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Real-time monitoring of earthquake-triggered surface deformation is becoming required to characterize the effect of an earthquake, either transient or permanent deformation. Indonesia as a country located in the active deformation region, through Geospatial Information Agency (BIG) has built 397 Real-Time Global Navigation Satellite Systems (RT-GNSS) stations that can be used to observe this phenomenon. The availability of RT-GNSS stations motivates us to provide real-time surface deformation information using the appropriate RT-GNSS processing method. We implement Precise Point Positioning with Regional Augmentation correction (PPP-RA) for stations if there are sufficient regional corrections, and Precise Point Positioning with Ambiguity Resolution (PPP-AR) otherwise. The result shows from Kota Fajar station in Sumatera Island (CKTF), the accuracy can be achieved at ± 1.4 cm, ± 1.8 cm, and ± 6.5 cm for the North, East, and Up components, respectively. we use the earthquake location information produced by Indonesia Tsunami Early Warning System (InaTEWS) operated by the Meteorological, Climatological, and Geophysical Agency (BMKG) to automatically collect the nearby stations from the epicenter. Then, we compute the displacement from each of its stations every second when the earthquake occurred. As a result, we can detect the transient deformation of the Banda Sea earthquake 7.6 Mw at depth of 108 km on January 9, 2023, with a maximum dynamic displacement at the nearest station to the source is 6.6 cm in the North-South direction and 8.7 cm in the East-West direction. This result suggests that this system is effective in displacement detection due to earthquakes., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

Real-time Global Navigation Satellite Systems (GNSS) are critical for precise and reliable positioning, navigation, and timing (PNT) services, including both civil applications with an accuracy of meter-level and geohazard early warning systems with an accuracy of cm- or even mm-level. For high-precision real-time GNSS applications, the precise orbits, clocks, hardware delays, and atmospheric information are estimated and disseminated in real time by the service provider. In this study, we introduce the current status and recent developments of the GFZ GNSS real-time analysis center. We introduce the data processing strategy for generating satellite orbits and clocks, hardware delays, and atmospheric information, and present the accuracy of the online operational products. We focus on the recent developments in improving the accuracy and reducing the latency of real-time products, such as shortening the ultra-rapid orbit processing time and improving the predicting accuracy, estimating orbits with real-time streaming data, and adopting the un-differenced ambiguity resolution in the estimation of real-time clocks and orbits. Lastly, we evaluate the real-time positioning performance using the GFZ real-time products, and demonstrate with the atmospheric augmentation information, the cm-level accuracy can be achieved within a few minutes., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

For microwave-based space geodetic techniques, co-located instruments within a few hundred meters are considered to share the same troposphere, and thus intra-/inter-technique tropospheric ties can be applied to improve the multi-technique integrated solution. The concept of applying tropospheric ties assumes that tropospheric parameters from each technique represent the true tropospheric state, i.e., (1) there should be no technique-related systematic bias, and (2) the technique-specific stochastic noise that leaks into atmospheric delay estimates should be minimized. However, this is usually not the case in reality, as the modeling and parameter estimation in the analysis of space geodetic techniques naturally contain systematic and stochastic uncertainty. For example, the multi-path effect and antenna phase center variation (PCV) error could introduce systematic biases in Global Navigation Satellite Systems (GNSS) tropospheric parameters, and the limitation of observation geometry in Very Long Baseline Interferometry (VLBI) could bias the horizontal gradients. Therefore, it is critical to identify and handle the systematic biases, and properly handle the stochastic part. In this study, we demonstrate that tropospheric parameter biases could be large, e.g., up to 5 mm in zenith total delay (ZTD). Ignoring systematic biases distorts the ground network, especially the VLBI network. For example, the systematic bias in ZTD shifts the network scale, and the bias in horizontal gradients rotates the network and deteriorates earth orientation parameters (EOP). We demonstrate that the GNSS and VLBI integrated solution can be improved after properly handling the tropospheric ties., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

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 km. Tropospheric delay vertical modeling precision of better than 3 mm is achieved on a global scale. The method provides numerical weather model‐derived precise tropospheric augmentation correction for real‐time space geodetic techniques., Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659, China Scholarship Council CSC, Helmholtz OCPC Program, https://cds.climate.copernicus.eu/cdsapp

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively.

