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Very Long Baseline Interferometry (VLBI) intensive (INT) sessions are critical for the rapid determination and densification of Universal Time 1‐Coordinate Universal Time (UT1‐UTC), which plays an important role in satellite geodesy and space exploration missions and is not predictable over longer time scales. Due to the limited observation geometry of INT sessions with two to three stations observing about 1 hr, tropospheric gradients cannot be estimated, which degrades the UT1‐UTC precision. We investigate the impact of tropospheric ties at Global Navigation Satellite Systems (GNSSs) and VLBI co‐located stations in INT sessions from 2001 to 2021. VLBI and GNSS observations are combined on the observation level. The results are evaluated by using both UT1‐UTC and Length of Day (LOD) from consecutive sessions. We demonstrate a better agreement of 10%–30% when comparing the derived LOD to GNSS LOD for INT1, INT2, and VGOS‐2 sessions; whereas, the agreement is not improved when directly comparing UT1‐UTC to the IERS Earth Orientation Parameters (EOPs) product, potentially because INT sessions also contribute to IERS EOP products. The major impact comes from tropospheric gradient ties, whereas applying zenith delay ties does not improve or even deteriorate UT1‐UTC agreement. Gradient ties also introduce systematic biases in UT1‐UTC by around −3 to −5 μs, except for the Russian INT sessions. Regression analysis shows that the east gradient introduces systematic effects in UT1‐UTC for sessions involving Germany and USA (Hawaii), whereas for Germany–Japan and Russian sessions, the north gradient also contributes systematically. Plain Language Summary: Universal Time 1‐Coordinate Universal Time (UT1‐UTC) gives the time difference of UT1, defined by Earth's rotation, and UTC, defined by atomic clocks. UT1‐UTC is essential for real‐time navigation and space exploration. The variation of the first‐order negative time derivative of UT1‐UTC, Length of Day (LOD), is induced by mass redistribution, including tides of the solid Earth and oceans, the liquid core of the Earth and atmospheric variation, and climate events such as El Niño. Very Long Baseline Interferometry (VLBI) observing active galactic nuclei is the only space geodetic technique that can determine UT1‐UTC unambiguously. The 1‐hr intensive (INT) sessions, designed for the rapid determination and densification of UT1‐UTC, are performed daily with two VLBI radio telescopes. Due to the limited observation geometry, tropospheric gradients cannot be modeled in INT sessions, deteriorating UT1‐UTC estimates. We demonstrate an improvement of 10%–30% in LOD by applying tropospheric ties at VLBI and Global Navigation Satellite Systems co‐locations, especially the tropospheric gradients ties. Tropospheric gradient ties also introduce a systematic effect of −3 to −5 μs on UT1‐UTC, especially the east gradient. Our study shows that tropospheric ties should be adopted in future VLBI analysis for optimal UT1‐UTC products. Key Points: Tropospheric ties are applied in a Global Navigation Satellite System–Very Long Baseline Interferometry (GNSS–VLBI) integrated solution analyzing VLBI intensive (INT) sessions from 2001 to 2021Length of Day (LOD) of IVS INT sessions shows a better agreement by 10%–30% when compared to GNSS LOD product, mainly due to gradient tiesGradient ties, especially the east one, introduce systematic biases of −3 to −5 μs in Universal Time 1‐Coordinate Universal Time of IVS INT sessions [ABSTRACT FROM AUTHOR]

Tropospheric delay modeling is challenging in high-precision Very Long Baseline Interferometry (VLBI) analysis due to the rapid water vapor variation and imperfect observation geometry, where observations from Global Navigation Satellite Systems (GNSS) co-locations can enhance the VLBI analysis. We investigate the impact of tropospheric ties in the VLBI and GNSS integrated processing during the CONT05–CONT17 campaigns, and present a method that automatically handles the systematic tropospheric tie biases. Applying tropospheric ties at VLBI–GNSS co-locations enhances the observation geometry and improves the solution reliability. The VLBI network is stabilized, with station coordinate repeatability improved by 12% horizontally and by 28% vertically, and the network scale improved by 32%. The Earth Orientation Parameters (EOP) improve by up to 20%. Both zenith delay and gradient ties contribute to the improvement of EOP, whereas the gradient ties contribute mainly to the improvement of length of day and celestial pole offsets. [ABSTRACT FROM AUTHOR]

• Estimating code hardware biases on BDS B1, B2, and B3 frequencies. • Integrating INS with BDS triple-frequency PPP. • Odometer, heading data, and motion information aiding PPP/INS. • Improving stability and precision of position and attitude of PPP. • Providing sub-millimeter-level relative measuring accuracy. The BeiDou global navigation satellite system (BDS), which is the first satellite navigation system that provides triple-frequency signals on B1, B2, and B3 for civil applications, has been applied widely around the Asian-Pacifica region. The current BDS precise point positioning (PPP) approaches are mainly based on the B1&B2 dual-frequency observations. To make full use of BDS' triple-frequency observations, the motion sensors measurements, and the platform motion information, this paper proposes an inertial sensor, odometer, and heading measurement tightly aided BDS triple-frequency PPP model. In this model, inertial sensor biases, odometer scale factor, residuals of slant ionospheric delays, and inter-frequency code biases are estimated simultaneously in a unique extended Kalman filter. The Rauch-Tung-Striebel (RTS) smoother is further adopted to reduce the solution's noises and enhance the stability and relative measuring accuracy. To evaluate the capability of this method, a set of triple-frequency BDS raw observations, inertial measurements, odometer data, and heading measurements collected by a customized hardware system on Lanzhou-Urumqi high speed railway track in China, are processed and analyzed. Results illustrated that both positioning accuracy and cycle slip detection capability are upgraded significantly by applying B3 frequency observations in BDS PPP. About 13–55% position accuracy enhancements from B3 observations, inertial sensors, and RTS smoother, and over 70% heading improvements from the aids of heading measurements can be obtained. Moreover, such multi-sensor tight integration system can directly provide millimeter-level positioning accuracy in term of repeatability and provide sub-millimeter-level accuracy indirectly by transforming attitude solutions into distance solutions. Such accuracy is much higher than the state-of-art GNSS and such method presents potential capability in 3D geometry measuring. [ABSTRACT FROM AUTHOR]

