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The last decade has witnessed a growing demand for precise positioning in many applications, including autonomous car navigation. The safety features in autonomous driving and Advanced Driver Assistance Systems (ADAS) require lane-level positioning accuracy. Such accuracy can be obtained from the Global Navigation Satellite Systems (GNSS) through either differential techniques or Precise Point Positioning (PPP). PPP is currently favored over differential GNSS because it provides a global solution without the need for local reference stations. Nevertheless, employing PPP for land vehicles would be challenging due to frequent signal degradation and blockage. Integrating PPP with an Inertial Navigation System (INS) can solve the solution continuity problem; however, the INS solution drifts over time, resulting in losing the desired accuracy. Implementing a reliable PPP/INS system that can preserve the required accuracy is not trivial, especially with financial and computational cost constraints. This article proposes the integration of PPP with the Reduced Inertial Sensor System (RISS) for lane-level car navigation. The high-precision needed in lane-level positioning can be achieved by integrating PPP with high-end INS. Since high-end INS are expensive, this work proposes the use of RISS instead of the traditional INS. RISS uses only one gyroscope and two accelerometers, which can save more than half the high-end INS cost. The proposed PPP/RISS system was tested through three road tests that included highway driving under several overpasses. The system was able to maintain horizontal position errors of less than 50 cm.

Global Navigation Satellite System (GNSS) buoys were used to retrieve the significant wave heights (SWHs) and dominant periods of waves in the Qingdao coastal waters off China. The precise point positioning (PPP) and postprocessed kinematic (PPK) techniques were used to obtain the absolute motion of the GNSS buoys. Even though PPP has relatively low absolute positioning accuracy, this accuracy has a minimal influence on the spectrum in the wave frequency band. SWH values calculated from the PPK and PPP modes are nearly identical, with correlation coefficients and symmetric regression slopes both higher than 0.99. The SWH values calculated from PPP also show good agreement with a dedicated wave buoy, with a correlation coefficient of 0.935 and a difference of 0.82 cm ± 4.63 cm. A GaoFen-1 satellite image was used to assess the GNSS PPP wave spectrum via the dispersion relationship; both exhibit wave spectra with two peaks, consistent with the wave characteristics in the area.

3-D computerized ionospheric tomography (CIT) is an ill-posed problem due to the insufficient amount of observations, it remains challenging for practical applications. In this article, we proposed an ionospheric tomography method that combined data-driven methods with compressed sensing (CS) to deal with the ill-posed problem. First, slant total electron content (STEC) data were extracted by undifferenced and uncombined precise point positioning (UCPPP) with known fixed station coordinates. Second, data-driven methods were adopted to construct the projection matrix from the ionospheric model. Third, compressed sensing was used to derive the sparse solution based on L₁ norm. The ionospheric tomography can be achieved well by using observations during the shorter time interval and in a sparse receiver distribution based on the property of compressed sensing. Results of experiment based on real Global Positioning System (GPS) observation data verified the effectiveness of the proposed methods. By comparing with the colocated ionosonde, it is found that the CS methods are more consistent with the actual ionospheric fluctuation than the modified constrained algebraic reconstruction technique (CART). In terms of the differential STEC (dSTEC) analysis, the error of the tomography model by Compressed Sensing-Principal Component Analysis (CS-PCA) is less than 0.2 TEC unit (TECU), and the time resolution is 5 min. The UCPPP with constraint by CS-PCA shows the best performance of 12.2%, 40.9% and 0.31% improvement in positioning accuracy, convergence time, and fixed rate over the UCPPP with constraint by modified CART. The proposed data-driven methods may be important for high-resolution 4-D ionospheric tomography in the future.

Single-frequency precise point positioning (PPP) is widely used with the advantage of cost-efficient, while its further development and application are limited by the difficulty of ionospheric delay correction and the long-time convergence, especially for real-time positioning. And the development of high-accuracy ionospheric models plays an important role for the correction of ionospheric delay in single-frequency PPP. In this paper, the final and rapid global ionospheric map (GIM) products released by Chinese Academy of Science (CAS), Center for Orbit Determination in Europe (CODE), European Space Agency (ESA), Jet Propulsion Laboratory (JPL), Universitat Politecnica de Catalunya (UPC), Wuhan University (WHU) and International GNSS Service (IGS) were used as external constraints in static, simulation kinematic and kinematic single-frequency PPP respectively. The performance and practicality of each product were analyzed by using IGS station observation data (September 2017 and January 2018, with different ionospheric activity levels) and a kinematic experiment. The results indicate that GIM products may improve convergence time in most areas of middle and high latitudes of the globe. However, the improvement of convergence time of some regions in low latitudes or near the equator with dense and uniform distributed IGS stations show even better performance than the regions in middle and high latitudes. Comparing with standard PPP (S-PPP), the convergence time of static PPP is reduced about 14–42% and 13–29% with GIM final and rapid products respectively. In simulation kinematic PPP, the convergence time improves 10–43% and 12–25% for final and rapid products respectively. In the kinematic positioning, the addition of external ionospheric constraints may speed up the convergence in the early stage of positioning and improve the accuracy to a certain extent. Among all GIM products, the final products show better performance than that of the rapid products obviously. The GIM products from CAS and CODE and UQRG from UPC express the best performance are recommended to process ionospheric delay in the high-accuracy positioning.

On February 11, 2019, the latest batch of four Galileo satellites has been commissioned for operational use, accelerating the evolution of the Galileo system toward Full Operational Capability (FOC). To exploit the advantages of the European GNSS constellation, all the Galileo signals in the E1 and E5 frequency band have been successfully integrated in Leica GNSS positioning technologies, with the expectation of improved availability, accuracy and reliability. From the user’s perspective, this paper assesses the benefits of Galileo to high-precision GNSS in the real-time kinematic (RTK), real-time precise point positioning (PPP) and post-processing scenarios. Representative measuring conditions, such as open sky, multipath environments and tree canopy, are considered. The RTK results show that in challenging environments, the integration of Galileo significantly improves the RTK fix availability and effectively reduces decimeter-to-meter-level position errors caused by incorrect ambiguity fixes. To characterize the RTK performance of individual GNSS systems, Galileo-only positions are compared with GPS-only and GLONASS-only solutions. The PPP results demonstrate how Galileo benefits the convergence time and positioning accuracy. The post-processing studies show that the inclusion of Galileo provides more accurate solutions for short data durations and long baselines, particularly for data collected under strong multipath conditions.

The purpose of the data assimilation is to use all the available information to determine as accurately as possible the state of the atmosphere. In this context we consider the assimilation of the GPS-ZTD (Global Positioning System – Zenith Total Delay) by a nudging scheme in Regional Atmospheric Modeling System at Institute of Atmospheric Sciences and Climate (RAMS@ISAC) at medium horizontal resolution (5 km). The water vapour mixing ratio ( q v ) given by the RAMS@ISAC is perturbed according to the differences between observed and simulated ZTD. To verify the impact of the GPS-ZTD data assimilation on the representation of the atmospheric humidity field, especially at the local scale, a numerical experiment was performed over central Italy area, over a one-month time frame. The studied network consists of 41 geodetic receivers and 3 single frequency receivers, this latter category of receivers has turned up more and more in marketing for the very low cost with respect to high level of performance. For what concerns all devices, processing was carried out in PPP (Precise Point Positioning) using goGPS, an Open Source Program Package for GNSS Positioning. For the application of PPP processing to single-frequency receivers, goSEID method (an alternative implementation of the SEID approach integrated in the goGPS open source software) was applied; the algorithm, starting from the observations of a unique (or more) dual frequency “reference” receiver, is able to generate L2 synthetic observations for any single frequency receiver located in its surroundings (15–20 km). Results show that the assimilation of GPS-ZTD has a positive impact on the simulation of the Integrated Water Vapour over the areas where GPS receivers are located. The results obtained, using data assimilation, were indeed compared with those obtained by the model without data assimilation of GPS-ZTD. The two outputs were subsequently evaluated against observations obtained from two geodetic receivers (ROUN and INGR) not used in the assimilation process. The result showed that the independent observation was more consistent with the model output in which also the single-frequency receivers had been assimilated. The assimilation of GPS-ZTD improves also the simulated precipitation, especially by reducing false alarms.

