days. [ABSTRACT FROM AUTHOR]

Differential Code Bias (DCB) is a crucially systematic error in satellite positioning and ionospheric modeling. This study aims to estimate the BeiDou-3 global navigation satellite system (BDS-3) satellite DCBs by using the single-frequency (SF) uncombined Precise Point Positioning (PPP) model. The experiment utilized BDS-3 B1 observations collected from 25 International GNSS Service (IGS) stations located at various latitudes during March 2023. The results reveal that the accuracy of estimating B1I-B3I DCBs derived from single receiver exhibits latitude dependence. Stations in low-latitude regions show considerable variability in the root mean square (RMS) of absolute offsets for satellite DCBs estimation, covering a wide range of values. In contrast, mid- to high-latitude stations demonstrate a more consistent pattern with relatively stable RMS values. Moreover, it has been observed that the stations situated in the Northern Hemisphere display a higher level of consistency in the RMS values when compared to those in the Southern Hemisphere. When incorporating estimates from all 25 stations, the RMS of the absolute offsets in satellite DCBs estimation consistently remained below 0.8 ns. Notably, after excluding 8 low-latitude stations and utilizing data from the remaining 17 stations, the RMS of absolute offsets in satellite DCBs estimation decreased to below 0.63 ns. These enhancements underscore the importance of incorporating a sufficient number of mid- and high-latitude stations to mitigate the effects of ionospheric variability when utilizing SF observations for satellite DCBs estimation. [ABSTRACT FROM AUTHOR]

The incorporation of multi-frequency signals into global navigation satellite systems (GNSS) has presented new possibilities for precise positioning and rapid ambiguity resolution. Inter-frequency clock bias (IFCB) pertains to the time-varying biases among distinct frequencies within carrier phase observations in GNSS signals. The appropriate handling of IFCB is critical in enhancing the accuracy and convergence time of precise point positioning (PPP) solutions. The focus of this study is on the proper modeling of phase IFCB in multi-GNSS multi-frequency PPP. In this paper, the optimal IFCB power spectral density value of 0.6 m/sqrt(s) is first determined. To obtain the optimal stochastic model for IFCB, a thorough comparison and analysis of the product correction and parameter estimation methods is conducted. Additionally, experiments are conducted on the effect of IFCB modeling on the performance of undifferenced and uncombined PPP using data from 130 multi-GNSS experiment stations across the globe over a period of one week in January 2022. The study reveals that the optimal power spectral density for IFCB is within [60, 0.006] m/sqrt(s), modeling IFCB as a random walk is feasible, and the PPP is comparable for the three IFCB processing schemes of product correction, random walk, and white noise. Meanwhile, it is not reasonable to treat IFCB as a random constant or neglect it in the multi-GNSS multi-frequency PPP. In the absence of product correction or for users who require immediate and continuous positioning solutions, modeling IFCBs as random walks can lead to more reliable positioning results and improved convergence performance. [ABSTRACT FROM AUTHOR]