The correction of higher-order ionospheric (HOI) delays remaining in the dual-frequency ionosphere-free combined observations is suggested after the confirmation of its impact on precise Global Navigation Satellite System (GNSS) data processing. However, in the precise orbit determination (POD) for generating ultra-rapid orbits, the higher-order corrections are not always considered most likely because a RT ionospheric model needed for calculating the higher-order corrections is hardly available or the HOI impact is believed rather small compared to the accuracy of the predicted orbit. With the increasing requirement on the positioning performances from various applications, providing more accurate and reliable ultra-rapid orbits becomes an essential task of the real-time GNSS precise positioning services. In this contribution, the temporal–spatial characteristics of HOI effects on GNSS observables are investigated thoroughly using data collected from International GNSS Service (IGS) global ground stations and fluctuations of the higher-order delays up to several centimeters are detected during periods of high ionospheric activity. Hereafter, we evaluate the HOI effects on the multi-GNSS POD based on a network with globally distributed IGS stations. Results show that owing to the applied HOI corrections, the agreement of overlapping orbits can be improved significantly for all satellites and especially in radial direction. The three-dimensional RMS values of the overlapping differences are reduced from 1.6, 2.0, 4.6 and 1.7 to 1.0, 1.1, 3.4, and 1.5 cm for GPS, GALILEO, BDS, and GLONASS, respectively. Furthermore, the orbit improvement is also confirmed by the satellite laser ranging (SLR) observations over a 2-month time period where the STD of SLR residuals is reduced by HOI corrections from 6.4 to 5.3 cm for the BDS-IGSO satellites. [ABSTRACT FROM AUTHOR]

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]

Single-frequency precise point positioning (SF-PPP) is a potential precise positioning technique due to the advantages of the high accuracy in positioning after convergence and the low cost in operation. However, there are still challenges limiting its applications at present, such as the long convergence time, the low reliability, and the poor satellite availability and continuity in kinematic applications. In recent years, the achievements in the dual-frequency PPP have confirmed that its performance can be significantly enhanced by employing the slant ionospheric delay and receiver differential code bias (DCB) constraint model, and the multi-constellation Global Navigation Satellite Systems (GNSS) data. Accordingly, we introduce the slant ionospheric delay and receiver DCB constraint model, and the multi-GNSS data in SF-PPP modular together. In order to further overcome the drawbacks of SF-PPP in terms of reliability, continuity, and accuracy in the signal easily blocking environments, the inertial measurements are also adopted in this paper. Finally, we form a new approach to tightly integrate the multi-GNSS single-frequency observations and inertial measurements together to ameliorate the performance of the ionospheric delay and receiver DCB-constrained SF-PPP. In such model, the inter-system bias between each two GNSS systems, the inter-frequency bias between each two GLONASS frequencies, the hardware errors of the inertial sensors, the slant ionospheric delays of each user-satellite pair, and the receiver DCB are estimated together with other parameters in a unique Kalman filter. To demonstrate its performance, the multi-GNSS and low-cost inertial data from a land-borne experiment are analyzed. The results indicate that visible positioning improvements in terms of accuracy, continuity, and reliability can be achieved in both open-sky and complex conditions while using the proposed model in this study compared to the conventional GPS SF-PPP. [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]

The frequency division multiple access adopted in present GLONASS introduces inter-frequency bias (IFB) at the receiver-end both in code and phase observables, which makes GLONASS ambiguity resolution rather difficult or even not available, especially for long baselines up to several thousand kilometers. This is one of the major reasons that GLONASS could hardly reach the orbit precision of GPS, both in terms of consistency among individual International GNSS Service (IGS) analysis centers and discontinuity at the overlapping day boundaries. Based on the fact that the GLONASS phase IFB is similar on L1 and L2 bands in unit of length and is a linear function of the frequency number, several approaches have been developed to estimate and calibrate the IFB for integer ambiguity resolution. However, they are only for short and medium baselines. In this study, a new ambiguity resolution approach is developed for GLONASS global networks. In the approach, the phase ambiguities in the ionosphere-free linear combination are directly transformed with a wavelength of about 5.3 cm, according to the special frequency relationship of GLONASS L1 and L2 signals. After such transformation, the phase IFB rate can be estimated and corrected precisely and then the corresponding double-differenced ambiguities can be directly fixed to integers even for baselines up to several thousand kilometers. To evaluate this approach, experimental validations using one-month data of a global network with 140 IGS stations was carried out for GLONASS precise orbit determination. The results show that the GLONASS double-difference ambiguity resolution for long baselines could be achieved with an average fixing-rate of 91.4 %. Applying the fixed ambiguities as constraints, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 37.2 % in ideal cases and with an averaged reduction of about 21.4 %, which is comparable with that by the GPS ambiguity resolution. The orbit improvement is also confirmed by the better agreement with the independent satellite laser ranging observations. [ABSTRACT FROM AUTHOR]

GLONASS could hardly reach the positioning performance of GPS, especially for fast and real-time precise positioning. One of the reasons is the phase inter-frequency bias (IFB) at the receiver end prevents its integer ambiguity resolution. A number of studies were carried out to achieve the integer ambiguity resolution for GLONASS. Based on some of the revealed IFB characteristics, for instance IFB is a linear function of the received carrier frequency and L1 and L2 have the same IFB in unit of length, most of recent methods recommend estimating the IFB rate together with ambiguities. However, since the two sets of parameters are highly correlated, as demonstrated in previous studies, observations over several hours up to 1 day are needed even with simultaneous GPS observations to obtain a reasonable solution. Obviously, these approaches cannot be applied for real-time positioning. Actually, it can be demonstrated that GLONASS ambiguity resolution should also be available even for a single epoch if the IFB rate is precisely known. In addition, the closer the IFB rate value is to its true value, the larger the fixing RATIO will be. Based on this fact, in this paper, a new approach is developed to estimate the IFB rate by means of particle filtering with the likelihood function derived from RATIO. This approach is evaluated with several sets of experimental data. For both static and kinematic cases, the results show that IFB rates could be estimated precisely just with GLONASS data of a few epochs depending on the baseline length. The time cost with a normal PC can be controlled around 1 s and can be further reduced. With the estimated IFB rate, integer ambiguity resolution is available immediately and as a consequence, the positioning accuracy is improved significantly to the level of GPS fixed solution. Thus the new approach enables real-time precise applications of GLONASS. [ABSTRACT FROM AUTHOR]

Precise knowledge and consistent modeling of the yaw-attitude of GNSS satellites are essential for high-precision data processing and applications. As the exact attitude control mechanism for the satellites of the BeiDou Satellite Navigation System (BDS) is not yet released, the reverse kinematic precise point positioning (PPP) method was applied in our study. However, we confirm that the recent precise orbit determination (POD) processing for GPS satellites could not provide suitable products for estimating BDS attitude using the reverse PPP because of the special attitude control switching between the nominal and the orbit-normal mode. In our study, we propose a modified processing schema for studying the attitude behavior of the BDS satellites. In this approach, the observations of the satellites during and after attitude switch are excluded in the POD processing, so that the estimates, which are needed in the reverse PPP, are not contaminated by the inaccurate initial attitude mode. The modified process is validated by experimental data sets and the attitude yaw-angles of the BDS IGSO and MEO satellites are estimated with an accuracy of better than $$9^{\circ }$$ . Furthermore, the results confirm that the switch is executed when the Sun elevation is about $$4^{\circ }$$ and the actual orientation is very close to its target one. Based on the estimated yaw-angles, a preliminary attitude switch model was established and reintroduced into the POD, yielding to a substantial improvement in the orbit overlap RMS. [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]