Accurate positioning and navigation play a vital role in vehicle-related applications, such as autonomous driving and precision agriculture. With the rapid development of Global Navigation Satellite Systems (GNSS), Precise Point Positioning (PPP) technique, as a global positioning solution, has been widely applied due to its convenient operation. Nevertheless, the performance of PPP is severely affected by signal interference, especially in GNSS-challenged environments. Inertial Navigation System (INS) aided GNSS can significantly improve the continuity and accuracy of navigation in harsh environments, but suffers from degradation during GNSS outages. LiDAR (Laser Imaging, Detection, and Ranging)-Inertial Odometry (LIO), which has performed well in local navigation, can restrain the divergence of Inertial Measurement Units (IMU). However, in long-range navigation, error accumulation is inevitable if no external aids are applied. To improve vehicle navigation performance, we proposed a tightly coupled GNSS PPP/INS/LiDAR (GIL) integration method, which tightly integrates the raw measurements from multi-GNSS PPP, Micro-Electro-Mechanical System (MEMS)-IMU, and LiDAR to achieve high-accuracy and reliable navigation in urban environments. Several experiments were conducted to evaluate this method. The results indicate that in comparison with the multi-GNSS PPP/INS tightly coupled solution the positioning Root-Mean-Square Errors (RMSEs) of the proposed GIL method have the improvements of 63.0%, 51.3%, and 62.2% in east, north, and vertical components, respectively. The GIL method can achieve decimeter-level positioning accuracy in GNSS partly-blocked environment (i.e., the environment with GNSS signals partly-blocked) and meter-level positioning accuracy in GNSS difficult environment (i.e., the environment with GNSS hardly used). Besides, the accuracy of velocity and attitude estimation can also be enhanced with the GIL method.

This study estimates station coordinates of GNSS CORS networks in Thailand, based on ITRF2014, by applying the Precise Point Positioning (PPP) technique computed by the GipsyX software. Datum trans...

In kinematic navigation and positioning, abnormal observations and kinematic model disturbances are one of the key factors affecting the stability and reliability of positioning performance. Generally, robust adaptive filtering algorithm is used to reduce the influence of them on positioning results. However, it is difficult to accurately identify and separate the influence of abnormal observations and kinematic model disturbances on positioning results, especially in the application of kinematic Precise Point Positioning (PPP). This has always been a key factor limiting the performance of conventional robust adaptive filtering algorithms. To address this problem, this paper proposes a two-step robust adaptive filtering algorithm, which includes two filtering steps: without considering the kinematic model information, the first step of filtering only detects the abnormal observations. Based on the filtering results of the first step, the second step makes further detection on the kinematic model disturbances and conducts adaptive processing. Theoretical analysis and experiment results indicate that the two-step robust adaptive filtering algorithm can further enhance the robustness of the filtering against the influence of abnormal observations and kinematic model disturbances on the positioning results. Ultimately, improvement of the stability and reliability of kinematic PPP is significant.

The continuously developing Global Navigation Satellite Systems (GNSS), in particular with the latest operational BDS and Galileo, provide good opportunities to enhance the performance of precise positioning. This study evaluates the performance of high-rate precise point positioning (PPP) applied for seismogeodesy with very recent BDS and Galileo. The static experiments with 20-Hz GNSS data show that Galileo and BDS-3/BDS-2 achieve comparable performances, with average 3D RMS values of 0.6–1.3 cm and 0.8–1.2 cm, respectively. In the dynamic experiments, we use a single-axis earthquake simulator of Quanser Shake Table II to simulate seismic waveforms of real earthquakes and collect 20-Hz GNSS data to evaluate the PPP performance. Taking the displacements recorded by the embedded encoder of the shake table as the truth, the accuracies of PPP displacements during the seismic events are 4–8 mm for GPS, 6–9 mm for BDS-2, and 3–6 mm for Galileo and BDS-3/BDS-2. By combining BDS-3 with BDS-2, the positioning accuracy of BDS is improved by 50% with respect to BDS-2 only. Galileo and BDS-3/BDS-2 perform slightly better than GPS, which is likely because the two latest operational systems use the more precise passive hydrogen maser clocks and have lower signal-in-space range error. The multi-GNSS solutions with GPS + Galileo + BDS-3/BDS-2 further improve the accuracy reaching 2–5 mm. We also identify a scale factor in the high-rate PPP displacements, which is probably induced by the dynamic stress error and related to the oscillating frequency. The scale factor reaches the maximum of 1.71 at an oscillating frequency around 2.5 Hz and then descends as the frequency increases. The improved performance of high-rate PPP augmented by the recent BDS-3 and Galileo is helpful to improve the practical level of high-rate GNSS in seismogeodesy and expand its applications to many other high-rate and high-accuracy applications.

With the accelerated development of multi constellation Global Navigation Satellite Systems (GNSS), the field of satellite navigation is going through profound changes. Depending on a single constellation may not be sufficient to guarantee a successful positioning accuracy at any time. Consequently, having several constellations that can be used for positioning offers the opportunity to maintain continuous positioning. This became possible with the global coverage of other constellations such as (BeiDou, GLONASS, Galileo, and GPS). For engineering and scientific applications, this will present both opportunities and obstacles. This paper develops a 4-system positioning model for all the available observations from other GNSS and benefits from them. The important enhancement of satellite visibility, precision dilution, spatial geometry, accuracy, convergence, continuity, and reliability that combined use of multi-GNSS achieve to accurate positioning is attentively inspected and assessed, particularly in strained environments, overall, in the horizontal and 10 cm vertical components with precise orbits the multi-GSS PPP has a precise accuracy greater than 4 cm.

In Global Navigation Satellite (GNSS)-based positioning, a user within a region covered by a network of reference stations can take advantage of the network-estimated parameters. The use of State Space Representation (SSR) parameters as GNSS-augmentation is valuable for Network-Real Time Kinematic (N-RTK) positioning and enables the ambiguity resolution for Precise Point Positioning (PPP) in the so-called PPP-RTK. SSR atmospheric corrections, i.e. tropospheric and ionospheric delays, are commonly estimated for the approximate user position by interpolation from values estimated for the reference stations. Widely used techniques are Inverse Distance Weighted, Ordinary Kriging and Weighted Least Squares (WLS). In this work, we analyze the interpolation quality of such techniques during severe weather events and Traveling Ionospheric Disturbances (TID). Furthermore, we propose modified WLS methods taking advantage of the physical atmospheric behavior during such events. Here, we exploit the use of Numerical Weather Models for tropospheric horizontal gradients information, and estimated TID parameters like wavelength and direction of propagation. Firstly, the interpolation is assessed using simulations considering artificial and real network geometries. Secondly, the proposed techniques are evaluated in post-processing using real SSR parameters generated by network computation of GNSS measurements. As examples, two severe weather events in North Europe in 2017, and one TID event over Japan in 2019 have been analyzed. The interpolation of SSR tropospheric and ionospheric parameters is evaluated. Considering the reference station positions as rover locations, the application of the modified WLS approach reduces the root mean square error in up to 80 % of the cases during sharp weather fluctuations. Also, the average error can be decreased in 64 % of the cases during the TID event investigated. Improvements up to factors larger than two are observed. Furthermore, specific cases are isolated showing particular tropospheric variations where significant errors (e.g. larger than 1 cm) can be reduced up to 20 % of the total amount. Finally, tropospheric and ionospheric messages are proposed to transmit to the user the information needed to implement the suggested interpolation properly.