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., China Scholarship Council http://dx.doi.org/10.13039/501100004543, Helmholtz-Zentrum Potsdam Deutsches GeoForschungsZentrum - GFZ (4217), ftp://geodesy.noaa.gov/cors/rinex/, ftp://ftp.gfz-potsdam.de/GNSS/products/mgex/, ftp://ftp.aiub.unibe.ch/CODE/

Comunicación expuesta online en el CYGNSS Science Team Summer Meeting celebrado del 27 al 29 de julio de 2021

BeiDou navigation satellite system is currently the only system which the whole constellation offers triple-frequency observation data, triple-frequency observation is conducive to carrier phase ambiguity fixing quickly and accurately. The algorithm of triple-frequency integer ambiguity resolution between BDS network RTK reference stations is proposed. The observation of B2 frequency and B3 frequency and the strict criterion of ambiguity fixing are used to determine extra-wide-lane integer ambiguity. The linear relationship between fixed extra-wide-lane integer ambiguity and other wide-lane integer ambiguity is selected as constraint conditions, then the wide-lane integer ambiguity, relative zenith tropospheric delay error and ionospheric delay error are estimated and the wide-lane integer ambiguity can be fixed by search mode. There is a kind of integer linear relationship between fixed wide-lane integer ambiguity and triple-frequency carrier phase integer ambiguity, this linear relationship is added to the observation model of carrier phase ambiguity parameter estimation and the integer ambiguity can be fixed. This algorithm is tested by the measured triple-frequency data of BDS CORS network. The results indicate that triple-frequency carrier phase ambiguity can be fixed accurately and effectively with the method.

System Erde; 8, Geodesy aims to determine the geometric figure and the gravitational field of the Earth, as well as its orientation in space. Steadily increasing accuracies, with which these tasks are being solved, are based on corresponding improvements in geodetic measuring data, both, on the quantitative as well as the qualitative level. Similar developments in the acquisition, processing and analysis of observation data, which have always been at the limit of the technically and scientifically feasible, are witnessed in the fields of seismology and geomagnetism as well. Recently however, innovative developments, building on Big Data approaches, are emerging with the combination of diverse data streams into integrated processing environments. Geodetic, seismological and geomagnetic observation data are fundamental for a better understanding of Earth system processes. The combination of these geoscience data collected by ground- and space-based sensors, their consistent processing, validation and assimilation into complex Earth system models contribute in an essential way to the future implementation of GGOS, the Global Geodetic Observing System.

System Erde; 7, Along with cell phones and the internet, satellite navigation is an integral part of everyday life. However, satellite navigation signals provide much more than precise information on user locations. Even before the GPS was declared fully operational in 1995, the potential for these globally and continuously available navigation signals for Earth observation and geoscientific applications was recognized. Such applications include the precise monitoring of continental plate movements with sub-mm/year accuracy (now used in real-time as part of early earthquake warning systems), regional and global atmospheric and ionospheric sounding to improve weather forecasts and climate change predictions, and for monitoring of water, ice, and land surfaces. The Earth observation prospects and related spectrum of applications are continuously growing, mainly stimulated by the transition from a single constellation (GPS) to Multi-GNSS (Global Navigation Satellite System) with the Russian GLONASS, Chinese BeiDou and European Galileo satellites and by the increasing number of GNSS receivers available both on the ground and aboard Low Earth Orbiting satellites.

GeoSHM (GNSS and Earth Observation for Structural Health Monitoring) is a feasibility study project funded under the Integrated Application Promotion (IAP) program of the European Space Agency (ESA) in August 2013. Through integrated use of GNSS, Remote Sensing technologies and environmental data, GeoSHM can offer bridge owners an effective tool to assess the operational conditions of their assets. A reference system that consists of four GNSS receivers and two anemometers was installed on the Forth Road Bridge (FRB) in Scotland. This first stage monitoring system is producing precise 3D real-time displacements under different loading conditions. It can also provide essential land movement information to assess potential threats due to underground water extraction, geo-hazards and other industrial activities. The GeoSHM Feasibility Study has proved that even a small scale monitoring system can make possible for the Bridgemaster of the FRB to fully understand the loading and response effect of the bridge, and identify unusual deformations under extreme weather conditions (wind gust, etc.). Furthermore, EO data has proved to be extremely useful for the subsidence detection, as the SAR interferometry images have shown that there is no significant subsidence of the towers of the FRB or in the surrounding area. Gathering real-time GNSS data has produced continuous and accurate estimation of the displacement time-series of the structure. The issues and gaps identified from GeoSHM FS will form a solid foundation for the next stage development of GeoSHM service – demonstration, which is a two-year project and have started in February 2016. A new consortium of GeoSHM has been formed, focusing on significant refinements to the system reliability, sensor integration, data acquisition, data transmission, data fusion and SHM information extraction. This further developed GeoSHM system will be installed on a few Chinese bridges and the reference monitoring system on the FRB will be expanded as a pre-operational system.

Global Positioning System (GPS) has been proved to be a powerful tool for measuring co-seismic ground displacements with an application to seismic source inversion. Whereas most of the tsunamis are triggered by large earthquakes, GPS can contribute to the tsunami early warning system (TEWS) by helping to obtain tsunami source parameters in near real-time. Toward the end of 2012, the second phase of the BeiDou Navigation Satellite System (BDS) constellation was accomplished, and BDS has been providing regional positioning service since then. Numerical results indicate that precision of BDS nowadays is equivalent to that of the GPS. Compared with a single Global Satellite Navigation System (GNSS), combined BDS/GPS real-time processing can improve accuracy and especially reliability of retrieved co-seismic displacements. In the present study, we investigate the potential of BDS to serve for the early warning system of tsunamis in the South China Sea region. To facilitate early warnings of tsunamis and forecasting capabilities in this region, we propose to distribute an array of BDS-stations along the Luzon Island (Philippines). By simulating an earthquake with Mw = 8 at the Manila trench as an example, we demonstrate that such an array will be able to detect earthquake parameters in real time with a high degree of accuracy and, hence, contribute to the fast and reliable tsunami early warning system in this region.