In this contribution, we present a GPS+GLONASS+BeiDou+Galileo four-system model to fully exploit the observations of all these four navigation satellite systems for real-time precise orbit determination, clock estimation and positioning. A rigorous multi-GNSS analysis is performed to achieve the best possible consistency by processing the observations from different GNSS together in one common parameter estimation procedure. Meanwhile, an efficient multi-GNSS real-time precise positioning service system is designed and demonstrated by using the multi-GNSS Experiment, BeiDou Experimental Tracking Network, and International GNSS Service networks including stations all over the world. The statistical analysis of the 6-h predicted orbits show that the radial and cross root mean square (RMS) values are smaller than 10 cm for BeiDou and Galileo, and smaller than 5 cm for both GLONASS and GPS satellites, respectively. The RMS values of the clock differences between real-time and batch-processed solutions for GPS satellites are about 0.10 ns, while the RMS values for BeiDou, Galileo and GLONASS are 0.13, 0.13 and 0.14 ns, respectively. The addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing, reduces the convergence time almost by 70 %, while the positioning accuracy is improved by about 25 %. Some outliers in the GPS-only solutions vanish when multi-GNSS observations are processed simultaneous. The availability and reliability of GPS precise positioning decrease dramatically as the elevation cutoff increases. However, the accuracy of multi-GNSS precise point positioning (PPP) is hardly decreased and few centimeter are still achievable in the horizontal components even with 40 $$^{\circ }$$ elevation cutoff. At 30 $$^{\circ }$$ and 40 $$^{\circ }$$ elevation cutoffs, the availability rates of GPS-only solution drop significantly to only around 70 and 40 %, respectively. However, multi-GNSS PPP can provide precise position estimates continuously (availability rate is more than 99.5 %) even up to 40 $$^{\circ }$$ elevation cutoff (e.g., in urban canyons). [ABSTRACT FROM AUTHOR]

The complementary advantages of GPS and seismic measurements are well recognized in seismotectonic monitoring studies. Therefore, integrated processing of the two data streams has been proposed recently in an attempt to obtain accurate and reliable information of surface displacements associated with earthquakes. A hitherto still critical issue in the integrated processing is real-time detection and precise estimation of the transient baseline error in the seismic records. Here, we report on a new approach by introducing the seismic acceleration corrected by baseline errors into the state equation system. The correction is performed and regularly updated in short epochs (with increments which may be as short as seconds), so that station position, velocity, and acceleration can be constrained very tightly and baseline error can be estimated as a random-walk process. With the adapted state equation system, our study highlights the use of a new approach developed for integrated processing of GPS and seismic data by means of sequential least-squares adjustment. The efficiency of our approach is demonstrated and validated using simulated, experimental, and real datasets. The latter were collected at collocated GPS and seismic stations around the 4 April 2010, E1 Mayor-Cucapah earthquake (Mw, 7.2). The results have shown that baseline errors of the strong-motion sensors are corrected precisely and high-precision seismic displacements are real-timely obtained by the new approach. [ABSTRACT FROM AUTHOR]

High-rate GPS and seismic sensors are mutually contributing to seismological applications for capturing earthquake-induced coseismic displacements. In this study, we propose an approach for tightly integrating GPS and strong motion data on raw observation level to increase the quality of the derived displacements. The performance of the proposed approach is demonstrated using 5 Hz high-rate GPS and 200 Hz strong motion data collected during the El Mayor–Cucapah earthquake (Mw 7.2, 2010 April 4) in Baja California, Mexico. The new approach not only takes advantages of both GPS and strong motion sensors, but also improves the reliability of the displacement by enhancing GPS integer-cycle phase ambiguity resolution, which is very critical for deriving displacements with highest quality. [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]

In order to improve the performance of precise point positioning (PPP), this paper presents a new data processing scheme to shorten the convergence time and the observation time required for a reliable ambiguity-fixing. In the new scheme, L1 and L2 raw observations are used and the slant ionospheric delays are treated as unknown parameters. The empirical spatial and temporal constraints and the ionospheric delays derived from a real-time available ionospheric model are all considered as pseudo-observations into the estimation for strengthening the solution. Furthermore, we develop a real-time computational procedure for generating uncalibrated phase delays (UPDs) on L1 and L2 frequencies. The PPP solution is first carried out on all reference stations based on the proposed scheme, undifferenced float ambiguities on L1 and L2 frequencies can be directly obtained from the new scheme. The L1 and L2 UPDs are then generated and broadcasted to users in real-time. This data product and also the performance of the new PPP scheme are evaluated. Our results indicate that the new processing scheme considering ionospheric characteristics can reduce the convergence time by about 30 % for float kinematic solutions. The observation time for a reliable ambiguity-fixing is shortened by 25 % compared to that of the traditional ambiguity-fixed kinematic solution. When the new method is used for static reference stations, the observation time for ambiguity-fixing is about 10 min in static mode and only 5 min if the coordinates are fixed to well-known values. [ABSTRACT FROM AUTHOR]

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]

The regional service of the Chinese BeiDou satellite navigation system is now in operation with a constellation including five Geostationary Earth Orbit satellites (GEO), five Inclined Geosynchronous Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Besides the standard positioning service with positioning accuracy of about 10 m, both precise relative positioning and precise point positioning are already demonstrated. As is well known, precise orbit and clock determination is essential in enhancing precise positioning services. To improve the satellite orbits of the BeiDou regional system, we concentrate on the impact of the tracking geometry and the involvement of MEOs, and on the effect of integer ambiguity resolution as well. About seven weeks of data collected at the BeiDou Experimental Test Service (BETS) network is employed in this experimental study. Several tracking scenarios are defined, various processing schemata are designed and carried out; and then, the estimates are compared and analyzed in detail. The results show that GEO orbits, especially the along-track component, can be significantly improved by extending the tracking network in China along longitude direction, whereas IGSOs gain more improvement if the tracking network extends in latitude. The involvement of MEOs and ambiguity-fixing also make the orbits better. [ABSTRACT FROM AUTHOR]

In this article, we partially confirm a conjecture, proposed by Cimpoeaş, Keller, Shen, Streib, and Young, on the Stanley depth of squarefree Veronese ideals I n, d . This conjecture suggests that, for positive integers 1 ≤ d ≤ n, . Herzog, Vlădoiu, and Zheng established a connection between the Stanley depths of quotients of monomial ideals and interval partitions of certain associated posets. Based on this connection, Keller, Shen, Streib, and Young recently developed a useful combinatorial tool to analyze the interval partitions of the posets associated with the squarefree Veronese ideals. We modify their ideas and prove the above conjecture for . We also obtain a lower bound of sdepth(I n, d ) for any 1 ≤ d ≤ n. Our results greatly improve Theorem 1.1 in [13], and moreover, our construction leads to a direct proof of this theorem without using graph theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring. [Copyright &y& Elsevier]