Satellite clock error prediction plays a key role in GNSS technology for Positioning, Navigation and Timing (PNT) service. However, due to the different types and quality of the space-borne atomic clocks, it is rather difficult to predict high-accuracy satellite clock errors by using one unique prediction model. In general, the performance of existing prediction models varies with different types of satellite clocks, lengths of fitting arcs and predicting arcs. In this article, three common-used prediction models e.g. polynomial model, grey model, and Auto-Regressive Integrated Moving Average (ARIMA) model are evaluated with GNSS precise satellite clock products provided by GFZ. The prediction precision of these models is calculated with respect to precise clock products, specified by different lengths of fitting arcs and prediction arcs respectively. Then, the clock errors predicted by these models are applied to kinematic Precise Point Positioning (PPP) separately and the corresponding positioning performance is discussed. The numerical results show that polynomial model performs the best compared to other two models. For 5-min prediction, the RMS values of predicted clock for GPS, Galileo, GLONASS, and BDS are 0.14 ns, 0.016 ns, 0.21 ns and 0.089 ns respectively. For kinematic PPP with 5-min predicted clock products, polynomial model has the minimum RMS values among three models, with 0.031 m, 0.026 m, and 0.068 m for east, north, and up components, respectively. Moreover, sub-decimeter can be reached for horizontal component with 1-hour predicted clock products. ARIMA model is comparable to polynomial model when the prediction arc is 5–15 min but becomes relatively worse with the increase of the length of prediction arc. Grey model is the worst among the three models, it can meet the requirement of sub-decimeter precision in kinematic PPP only if the prediction arc is shorter than 15 min.

The convergence period is of critical significance in Precise Point Positioning (PPP) applications. Current criterion for determining PPP convergence period is by comparing the positioning error to the ground truth. This experiment-based criterion can be influenced by many factors like the accuracy of ephemeris and the test area. One can hardly get a consistent result of the convergence period without abundant experiments. Consequently, the criterion is not suitable for global-wide PPP specification determination and relevant GNSS service design. In response, we build a new framework of PPP convergence period evaluation based on statistical analysis, with the definition of an indicator, Sequential Dilution of Precision (SDOP). The SDOP represents the propagation from measurement errors to the filter-derived positioning errors. And the framework is established based on SDOP to connect the measurement error, confidential probability, and PPP convergence period. Furthermore, the impact factors of PPP convergence are classified into three parts, satellite geometry, satellite movement, and un-modeled measurement error, which enables researchers to focus on a specific property for analysis. Specifically, the satellite movement can be described by DOP, and we further define the Speed-Up Ratio (SUR) to represent satellite movement. The SDOP is influenced by both DOP and SUR. The proposed framework and relevant variables are examined with both real data and simulated GNSS and Low Earth Orbit (LEO) data. The results are in good agreement with public recognition. Moreover, as an example usage, the global maps of PPP convergence period are presented using the new framework, which are almost impossible to be given with traditional experiment-based criterion. The variation of PPP convergence period through latitude, longitude, and positioning directions is clearly exhibited. The plots can play a significant part in PPP analysis and GNSS service design.

The orientation of GNSS satellites in space is a key quantity in GNSS data processing. It is required to correctly apply several force models and observation corrections. Incorrect or insufficient modeling of satellite attitude can lead to inconsistencies both among providers of GNSS products and between providers and users, which negatively affects the quality of combined products and positioning solutions. Exchanging satellite attitude information in the form of quaternions helps to eliminate or reduce those inconsistencies. This study presents the first systematic exchange of attitude data in a common format (called ORBEX) within the International GNSS Service (IGS). A comparison of attitude auxiliary data from seven IGS analysis centers over a one-year period shows significant differences for GPS and GLONASS satellites, but not for Galileo. These differences are mostly confined to eclipse periods but can reach up to 180°. Considering the attitude differences between analysis center solutions in an experimental clock combination significantly improved the consistency of analysis center solutions during eclipse periods. A kinematic PPP analysis covering ten globally distributed stations over one week resulted in an almost unanimous improvement when using the provided satellite attitude instead of a nominal model, with an average RMS reduction of 50% in the east and up components. The results presented in this study show that satellite attitude is important GNSS auxiliary data and making it available benefits both providers and users.

The gravity field is one of the Earth’s basic physical fields. The geoid can be calculated and the tectonic activity underground can be inversed by gravity anomaly. With the development of various ship-borne gravimeters and navigation technology, including the Global Navigation Satellite System (GNSS) and Strapdown Inertial Navigation System (SINS), the precision of marine gravimetry has been significantly improved (achieve or better than 1mGal). Errors arising from calculations of the correction term have become the main source of gravity measurement errors. At present, the traditional approach is to deploy a GNSS antenna, connect the GNSS antenna to the gravimeter, record the real-time position through data acquisition software, and then use this position to calculate the gravity correction item afterward. Two errors are inevitable. (1) The GNSS antenna position error is large. The pseudorange point positioning method is generally used to obtain real-time GNSS antenna positions, and the positioning accuracy is poor compared with that of precise point positioning. (2) The position coordinates of the gravimeter contain systematic errors related to the ship’s attitude. In this paper, a joint experiment including GNSS antenna arrays and ship-borne gravimeters was designed to evaluate the measurement accuracy via repeat lines on the same ship. The experimental results show the following: (1) attitude accuracies of 0.0299° for the yaw angle, 0.0361° for the pitch angle, and 0.1671° for the roll angle can be obtained at baseline lengths of 25 and 4 m. (2) The GNSS antenna array has an obvious role in determining the point acceleration in the low-frequency band (0–0.01 Hz) and the point position and velocity in the high-frequency band (0.01–1 Hz). (3) The vertical position eccentricity causes an absolute error of 1 mGal and a relative error of$${10}^{-1}$$10-1mGal in gravity measurements and can be corrected by the GNSS antenna array method. (4) Using a GNSS antenna array can obviously improve the measurement accuracy of an instrument with a precision equaling or exceeding 1 mGal, but cannot obviously improve that to an instrument with poor precision (2 mGal or below).