The precision orbit determination of challenging minisatellite payload (CHAMP) satellite was done based on position and navigation data analyst (PANDA) software which is developed in Wuhan University, using the onboard GPS data of year 2002 from day 126 to 131. The orbit accuracy was assessed by analyzing the difference from GFZ post-processed science orbits (PSO), the GPS carrier and pseudo-range data residuals and the satellite laser ranging (SLR) residuals.

PANDA (Position And Navigation Data Analyst) software is designed for data analysis of different satellite positioning and navigation systems, such as SLR, GPS and the future GALIEO. The software has being developed since 2000 at GPS Research Center of Wuhan University. A brief introduction of the software and its developing progress are given at first, and then the results of static positioning and GPS satellite orbit determination archived with PANDA are presented in this paper.

Using autocorrelation information of the pseudorange errors generated by selective availability (SA) frequency dithering, we have constructed a simple first order stochastic model for SA effects. This model has been used in a Kalman filter to account for the stochastic behavior of SA dithering in estimating satellite clock information in wide area differential GPS. We have obtained fifteen percent improvement in the user positioning using the correlation information on the satellite clock information in a Kalman filter, when comparing the results obtained using a regular least square estimation.

In recent times increasing numbers of high-rate GPS stations have been installed around the world and set-up to provide data in real-time. These networks provide a great opportunity to quickly capture surface displacements, which makes them important as potential constituents of earthquake/tsunami monitoring and warning systems. The appropriate GPS real-time data analysis with sufficient accuracy for this purpose is a main focus of the current GPS research. In this paper we propose an augmented point positioning method for GPS based hazard monitoring, which can achieve fast or even instantaneous precise positioning without relying on data of a specific reference station. The proposed method overcomes the limitations of the currently mostly used GPS processing approaches of relative positioning and global precise point positioning. The advantages of the proposed approach are demonstrated by using GPS data, which was recorded during the 2011 Tohoku-Oki earthquake in Japan.

Modern near-field tsunami early warning systems must provide a tsunami alarm as early as 5 to 10 minutes after an earthquake. Working within this time limit, traditional seismic methods tend to underestimate the total moment magnitude in case of giant (Sumatra 2004, Tōhoku 2011) as well as slow, ‘tsunami’ (Java 2006, Mentawai 2010) earthquakes. Moreover, representation of a tsunami source as a point-source, i.e. location plus magnitude, is usually insufficient for a reliable near-field early warning. Using numerical simulation of earthquake rupture and associated crustal deformation and tsunami wave’s propagation, we demonstrate that recent high-precision real-time Global Navigation Satellite System (GNSS) arrays may serve as a key component of near-field tsunami early warning system. The main advantage of the GNSS-arrays, placed close to an epicenter, is that they directly measure surface displacements necessary for tsunami source inversion already during the earthquake. Taking the Great March 2011 Tōhoku-oki earthquake as an example, we demonstrate the ability of real-time GNSS to provide qualified tsunami early warning in only three minutes after beginning of the earthquake. To do so, we combine real-time Precise Point Positioning (PPP) processing with fast slip inversion and on-the-fly tsunami simulation. This allows the observation of the earthquake growth in almost real-time (plus about one minute processing overhead) by simultaneously computing tsunami warning levels. Already three minutes after the earthquake begins, GNSS-derived moment magnitude estimation reaches its final value of Mw = 9.0 and tsunami forecasting stabilizes as well.

In [7] we obtained a formula for the Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring by relating it to the Hilbert depth of powers of the irrelevant maximal ideal. In this paper, we prove that these two Hilbert depth formulas are equivalent to each other. Our result reveals that there is a strong connection between these two classes of seemingly unrelated monomial ideals. We conjecture that their Stanley depths are equivalent as well., 7 pages

It is well known that Thom-Boardman symbols are realized by non-increasing 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 non-increasing sequence of nonnegative integers, there is a map-germ with the prescribed sequence as its Thom-Boardman symbol., 5 pages, no figures

This report studies the vertical crustal motion at tide gauges by analyzing GPS (Global Positioning System) height time series of about 370 GPS stations spanning 1994.0 to 2007.0. The procedure of generating a set of homogeneous GPS time series is described in detail. To estimate the vertical rate, the time series are modelled with seasonal (annual and semiannual) waves and step functions for jumps. To improve the quality of the time series, the ocean tide loading (OTL) corrections are renovated by replacing the OTL corrections derived from new ocean tides model directly on the solutions without re-analyzing the GPS data.