As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTDs) are analyzed from 51 permanent GPS sites in the western Mediterranean. The objectives are to estimate the error statistics necessary for future assimilation of GPS ZTD data in numerical models and to investigate the variability of the data in this area. The time series, which were derived continuously from November 1998 to June 2001, are compared with independent equivalent values derived from radiosonde profiles and the High-Resolution Limited-Area Model (HIRLAM) NWP model. Based on over two years of data, the difference between radiosonde and GPS ZTD has a standard deviation of 12 mm of delay and a bias of 7 mm of delay. Some sites have biases as high as 14 mm of delay. The bimodal distribution of residuals, with a higher bias for daytime launches, indicates these biases may be due to radiosonde day–night measurement biases. The biases between the GPS ZTD and HIRLAM estimates are smaller, but the 18-mm ZTD standard deviation is significantly greater. The standard deviation of the residuals depends strongly on the amount of humidity, which produces an annual signal because of the much higher variability of water vapor in the summer months. The better agreement with radiosonde data than HIRLAM estimates indicates that the NWP models will benefit from the additional information provided by GPS. The long-term differences between the observational data sources require further study before GPS-derived data become useful for climate studies. [ABSTRACT FROM AUTHOR]

To support real-time global navigation satellite systems (GNSS) precise applications, satellite clock corrections need to be precisely estimated at a high-rate update interval, which remains a challenge due to the rapid development of multi-GNSS constellations. In this study, we developed an undifferenced (UD) ambiguity resolution (AR) procedure to improve both the accuracy and computational efficiency for real-time multi-GNSS clock estimation realized by a square root information filter. In the proposed method, UD ambiguities are resolved after correcting the simultaneously estimated uncalibrated phase delays (UPD) and the fixed UD ambiguity parameters are eliminated immediately from the filter, so that the computational burden is significantly reduced. Moreover, based on the linear relationship between double-differenced (DD) and UD ambiguities, we investigated the difference between DD and UD AR in clock estimation. We found that the major reason why DD AR contributes little to the clock estimation while UD AR can speed up the convergence remarkably is that UD AR additionally provides a stable clock datum compared with DD AR. GNSS observations from about 100 globally distributed stations were processed with the proposed method to generate simulated real-time clocks and UPDs for GPS, Galileo, and BDS satellites over a one-month period. The results show that the percentage of wide-lane (WL) UPD residuals within ± 0.25 cycles and narrow-lane (NL) UPD residuals within ± 0.15 cycles are over 97.0% and 90.0%, respectively, which contributes to an ambiguity fixing rate of more than 90% for three systems. The mean daily standard deviation (STD) of the clocks of the UD-fixed solution with respect to Center for Orbit Determination in Europe 30 s final products is 0.021, 0.020, and 0.035 ns for GPS, Galileo, and BDS satellite, respectively, which is improved by 78.1%, 58.3%, and 79.8% compared to the float solution. Benefiting from the removal of fixed ambiguities, the average computation time per epoch was reduced from 3.88 to 1.05 s with a remarkable improvement of 72.9%. The quality of the satellite clock and UPD products was also evaluated by the performance of kinematic precise point positioning (PPP). The results show that fast and reliable multi-GNSS PPP-AR can be achieved with the derived UD-fixed clocks and UPDs, which outperforms that using DD-fixed clock and off-line UPD products with an average improvement of 7.9% and 19.9% in terms of convergence time and positioning accuracy, respectively. Furthermore, we demonstrated the effectiveness of the proposed UD AR method through a 7-day real-time clock estimation experiment. [ABSTRACT FROM AUTHOR]

Global navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of GNSS phase bias estimation encounters the rank-deficiency problem, making bias estimation a difficult task. Combining the Monte-Carlo-based methods and GNSS data processing procedure can overcome the problem and provide fast-converging bias estimates. The variance reduction of the estimation algorithm has the potential to improve the accuracy of the estimates and is meaningful for precise and efficient PNT services. In this paper, firstly, we present the difficulty in phase bias estimation and introduce the sequential quasi-Monte Carlo (SQMC) method, then develop the SQMC-based GNSS phase bias estimation algorithm, and investigate the effects of the low-discrepancy sequence on variance reduction. Experiments with practical data show that the low-discrepancy sequence in the algorithm can significantly reduce the standard deviation of the estimates and shorten the convergence time of the filtering. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including multi-global navigation satellite systems, artificial satellites, and remote sensing.

High-precision Global Navigation Satellite Systems (GNSS) orbits are critical for real-time clock estimation and precise positioning service; however, the prediction error grows gradually with the increasing prediction session. In this study, we present a new efficient precise orbit determination (POD) strategy referred to as the epoch-parallel processing to reduce the orbit update latency, in which a 24-h processing job is split into several sub-sessions that are processed in parallel and then stacked to solve and recover parameters subsequently. With a delicate handling of parameters crossing different sub-sessions, such as ambiguities, the method is rigorously equivalent to the one-session batch solution, but is much more efficient, halving the time-consuming roughly. Together with paralleling other procedures such as orbit integration and using open multi-processing (openMP), the multi-GNSS POD of 120 satellites using 90 stations can be fulfilled within 30 min. The lower update latency enables users to access orbits closer to the estimation part, that is, 30–60-min prediction with a 30-min update latency, which significantly improves the orbit quality. Compared to the hourly updated orbit, the averaged 1D RMS values of predicted orbit in terms of overlap for GPS, GLONASS, Galileo, and BDS MEO are improved by 39%, 35%, 41%, and 37%, respectively, and that of BDS GEO and IGSO satellites is improved by 47%. We also demonstrate that the boundary discontinuities of half-hourly orbit are within 2 cm for the GPS, GLONASS, and Galileo satellites, and for BDS the values are 2.6, 15.5, and 9.8 cm for MEO, GEO, and IGSO satellites, respectively. This method can also be implemented for any batch-based GNSS processing to improve the efficiency. [ABSTRACT FROM AUTHOR]

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm. [ABSTRACT FROM AUTHOR]

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]