The performance of multi-GNSS (GPS/Galileo) Single-Frequency Precise Point Positioning (SF-PPP) is studied for both static and kinematic PPP users. In the underlying multi-epoch model, the user ambiguities are assumed constant in time, while the positioning parameters are treated as constant (the static case) and fully unlinked in time (the kinematic case). To demonstrate the quality of single-frequency PPP-aided by European Galileo system besides GPS, experimental datasets of Victoria permanent GNSS network which is a sub-network of ARGN (Australian Regional GNSS Network) are analyzed using self-developed software routines. It is shown how Galileo system can enhance the SF-PPP performance as compared to GPS-only single-frequency for high grade geodetic receivers. Our numerical results demonstrate that multi-GNSS SF-PPP outperforms GPS-only in kinematic mode in terms of positioning accuracy. The standard deviation (STD) values of the positioning errors for multi-GNSS/GPS-only solutions are within 2 mm/4 mm (horizontal) and 4 mm/10 mm (vertical). The root-mean-squared error (RMS) values are also within 10 mm/10 mm (horizontal) and 35 mm/50 mm (vertical).

The ionosphere research team of Xi'an University of Science and Technology (XUST) has been committing to high-precision global ionospheric modeling research since 2012. The agency adopted spherical harmonic functions to generate GNSS (Global Navigation Satellite System) global ionospheric product XANG and multi-source data fusion global ionospheric product XAMG. In this essay, we take International GNSS Service (IGS) global ionospheric maps (GIMs) products as a reference to verify and analyze the accuracy of GIMs products produced by XUST in detail from three different aspects. The internal and external evaluation results of GNSS dSTEC indicate that the GIMs products of XUST are consistent with the GIMs products of other analysis centers. In contrast to the Jason-2/-3 VTEC, the STD between XANG and Jason-2 during 2016–2018 is about 2.42–3.11 TECU. The STD between XANG and Jason-3 is about 2.40–3.11 TECU, which is equivalent to that of China Academy of Sciences (CAS) and Jet Propulsion Laboratory (JPL), better than that of the Center for Orbit Determination in Europe (CODE), European Space Operations Center of European Space Agency (ESA) and Wuhan University (WHU), and slightly worse than that of Universitat Politecnica de Catalunya/IonSAT (UPC). Besides, we figure out that the accuracy of GIM products in approximately 60% of the ocean areas has been significantly improved after adding space-based data by comparing the two developed global ionospheric products. Finally, we evaluated the product performance of XUST in single-frequency precise point positioning (SF-PPP) with convergence time and positioning accuracy of standard single-frequency PPP as reference. In terms of average convergence time, the ionospheric delay processing capabilities of XANG and XAMG are comparable to other GIMs and even better than ESAG and JPLG in some regions. In terms of positioning accuracy, the positioning accuracy of XANG as an external ionospheric constraint is better than that of XAMG, and both are better than ESAG, JPLG and IGSG, and slightly worse than CASG and CODG.

Precise point positioning (PPP) is famous for its capability of high-precision positioning and its wide application in many fields. With the rapid development of BDS and Galileo, the number of GNSS satellites used for positioning has now exceeded 110. It brings both opportunities and challenges to PPP. Based on the data of 90 tracking stations of MGEX, this paper analyzed the impact of elevation masks on the performance of multi-GNSS kinematic PPP. The results show that the PODP increases as the elevation mask increases. In general, it will reduce the positioning accuracy and the convergence speed with the increasing of the elevation mask for the PPP float solution. Furthermore, when the elevation mask is below 25o, increasing the elevation mask has little effect on the position accuracy of the horizontal and vertical components in the first 10 min. But after 15 min, the effect on the vertical component became apparently. And after convergence, the RMS of multi-GNSS PPP float solution can reach 5 cm and 10 cm for the horizontal and vertical components when the elevation mask is below 25o. When the elevation mask is 30o, the RMS is still less than 6 cm for the horizontal component, while about 99% of the RMS is less than 11.5 cm for the vertical component. Thirdly, for multi-GNSS PPP AR, it can improve the TTFF and the fixing percentage by fixing the ambiguity subnet with higher elevation mask firstly. Moreover, when the elevation mask is below to 20o, the improvement is more obvious and when the elevation mask is larger than 25o, the TTFF may become longer in some cases.

The Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

Ambiguity Resolution in Precise Point Positioning (PPP-AR) is important to achieving high-precision positioning in wide areas. The International GNSS (Global Navigation Satellite System) Service (IGS) and some other academic organizations have begun to provide phase bias products to enable PPP-AR, such as the integer-clock like products by Centre National d’Etudes Spatials (CNES), Wuhan University (WUM) and the Center for Orbit Determination in Europe (CODE), as well as the Uncalibrated Phase Delay (UPD) products by School of Geodesy and Geomatics (SGG). To evaluate these disparate products, we carry out Global Positioning System (GPS)/Galileo Navigation Satellite System (Galileo) and BeiDou Navigation Satellite System (BDS-only) PPP-AR using 30 days of data in 2019. In general, over 70% and 80% of GPS and Galileo ambiguity residuals after wide-lane phase bias corrections fall in ± 0.1 cycles, in contrast to less than 50% for BeiDou Navigation Satellite (Regional) System (BDS-2); moreover, around 90% of GPS/Galileo narrow-lane ambiguity residuals are within ± 0.1 cycles, while the percentage drops to about 55% in the case of BDS products. GPS/Galileo daily PPP-AR can usually achieve a positioning precision of 2, 2 and 6 mm for the east, north and up components, respectively, for all phase bias products except those based on German Research Centre for Geosciences (GBM) rapid satellite orbits and clocks. Due to the insufficient number of BDS satellites during 2019, the BDS phase bias products perform worse than the GPS/Galileo products in terms of ambiguity fixing rates and daily positioning precisions. BDS-2 daily positions can only reach a precision of about 10 mm in the horizontal and 20 mm in the vertical components, which can be slightly improved after PPP-AR. However, for the year of 2020, BDS-2/BDS-3 (BDS-3 Navigation Satellite System) PPP-AR achieves about 50% better precisions for all three coordinate components.

Smartphones typically compute position using duty-cycled Global Navigation Satellite System (GNSS) L1 code measurements and Single Point Positioning (SPP) processing with the aid of cellular and other measurements. This internal positioning solution has an accuracy of several tens to hundreds of meters in realistic environments (handheld, vehicle dashboard, suburban, urban forested, etc.). With the advent of multi-constellation, dual-frequency GNSS chips in smartphones, along with the ability to extract raw code and carrier-phase measurements, it is possible to use Precise Point Positioning (PPP) to improve positioning without any additional equipment. This research analyses GNSS measurement quality parameters from a Xiaomi MI 8 dual-frequency smartphone in varied, realistic environments. In such environments, the system suffers from frequent phase loss-of-lock leading to data gaps. The smartphone measurements have low and irregular carrier-to-noise (C/N0) density ratio and high multipath, which leads to poor or no positioning solution. These problems are addressed by implementing a prediction technique for data gaps and a C/N0-based stochastic model for assigning realistic a priori weights to the observables in the PPP processing engine. Using these conditioning techniques, there is a 64% decrease in the horizontal positioning Root Mean Square (RMS) error and 100% positioning solution availability in sub-urban environments tested. The horizontal and 3D RMS were 20 cm and 30 cm respectively in a static open-sky environment and the horizontal RMS for the realistic kinematic scenario was 7 m with the phone on the dashboard of the car, using the SwiftNav Piksi Real-Time Kinematic (RTK) solution as reference. The PPP solution, computed using the YorkU PPP engine, also had a 5–10% percentage point more availability than the RTK solution, computed using RTKLIB software, since missing measurements in the logged file cause epoch rejection and a non-continuous solution, a problem which is solved by prediction for the PPP solution. The internal unaided positioning solution of the phone obtained from the logged NMEA (The National Marine Electronics Association) file was computed using point positioning with the aid of measurements from internal sensors. The PPP solution was 80% more accurate than the internal solution which had periodic drifts due to non-continuous computation of solution.

