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Abstract Accuracy of dynamic precise point positioning (PPP) degrades significantly under users' challenging environments because of the limited or unavailable GPS observations. To overcome such weakness, a tight-integration system of micro-electromechanical systems (MEMS) inertial measurement unit (IMU), odometer, and GPS ionospheric delay constrained PPP is investigated to provide users positions and attitudes with higher accuracy, reliability, and continuity under the weak GPS observability environments. In this approach, the data from different sensors are integrated in two joint extend Kalman filters (EKF). One is for PPP/INS tight-integration and the other one is for odometer aiding the solutions from INS or PPP/INS tight-integration modes. Here, the advantages of slow time-varying ionospheric delay, high-accuracy in short time of inertial navigation system (INS), and hardly-disturbed odometer are utilized effectively to enhance PPP solutions. The corresponding mathematical models are provided and are evaluated by a set of one-hour real land-borne test data collected from a MEMS IMU, an odometer, and a dual-frequency GPS receiver in suburbs of Wuhan city, China, and also a set of simulated weak satellites availability data which is to imitate the GPS availability under unban canyons. Results indicate that the fusion system can improve navigation accuracy of GPS or GPS/INS significantly. That are, more than fifty percentages position enhancements in north-east-down components, and about forty percentages attitude enhancements in roll-pitch-yaw direction under the weak GPS availability. [ABSTRACT FROM AUTHOR]

The unexpected observing environments in dynamic applications may lead to partial and/or complete satellite signal outages frequently, which can definitely impact on the positioning performance of the Precise Point Positioning (PPP) in terms of decreasing available satellite numbers, breaking the continuity of observations, and degrading PPP’s positioning accuracy. Generally, both the Inertial Navigation System (INS) and the multi-constellation Global Navigation Satellite System (GNSS) can be used to enhance the performance of PPP. This paper introduces the mathematical models of the multi-GNSS PPP/INS Tightly Coupled Integration (TCI), and investigates its performance from several aspects. Specifically, it covers (1) the use of the BDS/GPS PPP, PPP/INS, and their combination; (2) three positioning modes including PPP, PPP/INS TCI, and PPP/INS Loosely Coupled Integration (LCI); (3) the use of four various INS systems named navigation grade, tactical grade, auto grade, and Micro-Electro-Mechanical-Sensors (MEMS) one; (4) three PPP observation scenarios including PPP available, partially available, and fully outage. According to the statistics results, (1) the positioning performance of the PPP/INS (either TCI or LCI) mode is insignificantly depended on the grade of inertial sensor, when there are enough available satellites; (2) after the complete GNSS outages, the TCI mode expresses both higher convergence speed and more accurate positioning solutions than the LCI mode. Furthermore, in the TCI mode, using a higher grade inertial sensor is beneficial for the PPP convergence; (3) under the partial GNSS outage situations, the PPP/INS TCI mode position divergence speed is also restrained significantly; and (4) the attitude determination accuracy of the PPP/INS integration is highly correlated with the grade of inertial sensor. [ABSTRACT FROM AUTHOR]

Nowadays, Global Positioning System (GPS) plays an increasingly important role in retrieving real-time precise co-seismic displacements for geo-hazard monitoring and early warning. Several real-time positioning approaches have been demonstrated for such purpose, such as real-time kinematic relative positioning, precise point positioning, etc., where dual-frequency geodetic receivers are applied for the removal of ionosphere delays by inter-frequency combination. At the same time, it would be also useful to develop efficient algorithms for estimating precise displacements with low-cost GPS receivers since they can make a denser network or multi-sensors combination without putting too much financial burden. In this contribution, we present a new method to retrieve precise co-seismic displacements in real-time using a standalone single-frequency receiver. In the new method, observations prior to an earthquake are utilized to establish a precise ionospheric delay prediction model, so that precise co-seismic displacements can be obtained without any convergence process. Our method was validated with an outdoor experiment as well as by re-processing of 1-Hz GPS data collected by the GEONET network during the 2011 Tohoku Mw 9.0 earthquake. For the latter, RMS against dual-frequency receivers constituted 2 cm for horizontal components and 3 cm for the vertical component. We specially address the observation biases and their impact on the accuracy of single frequency positioning. Our approach makes real-time GPS displacement monitoring with dense network much more affordable in terms of financial costs. [ABSTRACT FROM AUTHOR]

Abstract: In order to speed up Precise Point Positioning (PPP)’s convergence, a combined PPP method with GPS and GLONASS which is based on using raw observations is proposed, and the positioning results and convergence time have been compared with that of single system. The ionospheric delays and receiver’s Differential Code Bias (DCB) corrections are estimated as unknown parameters in this method. The numerical results show that the combined PPP has not caused significant impacts on the final solutions, but it greatly improved Position Dilution of Precision (PDOP) and convergence speed and enhanced the reliability of the solution. Meanwhile, the convergence speed is greatly influenced by the receiver’s DCB, positioning results in horizontal which are better than 10cm can be realized within 10min. In addition, the ionosphere and DCB products can be provided with high precision. [Copyright &y& Elsevier]