Currently, with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSS), the real-time positioning and navigation are undergoing dramatic changes with potential for a better performance. To provide more precise and reliable ultra-rapid orbits is critical for multi-GNSS real-time positioning, especially for the three merging constellations Beidou, Galileo and QZSS which are still under construction. In this contribution, we present a five-system precise orbit determination (POD) strategy to fully exploit the GPS + GLONASS + BDS + Galileo + QZSS observations from CDDIS + IGN + BKG archives for the realization of hourly five-constellation ultra-rapid orbit update. After adopting the optimized 2-day POD solution (updated every hour), the predicted orbit accuracy can be obviously improved for all the five satellite systems in comparison to the conventional 1-day POD solution (updated every 3 h). The orbit accuracy for the BDS IGSO satellites can be improved by about 80, 45 and 50% in the radial, cross and along directions, respectively, while the corresponding accuracy improvement for the BDS MEO satellites reaches about 50, 20 and 50% in the three directions, respectively. Furthermore, the multi-GNSS real-time precise point positioning (PPP) ambiguity resolution has been performed by using the improved precise satellite orbits. Numerous results indicate that combined GPS + BDS + GLONASS + Galileo (GCRE) kinematic PPP ambiguity resolution (AR) solutions can achieve the shortest time to first fix (TTFF) and highest positioning accuracy in all coordinate components. With the addition of the BDS, GLONASS and Galileo observations to the GPS-only processing, the GCRE PPP AR solution achieves the shortest average TTFF of 11 min with 7∘ cutoff elevation, while the TTFF of GPS-only, GR, GE and GC PPP AR solution is 28, 15, 20 and 17 min, respectively. As the cutoff elevation increases, the reliability and accuracy of GPS-only PPP AR solutions decrease dramatically, but there is no evident decrease for the accuracy of GCRE fixed solutions which can still achieve an accuracy of a few centimeters in the east and north components. [ABSTRACT FROM AUTHOR]

All BeiDou navigation satellite system (BDS) satellites are transmitting signals on three frequencies, which brings new opportunity and challenges for high-accuracy precise point positioning (PPP) with ambiguity resolution (AR). This paper proposes an effective uncalibrated phase delay (UPD) estimation and AR strategy which is based on a raw PPP model. First, triple-frequency raw PPP models are developed. The observation model and stochastic model are designed and extended to accommodate the third frequency. Then, the UPD is parameterized in raw frequency form while estimating with the high-precision and low-noise integer linear combination of float ambiguity which are derived by ambiguity decorrelation. Third, with UPD corrected, the LAMBDA method is used for resolving full or partial ambiguities which can be fixed. This method can be easily and flexibly extended for dual-, triple- or even more frequency. To verify the effectiveness and performance of triple-frequency PPP AR, tests with real BDS data from 90 stations lasting for 21 days were performed in static mode. Data were processed with three strategies: BDS triple-frequency ambiguity-float PPP, BDS triple-frequency PPP with dual-frequency (B1/B2) and three-frequency AR, respectively. Numerous experiment results showed that compared with the ambiguity-float solution, the performance in terms of convergence time and positioning biases can be significantly improved by AR. Among three groups of solutions, the triple-frequency PPP AR achieved the best performance. Compared with dual-frequency AR, additional the third frequency could apparently improve the position estimations during the initialization phase and under constraint environments when the dual-frequency PPP AR is limited by few satellite numbers. [ABSTRACT FROM AUTHOR]

Relative positioning using multi-GNSS (global navigation satellite systems) can improve accuracy, reliability, and availability compared to the use of a single constellation system. Intra-system double-difference (DD) ambiguities (ISDDAs) refer to the DD ambiguities between satellites of a single constellation system and can be fixed to an integer to derive the precise fixed solution. Inter-system ambiguities, which denote the DD ambiguities between different constellation systems, can also be fixed to integers on overlapping frequencies, once the inter-system bias (ISB) is removed. Compared with fixing ISDDAs, fixing both integer intra- and inter-system DD ambiguities (IIDDAs) means an increase of positioning precision through an integration of multiple GNSS constellations. Previously, researchers have studied IIDDA fixing with systems of the same frequencies, but not with systems of different frequencies. Integer IIDDAs can be determined from single-difference (SD) ambiguities, even if the frequencies of multi-GNSS signals used in the positioning are different. In this study, we investigated IIDDA fixing for multi-GNSS signals of narrowly spaced frequencies. First, the inter-system DD models of multi-GNSS signals of different frequencies are introduced, and the strategy for compensating for ISB is presented. The ISB is decomposed into three parts: 1) a float approximate ISB number that can be considered equal to the ISB of code pseudorange observations and thus can be estimated through single point positioning (SPP); 2) a number that is a multiple of the GNSS signal wavelength; and 3) a fractional ISB part, with a magnitude smaller than a single wavelength. Then, the relationship between intra- and inter-system DD ambiguity RATIO values and ISB was investigated by integrating GPS L1 and GLONASS L1 signals. In our numerical analyses with short baselines, the ISB parameter and IIDDA were successfully fixed, even if the number of observed satellites in each system was small. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP) is a popular technology for precise applications based on the Global Navigation Satellite System (GNSS). Multi-GNSS combined PPP has become a hot topic in recent years with the development of multiple GNSSs. Meanwhile, with the operation of the real-time service (RTS) of the International GNSS Service (IGS) agency that provides satellite orbit and clock corrections to broadcast ephemeris, it is possible to obtain the real-time precise products of satellite orbits and clocks and to conduct real-time PPP. In this contribution, the real-time multi-GNSS orbit and clock corrections of the CLK93 product are applied for real-time multi-GNSS PPP processing, and its orbit and clock qualities are investigated, first with a seven-day experiment by comparing them with the final multi-GNSS precise product 'GBM' from GFZ. Then, an experiment involving real-time PPP processing for three stations in the Multi-GNSS Experiment (MGEX) network with a testing period of two weeks is conducted in order to evaluate the convergence performance of real-time PPP in a simulated kinematic mode. The experimental result shows that real-time PPP can achieve a convergence performance of less than 15 min for an accuracy level of 20 cm. Finally, the real-time data streams from 12 globally distributed IGS/MGEX stations for one month are used to assess and validate the positioning accuracy of real-time multi-GNSS PPP. The results show that the simulated kinematic positioning accuracy achieved by real-time PPP on different stations is about 3.0 to 4.0 cm for the horizontal direction and 5.0 to 7.0 cm for the three-dimensional (3D) direction. [ABSTRACT FROM AUTHOR]

We study a special class of quasi-cyclic codes, obtained from a cyclic code over an extension field of the alphabet field by taking its image on a basis. When the basis is equal to its dual, the dual code admits the same construction. We give some examples of self-dual codes and LCD codes obtained in this way. [ABSTRACT FROM AUTHOR]