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

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Etudes Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.

Light Detection and Ranging (LiDAR) based Simultaneous Localization and Mapping (SLAM) has drawn increasing interests in autonomous driving. However, LiDAR-SLAM suffers from accumulating errors which can be significantly mitigated by Global Navigation Satellite System (GNSS). Precise Point Positioning (PPP), an accurate GNSS operation mode independent of base stations, gains growing popularity in unmanned systems. Considering the features of the two technologies, LiDAR-SLAM and PPP, this paper proposes a SLAM system, namely P3-LOAM (PPP based LiDAR Odometry and Mapping) which couples LiDAR-SLAM and PPP. For better integration, we derive LiDAR-SLAM positioning covariance by using Singular Value Decomposition (SVD) Jacobian model, since SVD provides an explicit analytic solution of Iterative Closest Point (ICP), which is a key issue in LiDAR-SLAM. A novel method is then proposed to evaluate the estimated LiDAR-SLAM covariance. In addition, to increase the reliability of GNSS in urban canyon environment, we develop a LiDAR-SLAM assisted GNSS Receiver Autonomous Integrity Monitoring (RAIM) algorithm. Finally, we validate P3-LOAM with UrbanNav, a challenging public dataset in urban canyon environment. Comprehensive test results prove that, in terms of accuracy and availability, P3-LOAM outperforms benchmarks such as Single Point Positioning (SPP), PPP, LeGO-LOAM, SPP-LOAM, and the loosely coupled navigation system proposed by the publisher of UrbanNav.

This article proposes a new method for uncalibrated phase delay (UPD) estimation to improve the accuracy of precise point positioning (PPP), which uses only observation station data. This means that the station used to generate the UPDs is the same station to which they are applied. First, dual-frequency observation equations based on a raw PPP model are developed. Then, the UPDs are calculated from integer linear combinations of float ambiguities. Third, with the UPD corrections, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to obtain the integer ambiguities. Since only observation station data are used for UPD estimation, the partial ambiguity resolution (PAR) method is adopted to increase the possibility of finding a subset of integer ambiguities. The UPD estimation and ambiguity resolution are performed in each epoch. To obtain the correct integer ambiguity, the ratio test and success rate (bootstrapping) are used to evaluate the estimated integer ambiguity. Finally, by treating the integer ambiguities as constants, fixed solutions can be obtained. Quality control is also applied throughout the entire data processing procedure to obtain high quality float and fixed solutions. Data from 22 stations of the International Global Navigation Satellite System (GNSS) Service (IGS) in East Asia on day of year (DOY) 206, 2017, are used to verify the feasibility of this method. The experimental results show that compared with the float solution, the proposed method can significantly improve the accuracy in the east, north and up directions by 24%, 21% and 18% for static PPP and 36%, 18% and 34% for dynamic PPP, respectively. However, the accuracy of the proposed method is still lower than that of the fixed solutions obtained by the PRIDE-PPPAR software, in which the fractional cycle bias is computed based on reference network data. These findings sufficiently show that the proposed method can offer better solution accuracy than the float solution. However, the quality of the UPDs estimated only from observation station data is not as good as that of the estimates obtained based on reference network data.

The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than 1cm at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than 25cm in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than 1cm in the normal weather condition; however, the scales of the horizontal and 3D biases are concentrated in 1 to 10cm in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered.

The implementation of Intelligent Transport System (ITS) technology is expected to significantly improve road safety and traffic efficiency. One of the key components of ITS is precise vehicle positioning. Positioning with decimetre to sub-metre accuracy is a fundamental capability for self-driving, and other automated applications. Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) is an attractive positioning approach for ITS due to its relatively low-cost and flexibility. However, GNSS PPP is vulnerable to several effects, especially those caused by the challenging urban environments, where the ITS technology is most likely needed. To meet the high integrity requirements of ITS applications, it is necessary to carefully analyse potential faults and failures of PPP and to study relevant integrity monitoring methods. In this paper an overview of vulnerabilities of GNSS PPP is presented to identify the faults that need to be monitored when developing PPP integrity monitoring methods. These vulnerabilities are categorised into different groups according to their impact and error sources to assist integrity fault analysis, which is demonstrated with Failure Modes and Effects Analysis (FMEA) and Fault Tree Analysis (FTA) methods. The main vulnerabilities are discussed in detail, along with their causes, characteristics, impact on users, and related mitigation methods. In addition, research on integrity monitoring methods used for accounting for the threats and faults in PPP for ITS applications is briefly reviewed. Both system-level (network-end) and user-level (user-end) integrity monitoring approaches for PPP are briefly discussed, focusing on their development and the challenges in urban scenarios. Some open issues, on which further efforts should focus, are also identified.

The International GNSS Service (IGS) has been providing reliable Global Ionospheric Maps (GIMs) since 1998. The Ionosphere Associate Analysis Centers (IAACs) model the global ionospheric Total Electron Content (TEC) and generate the daily GIM products within the context of the IGS. However, the rapid and final daily GIM products have a latency of at least one day and one week or so, respectively. This limits the value of GIM products in real-time GNSS applications. We propose and develop an approach for near real-time modeling of global ionospheric TEC by using the hourly IGS data. We perform an experiment in a real operating environment to generate near real-time GIM (named BUHG) products for more than two years. Final daily GIM products, Precise Point Positioning (PPP) based VTEC resources, and JASON-3 Vertical TEC (VTEC) measurements are collected for testing the performance of BUHG. The results show that the performance of BUHG is very close to that of the daily GIM products. Also, there is good agreement between BUHG and PPP-derived VTEC as well as with JASON-3 VTEC. It is possible that BUHG would be further improved with an increase in available hourly GNSS data.

Galileo navigation system has significantly expanded satellite constellation over the last few years and now serves with 22 satellites in three orbital planes. The development of the Galileo is not only limited to the number of satellites in the space segment, but also the quality of the IGS MGEX products produced by different Analysis Centers has increased gradually and brought up the topic of investigation of the accuracy and precision of the Galileo-only positioning. However, almost all of the studies on Galileo-only positioning in the literature have been performed with Precise Point Positioning method and comprehensive studies with the relative positioning technique are quite a few. In this study, the development of the accuracy and precision of the Galileo from 2016 to the end of 2019 (4 years) has been investigated for the first time by means of relative positioning technique. For this purpose, data of eight GNSS stations selected from the IGS MGEX network were obtained and analyzed with GAMIT/GLOBK software as GPS-only and Galileo-only, separately. Using the daily solutions obtained from both navigation systems, time series were produced and the differences between them were compared in order to reveal the Galileo accuracy. According to the results, the accuracy of the Galileo was variable during the experiment and it could be examined in three periods. The averages of 3D positioning error in the first period (2016-2017) is 14.92 mm and improved by 56%, and decreased to 6.55 mm in the second period (2017-2018), and then improvement at 23% in the third period (2018 to the end of 2019) and decrescent to level of 5.13 mm on average for all stations. Similarly, standard deviations obtained from Galileo increased during the experiment and during the 3rd period it was closed to a few mm with GPS. It was concluded that the accuracy and precision of the Galileo showed parallel development and the development was directly related to the number of satellites in the Galileo constellation, and as a result, nowadays, Galileo-derived coordinates are close to the coordinates obtained from the GPS by a few mm.