The precise knowledge of aircraft position, velocity, and acceleration is a mandatory prerequisite for airborne gravimetry. For the determination of these quantities the Global Navigation Satellite System (GNSS) plays an important role. However, kinematic positioning over Antarctica is a challenging task which is different from positioning in low-latitude regions. The main reason is the sparse distribution of International GNSS Service (IGS) ground stations which is also difficult or impractical to be densified by setting up dedicated reference stations because of its hostile environment. Therefore, traditional double-differenced (DD) positioning using Global Positioning System (GPS) may be difficult to be applied. Precise Point Positioning (PPP) using a stand-alone receiver is recognized as a helpful tool for obtaining reliable and accurate trajectories of moving platforms based on precise orbit and clock products derived from a global reference network. Therefore, it is necessary to study the special characteristics of positioning over Antarctica and to exploit innovative and reliable approaches for precise position, velocity and acceleration determination. An extended precise positioning method called Precise Orbit Positioning (POP), which was originally developed in Salazar et al. (2009), is further developed towards application with multi-GNSS data. This approach takes advantage of a widely spaced network of ground stations to estimate satellite clock offsets and drifts and only relies on precise orbit information. It is illustrated that POP has the potential to achieve centimeter-level accuracy for the vertical component with sparse distributed reference stations. The aforesaid POP method is extended further to derive reliable and high accurate velocity and acceleration which are more important than position for airborne gravimetry. A GPS+GLONASS+Galileo+BDS four-system model is presented and proper weighting of different types of observations is investigated. The PPP solutions are also calculated with multi-GNSS observations for comparison. During static tests over Antarctica, it was found that POP derived velocity and acceleration tend to have much lower noise than the PPP solutions. Moreover, the addition of GLONASS, Galileo and BDS data can increase the accuracy of velocity and acceleration estimates by 32% and 43% with POP compared to a GPS-only solution when using data of 30-second sampling interval and the improvements are 28% and 31% with respect to the PPP solutions. Die genaue Kenntnis der Flugzeugposition, -geschwindigkeit und -beschleunigung ist eine zwingende Voraussetzung für die gravimetrische Vermessung aus der Luft. Für die Bestimmung dieser Größen spielt das Global Navigation Satellite System (GNSS) eine wichtige Rolle. Die kinematische Positionierung über der Antarktis ist jedoch eine anspruchsvolle Aufgabe, die sich von der Positionierung in Regionen mit niedriger Breite unterscheidet. Der Hauptgrund ist die spärliche Verteilung der Bodenstationen des Internationalen GNSS-Dienstes (IGS), die zudem aufgrund der widrigen Bedingungen in der Antarktis nur sehr schwierig durch die Einrichtung spezieller Referenzstationen verdichtet werden kann. Daher ist es schwierig, die traditionelle Doppeldifferenzmessung (DD) mit dem Global Positioning System (GPS) anzuwenden. Die präzise Punktpositionierung (PPP) mit einem eigenständigen Empfänger ist als hilfreiche Methode zur Erzielung zuverlässiger und genauer Trajektorien von bewegten Plattformen auf der Grundlage von präzisen Orbit- und Uhrenprodukten aus einem globalen Referenznetzwerk anerkannt. Einerseits kann die Genauigkeit von Echtzeitprodukten die Anforderung an die Trajektoriengewinnung für die luftgestützte Gravimetrie noch nicht erfüllen, andererseits weisen die IGS-Endprodukte noch eine tagesgebundene Diskontinuität auf. Zudem wurden bei Produkten neuerer GNSS-Systeme regionale Verzerrungen nachgewiesen, die die ganzzahlige Mehrdeutigkeitsauflösung der PPP erheblich verschlechtern können. Daher ist es notwendig, die besonderen Eigenschaften der Positionierung über der Antarktis zu untersuchen und innovative und zuverlässige Ansätze zur präzisen Positions-, Geschwindigkeits- und Beschleunigungsbestimmung zu entwickeln. Eine erweiterte präzise Positionierungsmethode namens Precise Orbit Positioning (POP), die ursprünglich in Salazar et al. (2009) entwickelt wurde, wurde in Richtung der Anwendung mit Multi-GNSS-Daten weiterentwickelt. Dieser Ansatz nutzt ein weit verzweigtes Netz von Bodenstationen, um Versatz und Drift der Satellitenuhren zu schätzen und stützt sich nur auf präzise Orbitinformationen. Die vorgenannte POP-Methode wurde weiter ausgebaut, um zuverlässige und hochpräzise Geschwindigkeit und Beschleunigung abzuleiten, die für die luftgestützte Gravimetrie wichtiger sind als die Position. Ein GPS+GLONASS+Galileo+BeiDou Viersystemmodell wird vorgestellt und die richtige Gewichtung verschiedener Arten von Beobachtungen untersucht. Die PPP-Lösungen werden auch mit Multi-GNSS-Beobachtungen zum Vergleich berechnet. Bei statischen Tests über der Antarktis wurde festgestellt, dass die von POP abgeleitete Geschwindigkeit und Beschleunigung tendenziell viel weniger verrauscht sind als die PPP-Lösungen. Darüber hinaus kann die Hinzufügung von GLONASS-, Galileo- und BDS-Daten die Genauigkeit der Geschwindigkeits- und Beschleunigungsschätzungen um 32% bzw. 43% gegenüber einer reinen GPS-Lösung bei Verwendung von Daten mit einem Abtastintervall von 30 Sekunden erhöht werden. Die Verbesserungen liegen dann bei 28% bzw. 31% gegenüber den PPP-Lösungen.