In recent years, the precise orbit determination (POD) of the regional Chinese BeiDou Navigation Satellite System (BDS) has been a hot spot because of its special constellation consisting of five geostationary earth orbit (GEO) satellites and five inclined geosynchronous satellite orbit (IGSO) satellites besides four medium earth orbit (MEO) satellites since the end of 2012. GEO and IGSO satellites play an important role in regional BDS applications. However, this brings a great challenge to the POD, especially for the GEO satellites due to their geostationary orbiting. Though a number of studies have been carried out to improve the POD performance of GEO satellites, the result is still much worse than that of IGSO and MEO, particularly in the along-track direction. The major reason is that the geostationary characteristic of a GEO satellite results in a bad geometry with respect to the ground tracking network. In order to improve the tracking geometry of the GEO satellites, a possible strategy is to mount global navigation satellite system (GNSS) receivers on MEO satellites to collect the signals from GEO/IGSO GNSS satellites so as that these observations can be used to improve GEO/IGSO POD. We extended our POD software package to simulate all the related observations and to assimilate the MEO-onboard GNSS observations in orbit determination. Based on GPS and BDS constellations, simulated studies are undertaken for various tracking scenarios. The impact of the onboard GNSS observations is investigated carefully and presented in detail. The results show that MEO-onboard observations can significantly improve the orbit precision of GEO satellites from metres to decimetres, especially in the along-track direction. The POD results of IGSO satellites also benefit from the MEO-onboard data and the precision can be improved by more than 50% in 3D direction. [ABSTRACT FROM AUTHOR]

The recent dramatic development of multi-GNSS (Global Navigation Satellite System) constellations brings great opportunities and potential for more enhanced precise positioning, navigation, timing, and other applications. Significant improvement on positioning accuracy, reliability, as well as convergence time with the multi-GNSS fusion can be observed in comparison with the single-system processing like GPS (Global Positioning System). In this study, we develop a numerical weather model (NWM)-constrained precise point positioning (PPP) processing system to improve the multi-GNSS precise positioning. Tropospheric delay parameters which are derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis are applied to the multi-GNSS PPP, a combination of four systems: GPS, GLONASS, Galileo, and BeiDou. Observations from stations of the IGS (International GNSS Service) Multi-GNSS Experiments (MGEX) network are processed, with both the standard multi-GNSS PPP and the developed NWM-constrained multi-GNSS PPP processing. The high quality and accuracy of the tropospheric delay parameters derived from ECMWF are demonstrated through comparison and validation with the IGS final tropospheric delay products. Compared to the standard PPP solution, the convergence time is shortened by 20.0, 32.0, and 25.0 % for the north, east, and vertical components, respectively, with the NWM-constrained PPP solution. The positioning accuracy also benefits from the NWM-constrained PPP solution, which was improved by 2.5, 12.1, and 18.7 % for the north, east, and vertical components, respectively. [ABSTRACT FROM AUTHOR]

This paper investigated quadratic residue codes over Fp + uFp + vFp + uvFp, where u² = u, v² = v, uv = vu and p is odd prime. At first, it introduced the basic knowledge of cyclic codes of length n over Fp + uFp + vFp + uvFp, then obtained the structures of quadratic residue codes over Fp + uFp + vFp + uvFp by applying their generating idempotents, and discussed the relations and dual properties between these codes and their extended codes. Finally, it gave the specific forms of generating idempotents of quadratic residue codes of length 11 over the ring F3 + uF3 + vF3 + uvF3 . [ABSTRACT FROM AUTHOR]

The deviations of the microwave signal transmitting point of Global Navigation Satellite Systems (GNSS) satellites with respect to the corresponding center-of-mass were and still are significant bias sources for GNSS-based terrestrial reference frames (TRF). Satellite phase center offsets (PCOs) and variations (PVs) are usually derived from GNSS observations from the tracking network of the International GNSS Service (IGS). Because of the strong correlation between the scale of the TRF and the satellite PCOs in the z-direction (z-PCOs), a no-net-scale (NNT) condition relative to, for instance, the International Terrestrial Reference Frame (ITRF) is commonly applied. One approach for estimating transmitter phase centers without constraining the scale is to consider space-based GNSS observations. Within this study, we estimate the satellite PCOs of the Global Positioning System (GPS) based on zero-difference ionosphere-free observations from six low Earth orbiters (LEOs) and ground networks with different numbers of stations. The six LEOs are different in their orbits, GPS receiver equipment, and tracking characteristics. We jointly estimate orbits, station coordinates, and GPS satellite PCOs in an integrated processing. The horizontal offsets are shown to significantly benefit from the LEOs onboard observations by reducing the correlation between these offsets and the GPS satellite orbit and attitude. Without applying a no-net-scale condition to the ground network, the GPS z-PCOs are estimated. By adding six LEOs, the correlation coefficients between the GPS z-PCOs and the scale is reduced significantly (about from 0.85 to 0.3), consequently, the precision of estimation is improved. When including the six LEOs, the GPS z-PCOs estimated without applying NNS are very stable. The estimated GPS z-PCOs have a −231 mm difference in average to the values in igs14 _ 2134.atx and the corresponding scale to IGS14 reference frame is +1.89 part per billion. The estimated GPS z-PCOs agree with previous studies based on Swarm satellites and Galileo. The improvement due to different numbers of LEOs and the impact of LEO z-PCO errors on the estimation are discussed. [ABSTRACT FROM AUTHOR]

Although the computational burden of global navigation satellite systems (GNSS) data processing is nowadays already a big challenge, especially for huge networks, integrated processing of denser networks with data of multi-GNSS and multi-frequency is desired in the expectation of more accurate and reliable products. Based on the concept of carrier range, in this study, the precise point positioning with integer ambiguity resolution is engaged to obtain the integer ambiguities for converting carrier phases to carrier ranges. With such carrier ranges and pseudo-ranges, rigorous integrated processing is realized computational efficiently for the orbit and clock estimation using massive networks. The strategy is validated in terms of computational efficiency and product quality using data of the IGS network with about 460 stations. The experimental validation shows that the computation time of the new strategy increases gradually with the number of stations. It takes about 14 min for precise orbit and clock determination with 460 stations, while the current strategy needs about 82 min. The overlapping orbit RMS is reduced from 27.6 mm with 100 stations to 24.8 mm using the proposed strategy, and the RMS could be further reduced to 23.2 mm by including all 460 stations. Therefore, the new strategy could be applied to massive networks of multi-GNSS and multi-frequency receivers and possibly to achieve GNSS data products of higher quality. [ABSTRACT FROM AUTHOR]