In modern-day multi-dimensional recreational drones (UAVs), the global navigation satellite system (GNSS) units in- use are commonly fraught with precise-point-positioning (PPP) data errors or inaccuracies, hence, necessitating this work. These data inaccuracies, occasioned by the system’s drawbacks such as sudden GPS lock or jamming, embedded device misalignment, drone’s limited communication coverage, signaling and detection, all contributes to the system’s PPP computation complexity. To mitigate PPP complexity, an intelligent and robust accurate continuous-discrete (ACD) based hybrid cubature-extended Kalman filter (C-EKF) computation model for an integrated GNSS unit is corroborated in this article. More precisely, time updates to the state and parameter sub-vectors for the GNSS unit is accomplished using the third-degree spherical-radial cubature rule. The system’s testbed simulation is then conducted using tightly-coupled units of (i) ring laser gyroscope (RLG) and (ii) micro-electro-mechanical system (MEMS) variants of the inertial measurement unit (IMU) to ascertain the PPP cooperative tendencies. Optimized performance comparisons of the proposed hybrid C-EKF over the existing cubature Kalman filter (CKF) and extended Kalman filter (EKF) models with-respect-to (w.r.t) its probabilistic outages, Yaw error-differences and ergodic capacities are demonstrated and presented.

Using of lattice packing theory for computation of precise satellite clock corrections based on measurements from a ground network of GNSS CDMA signals (network solution) is considered. Advantage of lattice packing theory for this task solution in comparison with algebraic graph theory is described. Network solution based on of algebraic graph theory was considered in previous paper of the authors [3]. The precise satellite clock corrections are transmitted into the user receiver and applied to get the user coordinates with the errors usually not exceeding 1–3 cm. Ambiguity resolution of carrier phase measurements is used to get such precise satellite clock corrections; it leads to a considerable increase in positioning accuracy and a significant reduction of convergence time for user solution.

This study proposes an enhanced multipath mitigation method based on multi-resolution carrier-to-noise-ratio (CNR) model and adaptive statistical test strategy for real-time kinematic precise point positioning (PPP) applications. The multi-resolution CNR model is established with GPS observation data collected from DOY 152 to 181 of 2019 by 230 globally distributed IGS stations, which used to analyze the relevant factors affecting CNR. Statistical results indicate that the CNR is not only related to the satellite elevation, but also closely related to the receiver types and specific satellite. The maximum difference between different receivers can reach 20 dB for the same satellite at the same elevation. In addition, the performance of the CNR is also obviously different between each satellite, and the maximum difference between different satellites is about 10 dB for the same receiver at the same elevation. Hence, in terms of the method which is based on CNR information for multipath detection and mitigation, the independence of receiver types, satellite and frequency must be considered. With the above analysis, this study developed a multi-resolution CNR model based on different receiver types, different satellites and different elevation firstly. Then, combined with the adaptive statistical test strategy which is based on the difference of CNR between inter-frequency and the difference of CNR between adjacent epochs, the multipath can be detected effectively. For the epoch which affected by multipath, the down-weighted strategy based on CNR is adopted to mitigate the influence of multipath on positioning. Real-time kinematic PPP data are collected to assess the proposed method, and the results demonstrate that the proposed method can detect the multipath effectively, and the detection rate can reach 90.28%. Moreover, after adopting the mitigation strategy, the RMS bias of the east, north and up components are improved about 19.95%, 17.89% and 23.07% compared to the original results, respectively. It is worth noting that this proposed method is also suitable for other GNSS, such as GLONASS and BDS, but the corresponding CNR model must be established simultaneously.

Precise extraction of ionospheric total electron content (TEC) observations with high precision is the precondition for establishing high-precision ionospheric TEC models. Nowadays, there are several ways to extract TEC observations, e.g., raw-code method (Raw-C), phase-leveled code method (PL-C), and undifferenced and uncombined precise point positioning method (UD-PPP); however, their accuracy is affected by multipath and noise. Considering the limitations of the three traditional methods, we try directly to use the phase observation based on zero-difference integer ambiguity to extract ionospheric observations, namely, PPP-Fixed method. The main goal of this work is to: 1) deduce the expression of ionospheric observables of these four extraction methods in a mathematical formula, especially the satellite and receiver hardware delays; 2) investigate the performance and precision of ionospheric observables extracted from different algorithms using two validation methods, i.e., the co-location experiment by calculating the single difference for each satellite, and the single-frequency PPP (SF-PPP) test by two co-location stations; and 3) use the short arc experiment to demonstrate the advantages of the PPP-Fixed method. The results show that single-difference mean errors of TEC extracted by PL-C, UD-PPP, and PPP-Fixed are 1.81, 0.59, and 0.15 TEC unit (TECU), respectively, and their corresponding maximum single-difference values are 5.12, 1.68, and 0.43 TECU, respectively. Compared with PL-C, the precision of the TEC observations extracted by the PPP-Fixed method is improved by 91.7%, while it is 67.3% for UD-PPP. The SF-PPP experiment shows that PPP-Fixed is the best among these methods in terms of convergence speed, correction accuracy, and reliability of positioning performance. Moreover, the PPP-Fixed method can achieve high accuracy even when the observed arc is short, e.g., within 40 min.

For precise position services, the real-time precise point positioning (PPP) is a promising technology. The real-time PPP performance is expected to be improved by multi-system combination. The performance of real-time multi-system PPP needs to be periodically investigated, with the increasing number of available satellites and the continuously improved quality of real-time precise products of satellite clocks and orbits. In this study, a comprehensive performance assessment is conducted for the four-system integrated real-time PPP (FSIRT-PPP) with GPS, BDS, Galileo and GLONASS in both static and kinematic modes. The datasets from 118 stations spanning approximately a month are used for analysis, and the real-time stream CLK93 is employed. The superior performance of FSIRT-PPP is validated by comparing with the results of GPS/BDS, GPS/Galileo, GPS/GLONASS, GPS-only, BDS-only, Galileo-only and GLONASS-only cases. The FSIRT-PPP using ionospheric-free (IF) combined observables can achieve a convergence time of 10.9, 4.8 and 11.8 min and a positioning accuracy of 0.4, 0.5 and 0.7 cm in the static mode in the east, north and up directions, respectively, while the derived statistic is 15.4, 7.0 and 16.4 min, and 1.6, 1.2 and 3.4 cm in the kinematic mode in the three directions, respectively. Moreover, we also compare the position solutions of real-time PPP adopting IF combined and uncombined (UC) observables, and prove the mathematical equivalence between the two PPP models in the converged stage, provided that there are no external ionospheric corrections or constraints given to the estimated ionospheric delays in the UC model. The difference between the fully converged positioning accuracy of IF-based and UC-based real-time PPP is marginal, but the UC-based real-time PPP has longer convergence time due to the influence of the significant unmodeled time-varying errors in the real-time precise products as well as the different parameterization between them. For completeness, the real-time kinematic PPP results in harsh environments and the post-processed PPP results are also presented.

The performance of precise point positioning (PPP) mainly depends on satellite orbit and clock accuracy. Ultra-rapid and rapid orbit/clock products have been creating by analysis centres (ACs) for ...