Global Navigation Satellite Systems (GNSS) play an important role in precise positioning for geodesy and surveying engineering. The key to the real-time GNSS precise positioning is the instantaneous integer ambiguity resolution. However, some of the biases in carrier phase observations cannot be removed by differencing between either stations or satellites, so the integer nature of the double-differenced ambiguities is destroyed and thus the ambiguities cannot be fixed to integers. Two typical biases are the inter-frequency bias (IFB) in GLObal NAvigation Satellite System (GLONASS) data processing and the inter-system bias (ISB) in multi-GNSS integration. Hence, the main objective of this thesis is the investigation, estimation and correction of these biases in carrier phase observations to achieve better positioning accuracy, reliability and availability through the improvement of its ambiguity resolution. The estimated parameters of the carrier phase IFB and ISB are usually the IFB rate and the fractional ISB (F-ISB), respectively. Most of the current methods estimate IFB rate or F-ISB together with the float ambiguities and usually need observations of relatively long time due to their high correlation. Theoretically, the performance of the ambiguity resolution depends on the quality of the given IFB rate/F-ISB value if the observations are precisely modelled. In other words, the closer the given IFB rate/F-ISB value to the truth value is, the better the resolution will be. Therefore, the RATIO in the ambiguity fixing can be applied as the qualification factor of the IFB rate/F-ISB value. Based on this fact, a new methodology based on particle filter is developed to estimate these biases in both post-processing and real-time mode in this study. In the proposed method, the IFB/ISB is represented by its samples (i.e. particles) with the weights determined by the designed likelihood function of the related RATIO given the sample values, so that the true bias value can be estimated successfully by the particle filter approach. The integer nature of the ambiguities in the models with IFB/ISB parameters is well utilised in the ambiguity resolution with the given IFB rate/F-ISB values. Thus, the new method can significantly reduce the convergence time and increase the reliability of the estimation without a priori values. Besides, when more than one bias parameter is included in the model, the multi-dimensional particle filter approach is developed to estimate more than one bias parameter simultaneously in GNSS precise positioning. In this case, the aforementioned benefits of the method are obviously enlarged. In the GLONASS data processing with a nonzero IFB rate, the method can estimate the IFB rate from observations of a few epochs. With the estimated IFB rate, the GLONASS fixed solutions are as accurate as the GPS fixed solutions in the experiments with short baselines. In addition, the bias in the estimated IFB rate when the state noise is set to a very small value or even zero is significant, but this bias can be removed by utilising the regularized particle filter (RPF) and the precision of the estimated IFB rate is continuously improved by new observations. An approach for adapting the number of particles in the estimation of the IFB rate is also proposed to reduce the calculation burden by relating the number of particles to the standard deviation of the weighted particles. In the estimation of the F-ISB in multi-GNSS integration, the new method based on particle filter largely reduces the convergence time and improves the reliability of F-ISB estimation when satellites from each system are not sufficient for independent positioning. Due to the periodic characteristics of ISB, the F-ISB particles can be separated into different groups leading to the divergence of the filtering. This problem is solved successfully by introducing the cluster analysis method which can detect the groups automatically so that they can be shifted together into one group in the filtering. The estimation of the phase IFB rate with the new method enables the usage of GLONASS in real-time kinematic positioning even when the IFB between receivers is large. The estimation of the phase F-ISB with the new method allows the precise positioning to be carried out with fewer satellites from each system than the number of satellites required by the current methods. Therefore, the IFB rate/F-ISB estimation significantly extends the application of real-time kinematic GNSS positioning. It also proves that the developed new method is capable of estimating biases quickly and accurately, which initiates a new way of bias estimation in GNSS precise positioning. Global Navigation Satellite Systems (GNSS) spielen eine wichtige Rolle bei der präzisen Positionierung für Geodäsie und Vermessungstechnik. Der Schlüssel für die präzise GNSS Echtzeitpositionierung ist die sofortige Auflösung der ganzzahligen Mehrdeutigkeit. Jedoch können einige der Bias in Trägerphasenbeobachtungen