Accurate tropospheric delays from Numerical Weather Models (NWM) are an important input to space geodetic techniques, especially for precise real‐time Global Navigation Satellite Systems, which are indispensable to earthquake and tsunami early warning systems as well as weather forecasting. The NWM‐based tropospheric delays are currently provided either site‐specific with a limited spatial coverage, or on two‐dimensional grids close to the Earth surface, which cannot be used for high altitudes. We introduce a new method of representing NWM‐derived tropospheric zenith hydrostatic and wet delays. A large volume of NWM‐derived data is parameterized with surface values and additional two or three coefficients for their vertical scaling to heights up to 14 km. A precision of 1–2 mm is achieved for reconstructing delays to the NWM‐determined delays at any altitudes. The method can efficiently deliver NWM‐derived tropospheric delays to a broader community of space geodetic techniques. Plain Language Summary: Precise positioning with microwave‐based space geodetic techniques, such as Global Navigation Satellite Systems (GNSS), requires accurate modeling of the atmospheric refraction. Numerical Weather Models (NWM) can provide tropospheric delays with an accuracy of 1–2 cm in zenith direction and are therefore useful for improving the data analysis. However, due to the large data volume to handle, NWM‐based products are typically provided only for selected sites, or on a global grid referring to a specific height. We provide an efficient method to represent the vertical profile of tropospheric delay from the Earth surface up to 14 km altitude with a precision of 1–2 mm. The method is used to preserve the precision of NWM‐derived tropospheric delays at the altitudes using three to four coefficients per geographic location (longitude, latitude) at the ground. This paves the way of applying the NWM‐based accurate tropospheric delays in space geodetic data analysis, especially for global augmentations of real‐time GNSS, which play a critical role in the rapid characterization and early warning of geohazards such as earthquake and tsunami, as well as kinematic platforms of high altitudes. Key Points: New method for precise modeling of the zenith hydrostatic and wet delays from the Earth surface up to an altitude of 14 kmTropospheric delay vertical modeling precision of better than 3 mm is achieved on a global scaleThe method provides numerical weather model‐derived precise tropospheric augmentation correction for real‐time space geodetic techniques [ABSTRACT FROM AUTHOR]

In the absence of detailed surface information, empirical solar radiation pressure (SRP) models, such as the five-parameter Empirical CODE Orbit Model (ECOM1) and its extended version-ECOM2, are widely used for modeling SRP forces acting on GNSS satellites. This study shows that the orbits of BeiDou-3 Inclined Geosynchronous Orbit satellites (IGSOs) determined with the ECOM1 model suffer from systematic once-per-revolution radial orbit errors, which can be partly reduced by the ECOM2 model. To eliminate such orbit errors, the BeiDou-3 IGSO optical coefficients are solved by using an adjustable box-wing (ABW) model and then introduced into an a priori box-wing SRP model to enhance the ECOM1 model (ECOM1 + BW). In the ABW solution, in addition to satellite body and solar panels, the contributions of the communication payloads installed on BeiDou-3 IGSO ± X panels on the SRP are also considered, which markedly improves the stability of the optical coefficient estimates. The efficiency of the developed a priori box-wing model is demonstrated through eliminated once-per-revolution radial orbit errors and decreased day boundary discontinuities. However, the orbit solutions still show significant degradations during eclipse seasons. The results of the first yaw-attitude analysis for eclipsing BeiDou-3 IGSOs show that their yaw behaviors are the same as those of BeiDou-3 CAST (China Academy of Space Technology) MEOs (Medium Earth Orbit satellites), and have been well considered in the study. This rules out the possibility that attitude errors are the potential reason for the orbit deterioration. By introducing a once-per-revolution sine term in the Sun direction ( D s term) and keeping D s active during the Earth's shadow transitions to the ECOM1 + BW model, the orbit performance inside the eclipse seasons is significantly improved and can be comparable to that outside the eclipse seasons. [ABSTRACT FROM AUTHOR]

The wet tropospheric correction (WTC) retrieved from the onboard calibration microwave radiometer (CMR) of Haiyang-2A (HY-2A) is critical in monitoring the global sea level. However, the CMR WTC became significantly biased from June 2017 due to the failure of the 18.7-GHz band, which caused massive errors in the sea surface height (SSH) measurements. We investigate the accuracy of the CMR WTC derived from the two remaining bands to address this problem. A comprehensive evaluation using multisource data demonstrates that the dual-band + backscattering coefficient (BC) algorithm achieves comparable accuracy to the three-band algorithm, and it does not suffer from any large errors when the equipment works well. Hence, we calibrated the HY-2A CMR data with the dual-band + BC algorithm when the 18.7-GHz band failed, and the accuracy of the CMR WTC is improved from 2.34 to 1.39 cm compared with European Center for Medium-Range Weather Forecasts (ECMWF) ERA5 data. In addition, the SSH measurements are improved significantly by a maximum of 2 cm in mean value using the dual-band + BC WTC during the failure period of HY-2A CMR. Compared with Jason-3 SSH measurements, the HY-2A with dual-band + BC shows a slightly larger difference than HY-2A with three-band by 0.1 cm in rms. This method prolongs the operational lifetime of the HY-2A CMR and could be used in the reprocessing of HY-2A observations. [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]

Ambiguity resolution dedicated to a single global positioning system (GPS) station can improve the accuracy of precise point positioning. In this process, the estimation accuracy of the narrow-lane fractional-cycle biases (FCBs), which destroy the integer nature of undifferenced ambiguities, is crucial to the ambiguity-fixed positioning accuracy. In this study, we hence propose the improved narrow-lane FCBs derived from an ambiguity-fixed GPS network solution, rather than the original (i.e. previously proposed) FCBs derived from an ambiguity-float network solution. The improved FCBs outperform the original FCBs by ensuring that the resulting ambiguity-fixed daily positions coincide in nature with the state-of-the-art positions generated by the International GNSS Service (IGS). To verify this improvement, 1 year of GPS measurements from about 350 globally distributed stations were processed. We find that the original FCBs differ more from the improved FCBs when fewer stations are involved in the FCB estimation, especially when the number of stations is less than 20. Moreover, when comparing the ambiguity-fixed daily positions with the IGS weekly positions for 248 stations through a Helmert transformation, for the East component, we find that on 359 days of the year the daily RMS of the transformed residuals based on the improved FCBs is smaller by up to 0.8 mm than those based on the original FCBs, and the mean RMS over the year falls evidently from 2.6 to 2.2 mm. Meanwhile, when using the improved rather than the original FCBs, the RMS of the transformed residuals for the East component of 239 stations (i.e. 96.4% of all 248 stations) is clearly reduced by up to 1.6 mm, especially for stations located within a sparse GPS network. Therefore, we suggest that narrow-lane FCBs should be determined with ambiguity-fixed, rather than ambiguity-float, GPS network solutions. [ABSTRACT FROM AUTHOR]

It is well known that Thom–Boardman symbols are realized by nonincreasing sequences of nonnegative integers. A natural question is whether the converse is also true. In this paper we answer this question affirmatively, that is, for any nonincreasing sequence of nonnegative integers, there is at least one map-germ with the prescribed sequence as its Thom–Boardman symbol. [ABSTRACT FROM AUTHOR]

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]

The article Integrated processing of ground- and space-based GPS observations: improving GPS satellite orbits observed with sparse ground networks, written by Wen Huang, Benjamin Männel, Pierre Sakic, Maorong Ge & Harald Schuh was originally published electronically on the publisher’s internet portal on [10 October 2020] without open access. [ABSTRACT FROM AUTHOR]