Precise point positioning (PPP) is a modeling and processing method that uses global navigation satellite system (GNSS) pseudorange and carrier‐phase observations, along with precise satellite orbit and clock products, for single‐receiver static or kinematic positioning with centimeter precision. As such it offers an attractive alternative to differential GNSS positioning‚ making it particularly suited for areas that lack dense GNSS network infrastructure.This chapter describes the PPP concept and provides a systematic treatment of the required models and its different mechanizations. Although PPP was originally conceived as an ionosphere‐free dual‐frequency technique, single‐ and multi‐frequency PPP are also presented. As PPP relies on accurate satellite position and clock data, we discuss the availability of these products and describe the different orbit and clock products that are available for post‐processed and real‐time PPP.With the ongoing proliferation of navigation satellite systems, the availability of more satellites and signals brings a range of improvements for PPP. We discuss multi‐frequency, multi‐GNSS PPP and also develop the models for ambiguity‐resolved PPP as a means for reducing the relatively long PPP convergence times. With multi‐GNSS PPP, new challenges are also introduced. We describe the need for modeling the inter‐system biases (ISBs) and show how they can be corrected so as to realize the tightest possible multiple systems integration. Finally, although PPP has been devised for precise positioning, we also discuss its application for water vapor estimation, ionospheric estimation‚ and time transfer.

This chapter describes the concepts and theory involved in relative global navigation satellite system (GNSS) positioning and navigation. It begins by describing the concepts and advantages of relative positioning in contrast to point positioning, and the conceptual and terminological similarities and differences between differential and relative positioning. A brief description of the generic GNSS observables used and a catalog of measurement errors are then provided, in order to present the necessary mathematical modeling and relative baseline estimation. Central to precise relative positioning is carrier‐phase integer ambiguity resolution, which is described, along with an algorithmic case study. All of these concepts are brought together to create real‐time kinematic (RTK) processing, as well as the follow‐on network RTK processing. The chapter concludes with a discussion of recent developments in relative positioning in terms of additional signals, multi‐constellations, and multi‐processing modes, such as network RTK combined with precise point positioning.

The tightly coupled global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) can provide high-precision position, velocity and attitude informa...

Determining the speed of tectonic plate displacement helps us to better understand tectonic activities of the area, and is a prerequisite to help forecast earthquakes. The determination of tectonic plate displacement by GNSS technology in Vietnam has been conducted since the 2000s, mainly using the relative positioning technique. The increasing accuracy of precise point positioning technique, and the number of CORS in Vietnam, will facilitate the accurate determination of tectonic velocities. Based on the GNSS data of some CORSs in Vietnam from 2016-2018, we have determined accurately their three-dimensional coordinates using a precise point positioning technique. After modeling periodic variations on the time series, we calculated the tectonic movement rate of 7 Vietnamese stations and 3 other stations in the region. Through analysis and comparison with other geology/plate motion models and GPS results, we conclude that this result is reliable. The velocity of tectonic motion in the North, East and Up components of Ha Noi, Da Nang and Ho Chi Minh City are respectively (-13.1, +32.8, -1.3), (-9.9, +31.0, +2.6) and (-10.3, +26.9, +2.7) mm/year.

Multi-global navigation satellite system (GNSS) real-time (RT) single-frequency (SF) positioning with a low-cost receiver has received increasing attention in recent years due to its large amount of possible applications. One major challenge in single-frequency positioning is the effective mitigation of the ionospheric delays since it is a dominant error source. Nowadays, a high-precision RT ionospheric vertical total electron content (VTEC) product is released by the Centre National d’Etudes Spatiales (CNES) through its real-time service (RTS). The effect of this product on RT single-frequency positioning needs to be investigated. In this study, we provide an evaluation of the quality of multi-GNSS CLK93 orbit and clock products through the comparison to the final precise products, and comprehensively evaluate the impact of CNES VTEC products on multi-GNSS RT-SF-SPP (Standard Point Positioning)/PPP (Precise Point Positioning) performances. Datasets from 46 Multi-GNSS Experiment (MGEX) stations and the CLK93 corrections for 14 consecutive days in 2019 are collected to process with different scenarios. Experimental results show that the CNES VTEC products can replace the final GIM products in the single- and multi-GNSS SF-SPP with the same positioning accuracy requirements during the period of mild solar activity (Kp index is less than 3). Regarding the kinematic RT-SF-PPP, the (re-)convergence also can be improved by adopting the prior CNES-VTEC constrains. Compared with the IF RT-SF-PPP with quad-constellation, the positioning accuracy of the CNES-VTEC-constrained RT-SF-PPP can be improved by about 10.30%, in which the average RMS can achieve 17.9, 19.8 and 32.3 cm in the North, East and Up components, respectively. Compared with the final precise products of GBM, the satellite orbit accuracy of CLK93 products is 4, 5, 12 and 16 cm for GPS, Galileo, GLONASS and BDS, respectively. As for the CLK93 satellite clock, its RMS accuracy of GPS, Galileo, GLONASS and BDS is 0.3, 0.4, 2.5 and 1.8 ns, respectively.

This study assesses the precision of zenith tropospheric delay (ZTD) obtained through triple-constellation global navigation satellite system (GNSS) precise point positioning (PPP). Various ZTD estimates are obtained as by-products from GPS-only, GPS/Galileo, GPS/BeiDou, and triple-constellation GPS/Galileo/BeiDou PPP solutions. Triple-constellation GNSS observations from a number of globally distributed reference stations are processed over a period of seven days in order to investigate the daily performance of the ZTD estimates. The estimated ZTDs are then validated by comparing them with the International GNSS Service (IGS) tropospheric products and the University of New Brunswick (UNB3m) model counterparts. It is shown that the ZTD estimates agree with the IGS counterparts with a maximum standard deviation (STD) of 2.4 cm. It is also shown that the precision of estimated ZTD from the GPS/Galileo and GPS/Galileo/BeiDou PPP solutions is improved by about 4.5 and 14%, respectively, with respect to the GPS-only PPP solution. Moreover, it is found that the estimated ZTD agrees with the UNB3m model with a maximum STD of 3.1 cm. Furthermore, the GPS/Galileo and GPS/Galileo/BeiDou PPP enhance the precision of the ZTD estimates by about 6.5 and 10%, respectively, in comparison with the GPS-only PPP solution.

Multi-constellation GNSS precise point positioning (PPP) typically uses the extended Kalman filter (EKF) for kinematic applications. Unfortunately, the obtained positioning accuracy in this approac...