nicht durch Differenzbildung entweder zwischen Stationen oder Satelliten entfernt werden, so dass die ganzzahlige Natur der Mehrdeutigkeit durch doppelte Differenzbildung zerstört werden kann und somit können die Mehrdeutigkeit nicht als ganze Zahlen festgelegt werden. Zwei typische Biasarten sind die Inter-Frequency-Bias (IFB) in der Prozessierung von GLObal NAvigation Satellite System (GLONASS) Daten und die Inter-System-Bias (ISB) für Integration von mehreren GNSS. Daher ist das Hauptziel dieser Arbeit die Untersuchung, Schätzung und Korrektur dieser Bias in Trägerphasenbeobachtungen um bessere Positionierungsgenauigkeit, Zuverlässigkeit und Verfügbarkeit durch die Verbesserung der Auflösung von Mehrdeutigkeiten zu erreichen. Die geschätzten Parameter der IFB und ISB von Trägerphasen sind normalerweise die IFB Rate und der bruchzahlige Teil von ISB (F-ISB). Die meisten der aktuellen Methoden schätzen die IFB Rate oder F-ISB zusammen mit den nicht-ganzzahligen Mehrdeutigkeiten und brauchen aufgrund ihrer hohen Korrelation meistens relativ lange Beobachtungszeitintervalle. Theoretisch hängt die Leistung der Auflösung von Mehrdeutigkeiten von der Qualität des gegebenen Wertes von IFB Rate/F-ISB ab, wenn die Beobachtungen präzise modelliert werden. Mit anderen Worten, je näher der gegebene Wert von IFB Rate/F-ISB an dem wahren Wert liegt, desto besser ist die Auflösung. Daher kann RATIO in der Festlegung von Mehrdeutigkeiten als Qualifizierungsfaktor des Wertes von IFB-Rate/F-ISB angewendet werden. Aufgrund dieser Tatsache wurde in dieser Arbeit eine neue auf dem Partikelfilter basierende Methode entwickelt, um diese Bias sowohl in Post-Prozessierung als auch im Echtzeit-Modus zu schätzen. Bei dem vorgeschlagenen Verfahren wird die IFB/ISB durch deren Stichproben (d.h. Partikel) repräsentiert, mit den Gewichten die durch die konstruierte Wahrscheinlichkeitsverteilung (Likelihood-Funktion) von dem dazugehörigen RATIO für die gegebenen Stichprobenwerte so festgelegt werden, dass der wahre Biaswert mit dem Partikelfilterverfahren erfolgreich geschätzt werden kann. Die ganzzahlige Natur der Mehrdeutigkeiten in den Modellen mit IFB/ISB-Parametern wird in der Auflösung von Mehrdeutigkeit mit dem gegebenen Wert von IFB Rate/F-ISB vorteilhaft verwendet. Somit kann das neue Verfahren die Konvergenzzeit erheblich verringern und die Zuverlässigkeit der Schätzung ohne a priori Werte erhöhen. Außerdem, für den Fall wenn mehr als ein Bias-Parameter in dem Modell enthalten ist, wurde der mehrdimensionale Partikelfilter-Ansatz entwickelt, um mehr als einen Bias-Parameter gleichzeitig innerhalb der präzisen GNSS-Positionierung abzuschätzen. In diesem Fall sind die oben genannten Vorteile des Verfahrens noch offensichtlicher. In der GLONASS-Datenverarbeitung mit einer Nicht-Null IFB Rate kann das Verfahren die IFB Rate aus den Beobachtungen von einigen wenigen Epochen abschätzen. Mit der geschätzten IFB Rate sind in den Experimenten mit kurzen Basislinien die GLONASS Lösungen mit festgesetzten Mehrdeutigkeiten so genau wie die dazugehörigen GPS Lösungen. Zusätzlich ist das Bias in der geschätzten IFB Rate, wenn das Zustandsrauschen als ein sehr kleiner Wert oder sogar Null festgelegt wird, signifikant, kann aber mit dem regularisierten Partikelfilter (RPF) entfernt werden und die Präzision des geschätzten IFB wird mit neuen Beobachtungen kontinuierlich verbessert. Ein Ansatz für die Anpassung der Anzahl der Teilchen in der Schätzung der IFB Rate wurde auch vorgeschlagen, um die Berechnungslast zu reduzieren, indem die Anzahl der Partikel mit der Standardabweichung der gewichteten Teilchen in Beziehung gesetzt wurde. In der Schätzung der F-ISB in der Integration von mehreren GNSS reduziert das neue auf dem Partikelfilter basierende Verfahren weitgehend die Konvergenzzeit und verbessert die Zuverlässigkeit der F-ISB Schätzung, wenn Satelliten von jedem einzelnen System zu wenige für eine unabhängige Positionierung sind. Aufgrund der periodischen Eigenschaften von ISB, können die F-ISB Partikel in verschiedene Gruppen getrennt werden, was zur Divergenz der Filterung führen kann. Dieses Problem wird durch die Einführung der Cluster-Analyse, die die Gruppen automatisch erkennen kann, so dass sie in der Filterung in eine Gruppe zusammengeführt werden können, erfolgreich gelöst. Die Schätzung der IFB Rate der Phase mit dem neuen Verfahren ermöglicht die Nutzung von GLONASS in Echtzeit für kinematische Positionierung, auch wenn das Bias zwischen den Empfängern groß ist. Die Schätzung des F-ISB der Phase mit dem neuen Verfahren erlaubt, dass die präzise Positionierung mit weniger Satelliten von jedem System durchgeführt wird, als erforderlich für gängige Methoden. Daher erweitert die Schätzung der IFB Rate/F-ISB bedeutend die Anwendung von kinematischen GNSS Echtzeitpositionierung. Es beweist auch, dass die entwickelte neue Methode Bias schnell und genau schätzen kann, und eine neue Art der Biasschätzung in der präzisen GNSS Positionierung einführt.