Abstract: Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10cm accuracy, PPP with ambiguity-fixing of 2–5cm accuracy, PPP using single-frequency receiver with accuracy of better than 50cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only. [Copyright &y& Elsevier]

Abstract Global Navigation Satellite System (GNSS) has been widely used in many geosciences areas with its Positioning, Navigation and Timing (PNT) service. However, GNSS still has its own bottleneck, such as the long initialization period of Precise Point Positioning (PPP) without dense reference network. Recently, the concept of PNTRC (Positioning, Navigation, Timing, Remote sensing and Communication) has been put forward, where Low Earth Orbit (LEO) satellite constellations are recruited to fulfill diverse missions. In navigation aspect, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites but with much faster geometric change to enhance GNSS capability, which is named as LEO constellation enhanced GNSS (LeGNSS). As a result, the initialization time of PPP is expected to be shortened to the level of a few minutes or even seconds depending on the number of the LEO satellites involved. In this article, we simulate all the relevant data from June 8th to 14th, 2014 and investigate the feasibility of LeGNSS with the concentration on the key issues in the whole data processing for providing real-time PPP service based on a system configuration with fourteen satellites of BeiDou Navigation Satellite System (BDS), twenty-four satellites of the Global Positioning System (GPS), and sixty-six satellites of the Iridium satellite constellations. At the server-end, Precise Orbit Determination (POD) and Precise Clock Estimation (PCE) with various operational modes are investigated using simulated observations. It is found out that GNSS POD with partial LEO satellites is the most practical mode of LeGNSS operation. At the user-end, the Geometry Dilution Of Precision (GDOP) and Signal-In-Space Ranging Error (SISRE) are calculated and assessed for different positioning schemes in order to demonstrate the performance of LeGNSS. Centimeter level SISRE can be achieved for LeGNSS. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a method of real-time monitoring and modeling the ionospheric Total Electron Content (TEC) by Precise Point Positioning (PPP). Firstly, the ionospheric TEC and receiver’s Differential Code Biases (DCB) are estimated with the undifferenced raw observation in real-time, then the ionospheric TEC model is established based on the Single Layer Model (SLM) assumption and the recovered ionospheric TEC. In this study, phase observations with high precision are directly used instead of phase smoothed code observations. In addition, the DCB estimation is separated from the establishment of the ionospheric model which will limit the impacts of the SLM assumption impacts. The ionospheric model is established at every epoch for real time application. The method is validated with three different GNSS networks on a local, regional, and global basis. The results show that the method is feasible and effective, the real-time ionosphere and DCB results are very consistent with the IGS final products, with a bias of 1–2 TECU and 0.4ns respectively. [Copyright &y& Elsevier]

Abstract: A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30min, a horizontal resolution of 40km and a vertical resolution of 500m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles. [Copyright &y& Elsevier]

Low Earth Orbit (LEO) enhanced Global Navigation Satellite System (LeGNSS) has been recognized as the promising positioning system in the near future where mega-constellations of LEO satellites are used for precise positioning. Fast Precise Point Positioning (PPP) convergence can be achieved if LEO constellations are employed into current GNSS due to the fast motion of LEO satellites. In order to fulfill this purpose, it is of great importance to design a LEO constellation or to conduct LEO constellation optimization for global precise positioning. In this article, several aspects of LEO constellations in terms of number of LEO orbital planes, number of LEO satellites, and the selection of orbital inclinations are statistically analyzed to find out the suitable LEO constellation for LeGNSS. It is shown that the combination of several LEO constellations with different inclinations together as a whole would be much more appropriate to get a more uniform distribution of the number of visible LEO satellites along the latitude for global fast convergent PPP. With a total 240 LEO satellites of orbital inclinations at 90°, 60°, and 35° selected in this article, one minute convergence time for PPP is achieved on a global scale. [ABSTRACT FROM AUTHOR]

Since China’s BeiDou satellite navigation system (BDS) began to provide regional navigation service for Asia-Pacific region after 2012, more new generation BDS satellites have been launched to further expand BDS’s coverage to be global. In this contribution, precise positioning models based on BDS and the corresponding mathematical algorithms are presented in detail. Then, an evaluation on BDS’s real-time dynamic positioning and navigation performance is presented in Precise Point Positioning (PPP), Real-time Kinematic (RTK), Inertial Navigation System (INS) tightly aided PPP and RTK modes by processing a set of land-borne vehicle experiment data. Results indicate that BDS positioning Root Mean Square (RMS) in north, east, and vertical components are 2.0, 2.7, and 7.6 cm in RTK mode and 7.8, 14.7, and 24.8 cm in PPP mode, which are close to GPS positioning accuracy. Meanwhile, with the help of INS, about 38.8%, 67.5%, and 66.5% improvements can be obtained by using PPP/INS tight-integration mode. Such enhancements in RTK/INS tight-integration mode are 14.1%, 34.0%, and 41.9%. Moreover, the accuracy of velocimetry and attitude determination can be improved to be better than 1 cm/s and 0.1°, respectively. Besides, the continuity and reliability of BDS in both PPP and RTK modes can also be ameliorated significantly by INS during satellite signal missing periods. [ABSTRACT FROM AUTHOR]