The tropospheric delay is an essential source of error for positioning using the Global Navigation Satellite System (GNSS). Scientific applications of GNSS positioning such as the study of earth crust deformation and earthquake prediction require high accuracy in positioning, an analysis of tropospheric delay calculations is needed to improve the accuracy of GNSS positioning. One part of the tropospheric delay is Zenith tropospheric delays (ZTD), which are estimated using the Precise Point Positioning (PPP) method. ZTD estimates can be beneficial for meteorological applications, for example, is the estimation of water vapor levels in the atmosphere from the estimated ZTD. We use GNSS data from the BAKO station in Cibinong and JOG2 station located in Yogyakarta. The GNSS data format is an Independent Exchange Receiver (RINEX), which we extracted using the sophisticated open-source GNSS software, called goGPS version 1.0 Beta from Geomatics Research and Development s.r.l. - Lomazzo, Italy. We validate the results of the extraction process with two international tropospheric products from International GNSS Services (IGS) with commercial software Bernese version 5 and the University of Nevada Reno (UNR) with software from NASA Jet Propulsion Laboratory (JPL) namely GIPSY / OASIS II. Epoch in this study, we use days of the year (DOY) 022-025 / 22-25 January representing the rainy season and DOY 230-233 to coincide on August 17-20 representing the dry season 2018. Our results obtained ZTD values both in January and August, and the two BAKO and JOG2 stations were consistent and worked well at different times and stations. RMS throughout DOY, both at BAKO and JOG2 stations, show small values

The Precise Point Positioning (PPP) is an absolute positioning method which emerged as an alternative to the relative positioning method. This method is widely used in many applications in recent years. In this method the static and kinematic positioning can be performed with high accuracy by using single GNSS receiver. In the last few years, the PPP method has started to be used in real time (RT-PPP) thanks to the real-time precise products (satellite orbit and clock data) produced by different organizations like IGS, BKG, CNES, ESA, EUREF, GFZ etc. The high interest in RT-PPP has accelerated the development of this method and many software have been developed. Recently, some of the software have ability to apply integer ambiguity resolution (AR). For this purpose, in this study the positioning performance of RT-PPP method was tested using two options of PPP-WIZARD software (RT-PPP, RT-PPP-AR). Three IGS stations were chosen in different geographical regions. The real-time coordinates of the stations belong to the observation period of about 4 hours were derived simultaneously with the RT-PPP and RT-PPP-AR options in 1 second epoch interval. The results obtained are given in a comparative approach.

The single initial Global Positioning System (GPS) has been expanded into multiple global and regional navigation satellite systems (multi-GNSS/RNSS) as the Global Navigation Satellite System (GLONASS) is restored and the BeiDou Navigation Satellite System (BDS), Galileo Satellite Navigation System (Galileo) and Quasi-Zenith Satellite System (QZSS) evolve. Using the differences among these five systems, the paper constructs a consolidated multi-GNSS/RNSS precise point positioning (PPP) observation model. A large number of datasets from Multi-GNSS Experiment (MGEX) stations are employed to evaluate the PPP performance of multi-GNSS/RNSS. The paper draws three main conclusions based on the experimental results. (1) The combined GPS/GLONASS/Galileo/BDS/QZSS presents the PPP with the shortest mean convergence time of 11·5 min, followed by that of GPS/GLONASS/Galileo/BDS (12·4 min). (2) The combined GPS/GLONASS/BDS/Galileo/QZSS shows the optimal PPP performance when the cut-off elevation angle is basically the same because of the rich observation data due to a large number of satellites. To be specific, for combined GPS/GLONASS/BDS/Galileo/QZSS, the PPP convergence percentage is 80·9% higher relative to other combined systems under 35° cut-off elevation angle, and the percentages of the root mean square values of PPP within 0–5 cm are enhanced by 80·5%, 81·5% and 87·3% in the North, East and Up directions relative to GPS alone at 35° cut-off elevation angle. (3) GPS alone fails to conduct continuous positioning due to the insufficiency of visible satellites at 40° cut-off elevation angle, while the kinematic PPP of multi-GNSS/RNSS remains capable of obtaining positioning solutions with relatively high accuracy, especially in the horizontal direction.

Accurate navigation is required in many Unmanned Aerial Vehicle (UAV) applications. In recent years, GNSS Precise Point Positioning (PPP) has been recognised as an efficient approach for providing precise positioning services. In contrast to the widely used Real-Time Kinematic (RTK), PPP is independent of reference stations, which greatly broadens its scope of application. However, the accuracy and reliability of PPP can be significantly decreased by poor GNSS satellite geometry and outage. In response, a real-time four-constellation GNSS PPP is applied to improve the geometry in this work, and PPP is tightly coupled with an Inertial Measurement Unit (IMU) to smooth the position and velocity output, thus improving the robustness of the navigation solution. Experimental flight tests are carried out using a UAV in an open-sky area, and GNSS-challenged environments are simulated. The results show that the four-constellation GNSS PPP/IMU integration reduces the Root-Mean-Square (RMS) Three-Dimensional (3D) positioning and velocity error by 76.4% and 67.1%, respectively, in open sky with respect to the one-GNSS PPP. Under scenarios where GNSS measurements are insufficient, the coupled system can still provide continuous solutions. Moreover, the coupled PPP/IMU system can also maintain the convergence of PPP during GNSS-challenged periods and can greatly shorten the re-convergence period of PPP when the UAV returns to the open sky.

In this paper, the potentials of using Global Navigation Satellite System (GNSS) techniques in the complex calibration procedure of the tracking sensors for missile test range applications have been presented. The frequently used tracking sensors in test range applications are- electro-optical tracking stations (EOTS) and tracking radars. Over the years, the EOTS are used as the reference for bias estimation of the radars. With the introduction of GPS in test range applications, especially the DGPS, the reference for bias estimation got shifted to DGPS from the EOTS. However, the achievable position solution accuracy is limited to the order of a few meters for DGPS, EOTS, and Radars. With the evolution of Multi-constellation GNSS and carrier-phase based measurement techniques in satellite navigation, achievable position solution accuracies may be improved to sub-meter level. New navigation techniques like real time kinematic (RTK) and precise point positioning have the potentials for use in the calibration procedures of the missile test ranges to the accuracies of centimeter-level. Moreover, because of the availability of a large number of navigation signals over the Indian region, multi-constellation GNSS receivers can enhance signal availability, reliability, and accuracies during the calibration of missile test ranges. Currently available compact, low-cost GNSS modules also offer the possibilities of using these for cost-effective, networked RTK for dynamic calibration of test ranges reducing cost and resource requirements.

This paper theoretically derives the equivalence conditions for the loosely and tightly coupled GNSS/INS integration algorithms. Firstly, the equivalence is proved when using single epoch GNSS measurements, which means the GNSS processor provides standalone solution. Then, the equivalence proof is further extended for the filtering solutions, which are usually applied for differential GNSS and precise point positioning. Based on these, different state and measurement models for GNSS/INS integration navigation are summarized, and natural differences among these models are discussed. This indicates that once the same measurement and predict information are used, the integration would be equivalent no matter what kind of coupling schemes are used. A flight dataset with GNSS and tactical IMU data is used to evaluate the equivalence and discrepancies among four different measurement models, and the results confirm the theoretical derivations.

Real-time single-frequency precise point positioning (RT-SFPPP) of low-cost has been attracting increasing attention in numerous global navigation satellite system (GNSS) applications. Nowadays, three multi-GNSS RT-SFPPP models are widely applied, i.e. ionosphere-corrected (IC), ionospherefree (IF) and ionosphere-weighted (IW) models. A comprehensive evaluation of the three models using CLK93 products is performed in the aspect of observation residuals, positioning accuracy and convergence. Data sets with quad-system are collected from 16 multi-GNSS experiments (MGEX) stations and are analysed in the simulated kinematic precise point positioning (PPP). Besides, kinematic PPP for a 5-h shipborne data set is also conducted. Experimental results show that the positioning accuracy of IW model using MGEX data is better than that of both IC and IF models. Regarding the kinematic shipborne test, positioning accuracy of IF/IW model is of 0.27/0.26, 0.21/0.26 and 0.49/0.48 m for the N, E and U components, respectively, which is much better than that of IC model. As for average convergence time, IW model shows the best performance, which is at least 25% faster than the IF model. Different from both IF and IW models, the amplification of ionospheric errors has some impact on the positioning performance of the IC model at different frequencies.