Wide-lane (WL) uncalibrated phase delay (UPD) is usually derived from Melbourne–Wübbena (MW) linear combination and is a prerequisite in Global Navigation Satellite Systems (GNSS) precise point positioning (PPP) ambiguity resolution (AR). MW is a linear combination of pseudorange and phase, and the accuracy is limited by the larger pseudorange noise which is about one hundred times of the carrier phase noise. However, there exist inconsistent pseudorange biases which may have detrimental effect on the WL UPD estimation, and further degrade user-side ambiguity fixing. Currently, only the large part of pseudorange biases, e.g., the differential code bias (DCB), are available and corrected in PPP-AR, while the receiver-type-dependent biases have not yet been considered. Ignoring such kind of bias, which could be up to 20 cm, will cause the ambiguity fixing failure, or even worse, the incorrect ambiguity fixing. In this study, we demonstrate the receiver-type-dependent WL UPD biases and investigate their temporal and spatial stability, and further propose the method to precisely estimate these biases and apply the corrections to improve the user-side PPP-AR. Using a large data set of 1560 GNSS stations during a 30-day period, we demonstrate that the WL UPD deviations among different types of receivers can reach ± 0.3 cycles. It is also shown that such kind of deviations can be calibrated with a precision of about 0.03 cycles for all Global Positioning System (GPS) satellites. On the user side, ignoring the receiver-dependent UPD deviation can cause significant positioning error up to 10 cm. By correcting the deviations, the positioning performance can be improved by up to 50%, and the fixing rate can also be improved by 10%. This study demonstrates that for the precise and reliable PPP-AR, the receiver-dependent UPD deviations cannot be ignored and have to be handled. [ABSTRACT FROM AUTHOR]

In a conventional Unmanned aerial vehicles (UAV) navigational system Global Navigation Satellite System (GNSS) sensor is often a main source of data for trajectory generation. Even video tracking based systems need some GNSS data for proper work. The goal of this study is to develop an optics-based system to estimate the ground speed of the UAV in the case of the GNSS failure, jamming, or unavailability. The proposed approach uses a camera mounted on the fuselage belly of the UAV. We can obtain the ground speed of the airplane by using the digital cropping, the stabilization of the real time image, and template matching algorithms. By combining the ground speed vector components with measurements of airspeed and altitude, the wind velocity and drift are computed. The obtained data were used to improve efficiency of the video-tracking based on a navigational system. An algorithm allows this computation to be performed in real time on board of a UAV. The algorithm was tested in Software-in-the-loop and implemented on the UAV hardware. Its effectiveness has been demonstrated through the experimental test results. The presented work could be useful for upgrading the existing MUAV products (with embedded cameras) already delivered to the customers only by updating their software. It is especially significant in the case when any necessary hardware upgrades would be economically unjustified or even impossible to be carried out. [ABSTRACT FROM AUTHOR]

The precise orbit determination (POD) of Global Navigation Satellite System (GNSS) satellites and low Earth orbiters (LEOs) are usually performed independently. It is a potential way to improve the GNSS orbits by integrating LEOs onboard observations into the processing, especially for the developing GNSS, e.g., Galileo with a sparse sensor station network and Beidou with a regional distributed operating network. In recent years, few studies combined the processing of ground- and space-based GNSS observations. The integrated POD of GPS satellites and seven LEOs, including GRACE-A/B, OSTM/Jason-2, Jason-3 and, Swarm-A/B/C, is discussed in this study. GPS code and phase observations obtained by onboard GPS receivers of LEOs and ground-based receivers of the International GNSS Service (IGS) tracking network are used together in one least-squares adjustment. The POD solutions of the integrated processing with different subsets of LEOs and ground stations are analyzed in detail. The derived GPS satellite orbits are validated by comparing with the official IGS products and internal comparison based on the differences of overlapping orbits and satellite positions at the day-boundary epoch. The differences between the GPS satellite orbits derived based on a 26-station network and the official IGS products decrease from 37.5 to 23.9 mm ( 34 % improvement) in 1D-mean RMS when adding seven LEOs. Both the number of the space-based observations and the LEO orbit geometry affect the GPS satellite orbits derived in the integrated processing. In this study, the latter one is proved to be more critical. By including three LEOs in three different orbital planes, the GPS satellite orbits improve more than from adding seven well-selected additional stations to the network. Experiments with a ten-station and regional network show an improvement of the GPS satellite orbits from about 25 cm to less than five centimeters in 1D-mean RMS after integrating the seven LEOs. [ABSTRACT FROM AUTHOR]

Low Earth Orbit (LEO) satellites have been widely used in scientific fields or commercial applications in recent decades. The demands of the real time scientific research or real time applications require real time precise LEO orbits. Usually, the predicted orbit is one of the solutions for real time users, so it is of great importance to investigate LEO orbit prediction for users who need real time LEO orbits. The centimeter level precision orbit is needed for high precision applications. Aiming at obtaining the predicted LEO orbit with centimeter precision, this article demonstrates the traditional method to conduct orbit prediction and put forward an idea of LEO orbit prediction by using onboard accelerometer data for real time applications. The procedure of LEO orbit prediction is proposed after comparing three different estimation strategies of retrieving initial conditions and dynamic parameters. Three strategies are estimating empirical coefficients every one cycle per revolution, which is the traditional method, estimating calibration parameters of one bias of accelerometer hourly for each direction by using accelerometer data, and estimating calibration parameters of one bias and one scale factor of the accelerometer for each direction with one arc by using accelerometer data. The results show that the predicted LEO orbit precision by using the traditional method can reach 10 cm when the predicted time is shorter than 20 min, while the predicted LEO orbit with better than 5 cm for each orbit direction can be achieved with accelerometer data even to predict one hour. [ABSTRACT FROM AUTHOR]

The calibration microwave radiometer (CMR) on board the Haiyang-2A (HY-2A) satellite provides wet tropospheric delay correction for altimetry data, which can also contribute to the understanding of climate system and weather processes. The ground-based global navigation satellite system (GNSS) provides precise precipitable water vapor (PWV) with high temporal resolution and could be used for calibration and monitoring of the CMR data, and shipborne GNSS provides accurate PWV over open oceans, which can be directly compared with uncontaminated CMR data. In this study, the HY-2A CMR water vapor product is validated using ground-based GNSS observations of 100 International GNSS Service (IGS) stations along the global coastline and 56 d shipborne GNSS observations over the Indian Ocean. The processing strategy for GNSS data and CMR data is discussed in detail. Special efforts were made in the quality control and reconstruction of contaminated CMR data. The validation result shows that HY-2A CMR PWV agrees well with ground-based GNSS PWV with 2.67 mm as the root mean square (rms) within 100 km. Geographically, the rms is 1.12 mm in the polar region and 2.78 mm elsewhere. The PWV agreement between HY-2A and shipborne GNSS shows a significant correlation with the distance between the ship and the satellite footprint, with an rms of 1.57 mm for the distance threshold of 100 km. Ground-based GNSS and shipborne GNSS agree with HY-2A CMR well. [ABSTRACT FROM AUTHOR]