Lots of ambiguities in un-differenced (UD) model lead to lower calculation efficiency, which isn’t appropriate for the high-frequency real-time GNSS clock estimation, like 1 Hz. Mixed differenced model fusing UD pseudo-range and epoch-differenced (ED) phase observations has been introduced into real-time clock estimation. In this contribution, we extend the mixed differenced model for realizing multi-GNSS real-time clock high-frequency updating and a rigorous comparison and analysis on same conditions are performed to achieve the best real-time clock estimation performance taking the efficiency, accuracy, consistency and reliability into consideration. Based on the multi-GNSS real-time data streams provided by multi-GNSS Experiment (MGEX) and Wuhan University, GPS + BeiDou + Galileo global real-time augmentation positioning prototype system is designed and constructed, including real-time precise orbit determination, real-time precise clock estimation, real-time Precise Point Positioning (RT-PPP) and real-time Standard Point Positioning (RT-SPP). The statistical analysis of the 6 h-predicted real-time orbits shows that the root mean square (RMS) in radial direction is about 1–5 cm for GPS, Beidou MEO and Galileo satellites and about 10 cm for Beidou GEO and IGSO satellites. Using the mixed differenced estimation model, the prototype system can realize high-efficient real-time satellite absolute clock estimation with no constant clock-bias and can be used for high-frequency augmentation message updating (such as 1 Hz). The real-time augmentation message signal-in-space ranging error (SISRE), a comprehensive accuracy of orbit and clock and effecting the users’ actual positioning performance, is introduced to evaluate and analyze the performance of GPS + BeiDou + Galileo global real-time augmentation positioning system. The statistical analysis of real-time augmentation message SISRE is about 4–7 cm for GPS, whlile 10 cm for Beidou IGSO/MEO, Galileo and about 30 cm for BeiDou GEO satellites. The real-time positioning results prove that the GPS + BeiDou + Galileo RT-PPP comparing to GPS-only can effectively accelerate convergence time by about 60%, improve the positioning accuracy by about 30% and obtain averaged RMS 4 cm in horizontal and 6 cm in vertical; additionally RT-SPP accuracy in the prototype system can realize positioning accuracy with about averaged RMS 1 m in horizontal and 1.5–2 m in vertical, which are improved by 60% and 70% to SPP based on broadcast ephemeris, respectively. [ABSTRACT FROM AUTHOR]

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

Abstract: Currently, ground-based Global Navigation Satellite System (GNSS) stations of the International GNSS Service (IGS) are distributed unevenly around the world. Most of them are located on the mainland, while only a small part of them are scattered on some islands in the oceans. As a consequence, many unreasonable zero values (in fact negative values) appear in Vertical Total Electron Content (VTEC) of European Space Agency (ESA) and Center for Orbit Determination in Europe (CODE) IONEX products, especially in 2008 and 2009 when the solar activities were rather quiet. To improve this situation, we directly implement non-negative physical constraints of ionosphere for global ionosphere maps (GIM) with spherical harmonic functions. Mathematically, we propose an inequality-constrained least squares method by imposing non-negative inequality constraints in the areas where negative VTEC values may occur to reconstruct GIM models. We then apply the new method to process the IGS data in 2008. The results have shown that the new algorithm efficiently eliminates the unwanted behavior of negative VTEC values, which could otherwise often be seen in the current CODE and ESA GIM products in both middle and high latitude areas of the Southern Hemisphere (45°S∼90°S) and the Northern Hemisphere (50°N∼90°N). About 64% of GPS receivers’ DCBs have been significantly improved. Finally, we compare the GIM results between with and without the inequality constraints, which has clearly shown that the GIM result with inequality constraints is significantly better than that without the inequality constraints. The inequality-constrained GIM result is also highly consistent with the final IGS products in terms of root mean squared (RMS) and mean VTEC. [Copyright &y& Elsevier]

Abstract: PPP with low-cost, single-frequency receivers has been receiving increasing interest in recent years because of its large amount of possible users. One crucial issue in single-frequency PPP is the mitigation of ionospheric delays which cannot be removed by combining observations on different frequencies. For this purpose, several approaches have been developed, such as, the approach using ionospheric model corrections with proper weight, the GRAPHIC (Group and Phase Ionosphere Calibration) approach, and the method to model ionospheric delays over a station with a low polynomial or stochastic process. From our investigation on the stochastic characteristics of the ionospheric delay over a station, it cannot be precisely represented by either a deterministic model in the form of a low-order polynomial or a stochastic process for each satellite, because of its strong irregular spatial and temporal variations. Therefore, a novel approach is developed accordingly in which the deterministic representation is further refined by a stochastic process for each satellite with an empirical model for its power density. Furthermore, ionospheric delay corrections from a constructed model using GNSS data are also included as pseudo-observations for a better solution. A large data set collected from about 200 IGS stations over one month in 2010 is processed with the new approach and several commonly adopted approaches for validation. The results show its significant improvements in terms of positioning accuracy and convergence time with a negligible extra processing time, which is also demonstrated by data collected with a low-cost, handheld, single-frequency receiver. [Copyright &y& Elsevier]