The Global Geodetic Reference Frame (GGRF) plays a fundamental role in geodesy and related Positioning, Navigation, and Timing applications, and allows to quantify the Earth’s change in space and time. The ITRF and ICRF are the two most important components to realize GGRF, while the determination of these two reference frames relies on the combination of several space geodetic techniques, mainly, VLBI, SLR, GNSS, and DORIS. The combination is currently done on either the parameter level, or the normal equation level. However, the combination on the observation level, or the so-called integrated processing of multi-technique on the observation level, provides the results of best consistency, robustness, and accuracy. This thesis focuses on the investigation of the integrated processing of GNSS and VLBI on the observation level. The benefits of integrated processing are demonstrated in terms of TRF, CRF, and EOP, while the impact of global ties (EOP), tropospheric ties, and local ties are underlined. Several issues in integrated processing are addressed, including the systematic bias in ties (for instance, LOD and tropospheric ties), the relative weighting. An automatic reweighting strategy based on the normalized residuals is developed, which can properly handle the uncertainty of the ties without losing too much constraint. A software with state-of-the-art modules is the prerequisite to perform integrated processing. Based on the GNSS data processing software: Positioning And Navigation Data Analyst (PANDA), the VLBI and SLR modules are implemented in the common least-squares estimator. Therefore, the best consistency can be guaranteed. The software capability is demonstrated with the single-technique solutions. The station coordinate precision is at millimeter level for both GNSS and VLBI, while the EOP estimates are comparable to other Analysis Centers and the IERS products. It is also demonstrated that the SLR station coordinate precision is improved by 20% to 30% with additional GLONASS and GRACE satellites to contributing to the LAGEOS and ETALON constellation. Focusing on the tropospheric ties in GNSS and VLBI integrated processing, its contribution is demonstrated for the first time comprehensively. Applying tropospheric ties improves the VLBI station coordinate precision by 12% on the horizontal components and up to 30% on the vertical component. The network scale repeatability is reduced by up to 33%. The EOP estimates are also improved significantly, for instance, 10% to 30% for polar motion, and up to 10% for other components. Furthermore, applying the gradient ties in the VLBI intensive sessions reduces the systematic bias in UT1-UTC estimates. The consistent TRF, CRF, and EOP are achieved in the integrated VLBI and GNSS solution. Applying the global ties, tropospheric ties, and local ties stables the reference frame. The ERP estimates in the integrated solution are dominated by the GNSS technique, and the VLBI technique introduces additional 10% improvement on the y-pole component in terms of the day-boundary-discontinuity. The UT1-UTC and celestial pole offsets are also slightly improved in the integrated solution. It is also demonstrated that applying the LTs inappropriately distorts the network and introduces systematic biases to the ERP estimates, addressing the necessity of updating the local surveys. Moreover, the coordinates of AGN are also enhanced by up to 20% in the integrated solutions, especially the southern ones. This study reveals the importance of integrated processing of multi-technique on the observation level, as the best consistency can be achieved, and the applied ties improve the solutions significantly. It is strongly recommended that for the future realization of celestial and terrestrial reference frames, the concept of integrated processing on the observation level should be implemented, and all the possible ties should be applied, including the global ties (EOP), local ties, space ties, and tropospheric ties. Such kind of integrated solution of all the four techniques can provide robust estimates of the reference frames and EOP, with the advantage of each technique exploited to its full extend. Der Globale Geodätische Referenzrahmen (Global Geodetic Reference Frame, GGRF) spielt eine fundamentale Rolle in der Geodäsie und den damit verbundenen Positionierungs-, Navigations- und Zeitmessungsanwendungen (Positioning, Navigation, and Timing, PNT) und ermöglicht die Quantifizierung der Veränderung der Erde in Raum und Zeit. Der ITRF und der ICRF sind die beiden wichtigsten Komponenten zur Realisierung des GGRF, wobei die Bestimmung dieser beiden Referenzrahmen auf der Kombination verschiedener raumgeodätischer Techniken beruht, hauptsächlich VLBI, SLR, GNSS und DORIS. Die Kombination wird derzeit entweder auf der Parameterebene oder auf der Normalgleichungsebene durchgeführt. Die Kombination auf der Beobachtungsebene oder die sogenannte integrierte Daten-Verarbeitung von Multi-Techniken auf der Beobachtungsebene, bietet jedoch eine Lösung mit der besten Konsistenz, Robustheit und Genauigkeit. Diese Arbeit konzentriert sich auf die Untersuchung der integrierten Daten-Verarbeitung von GNSS und VLBI auf der Beobachtungsebene. Die Vorteile der integrierten Lösung werden in Bezug auf TRF, CRF, und EOP aufgezeigt, während die Auswirkungen von „Global Ties (EOP), Tropospheric Ties, and Local Ties“ hervorgehoben werden. Einige Punkte der integrierten Verarbeitung werden in dieser Arbeit untersucht, einschließlich der systematischen Abweichungen von „Ties“ (z.B. LOD und Tropospheric Ties), der relativen Gewichtung usw. Anhand der normalisierten Residuen wird eine automatische Umgewichtungsstrategie entwickelt, mit der die Unsicherheit der „Ties“ angemessen behandelt werden kann, ohne dass zu viel Einschränkung dabei verloren geht. Eine Software mit modernsten Modulen ist die Voraussetzung für die integrierte Daten Verarbeitung. Basierend auf der GNSS-Datenverarbeitungssoftware Paket: Positioning And Navigation Data Analyst (PANDA) werden die Module VLBI und SLR in demselben Least-Squares-Estimator wie GNSS implementiert, damit kann man die beste Konsistenz in der Datenverarbeitung erreichen. In dieser Arbeit wird die Leistungsfähigkeit der Software mit den Ein-Technik-Lösungen demonstriert. Die Genauigkeit der Stationskoordinaten liegt sowohl für GNSS als auch für VLBI im Millimeterbereich, und die geschätzten EOP-Parameter sind auch mit der anderer Analysezentren und den IERS-Produkten vergleichbar. Es wird auch gezeigt, dass die Koordinatengenauigkeit der SLR-Station um 20-30% verbessert wird, wenn zusätzliche GLONASS- und GRACE-Satelliten zur LAGEOS und ETALON-Konstellation beitragen. Mit dem Schwerpunkt auf den „Tropospheric Ties“ in der integrierten GNSS- und VLBI- Daten Verarbeitung wird ihr Beitrag zum ersten Mal umfassend dargestellt. Die Anwendung der „Tropospheric Ties“ verbessert die Genauigkeit der VLBI-Koordinaten um 12% bei der horizontalen Komponente und bis zu 30% bei der vertikalen Komponente. Die Genauigkeit im Netzwerkmaßstab wird um bis zu 33% verbessert. Auch die EOP-Bestimmungen werden deutlich verbessert, z.B. um 10-30% bei polaren Bewegungen und bis zu 10% bei anderen Komponenten. Darüber hinaus reduziert die Einführung der „Gradient Ties“ in der VLBI-Intensivsession die systematische Abweichung in den dUT1-Bestimmungen. Die konsistente TRF, CRF, und EOP werden bei der integrierten VLBI- und GNSS-Lösung erreicht. Die Anwendung der „Global Ties, Tropospheric Ties and Local Ties“ stabilisiert die Bestimmungen des Referenzrahmens. Die ERP-Bestimmungen in der integrierten Lösung werden von der GNSS-Technik dominiert, und die VLBI-Technik bringt eine zusätzliche Verbesserung um 10% auf die Tagesgrenzen-Diskontinuität (day-boundary-discontinuity, DBD) für die y-Pol-Komponente. Die dUT1- und CPO werden in der integrierten Lösung ebenfalls leicht verbessert. Es wird auch gezeigt, dass eine ungeeignete Anwendung der LTs das Netzwerk verzerrt und systematische Abweichungen in die ERP-Bestimmungen einführt, wodurch die Notwendigkeit einer Aktualisierung der lokalen Tie Messungen deutlich wird. Darüber hinaus werden die Koordinaten der AGN in den integrierten Lösungen um bis zu 20% verbessert, insbesondere im Süden. Diese Arbeit zeigt die Bedeutung der integrierten Daten Verarbeitung von Multi-Technik auf der Beobachtungsebene, da die beste Konsistenz erreicht werden kann und die angewandten „Ties“ die Lösungen erheblich verbessern. Es wird nachdrücklich empfohlen, für die zukünftige Realisierung von himmelsfesten und erdfesten Referenzrahmen das Konzept der integrierten Verarbeitung auf Beobachtungsebene durchzuführen und alle möglichen „Ties“ anzuwenden, einschließlich der „Global Ties (EOP), Local Ties, Space Ties, and Tropospheric Ties“. Eine solche integrierte Lösung aller vier Techniken kann die robusten Bestimmungen der Referenzrahmen und der EOP liefern, wobei die Vorteile jeder Technik voll ausgeschöpft werden.