Improving the Geodetic Infrastructure for Bathymetry and 3D Navigation in the German Exclusive Economic Zone of the North and Baltic Sea

Surveying and navigation became much easier, more accurate and operational thanks to the Global Positioning System. The use of this technology in height determination, bathymetry and 3-D navigation is not only limited by the reduced accuracy compared to the horizontal component. It supposes additional information about the geodetic height reference surface in order to leverage the full potential of this technology. The corresponding models, measurements and activities which are necessary to improve this part of the geodetic infrastructure are usually behind the curtain. This article emphasizes the need of a common cross-border geodetic infrastructure and the relevance of precise models of the height reference surface for GNSS-aided height determinations. The need of gravimetric surveys for the determination and improvement of these models is explained. Finally, it gives an overview about the gravimetric surveys which were carried out in the German Exclusive Zone of the North and Baltic Sea over more than one decade and provides some insight into practical aspects and challenges of this kind of surveys.En un proyecto de dos años de investigación y desarrollo, se desarrolló el prototipo de un servicio en tiempo real basado en GNSS (Sistema Global de Navegación por Satélite) usando un enfoque SSR-RTK (Cinemática en Tiempo Real – Representación del Espacio Nacional) para la zona económica exclusiva alemana en el Mar del Norte. Como el área de levantamientos del Mar del Norte solo se puede representar mediante una distribución heterogénea de Estaciones de Referencia GNSS en Funcionamiento Constante, el algoritmo de cálculo y el modelado de los datos de corrección del GNSS son particularmente importantes. Las mediciones marítimas en el área de levantamientos han confirmado la funcionalidad básica del prototipo hasta casi el 90% de disponibilidad de la determinación de estado RTK con tiempos de inicialización de menos de dos minutos. Se usaron mediciones en tierra y mar además de una estación de control permanente para demostrar los objetivos de calidad.Dans le cadre d’un projet de recherche et développement de deux ans, le prototype d’un service en temps réel basé sur un GNSS (Global Navigation Satellite System) utilisant une approche SSR-RTK (State Space Representation-Real Time Kinema-tic) a été développé pour la zone économique exclusive allemande en mer du Nord. Étant donné que la zone d’étude de la mer du Nord ne peut être représentée qu’avec une distribution hétérogène des stations de référence GNSS en exploitation continue, l’algorithme de calcul et la modélisation des données de correction GNSS sont particulièrement importants. Les mesures à la mer dans la zone d’étude ont confirmé la fonctionnalité de base du prototype grâce à une disponibilité de près de 90% du correctif RTK avec des temps d’initialisation inférieurs à deux minutes. Des mesures en mer et à terre ainsi qu’une station de contrôle permanente ont été utili-sées pour démontrer les objectifs de qualité

Precise orbit determination based on COST-G time-variable gravity fields

The Combination Service for Time-variable Gravity fields (COST-G) provides monthly gravity fields, combined from the individual solutions of the COST-G analysis centers and additional partner analysis centers derived from GRACE/GRACE-FO inter-satellite GPS and K-band ranging data. The Precise Orbit Determination (POD) of Earth observation satellites in Low Earth Orbits (LEO) relies on accurate and up-to-date information on the Earthâ?Ts gravity field and its time-variations. We study POD results of the Sentinel-2B, -3B and -6A satellites based either on the monthly COST-G combinations, available with a latency of 2-3 months, or on Fitted Signal Models (FSM) derived on the basis of the COST-G time-series of monthly gravity fields, which allow for the prediction of secular and seasonal gravity variations over several months and therefore may be used in operational LEO POD. Special focus is put on the fit interval of the FSM and the impact of episodic events, e.g. the massive ice melt in Greenland in the summer of 2019, on the performance of the gravity-predictions for POD

Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica

Conventional relative kinematic positioning is difficult to be applied in the polar region of Earth since there is a very sparse distribution of reference stations, while precise point positioning (PPP), using data of a stand-alone receiver, is recognized as a promising tool for obtaining reliable and accurate trajectories of moving platforms. However, PPP and its integer ambiguity fixing performance could be much degraded by satellite orbits and clocks of poor quality, such as those of the geostationary Earth orbit (GEO) satellites of the BeiDou navigation satellite system (BDS), because temporal variation of orbit errors cannot be fully absorbed by ambiguities. To overcome such problems, a network-based processing, referred to as precise orbit positioning (POP), in which the satellite clock offsets are estimated with fixed precise orbits, is implemented in this study. The POP approach is validated in comparison with PPP in terms of integer ambiguity fixing and trajectory accuracy. In a simulation test, multi-GNSS (global navigation satellite system) observations over 14 days from 136 globally distributed MGEX (the multi-GNSS Experiment) receivers are used and four of them on the coast of Antarctica are processed in kinematic mode as moving stations. The results show that POP can improve the ambiguity fixing of all system combinations and significant improvement is found in the solution with BDS, since its large orbit errors are reduced in an integrated adjustment with satellite clock offsets. The four-system GPS+GLONASS+Galileo+BDS (GREC) fixed solution enables the highest 3D position accuracy of about 3.0 cm compared to 4.3 cm of the GPS-only solution. Through a real flight experiment over Antarctica, it is also confirmed that POP ambiguity fixing performs better and thus can considerably speed up (re-)convergence and reduce most of the fluctuations in PPP solutions, since the continuous tracking time is short compared to that in other regions

The GFZ GRACE RL06 Monthly Gravity Field Time Series: Processing Details and Quality Assessment

Time-variable gravity field models derived from observations of the Gravity Recovery and Climate Experiment (GRACE) mission, whose science operations phase ended in June 2017 after more than 15 years, enabled a multitude of studies of Earth’s surface mass transport processes and climate change. The German Research Centre for Geosciences (GFZ), routinely processing such monthly gravity fields as part of the GRACE Science Data System, has reprocessed the complete GRACE mission and released an improved GFZ GRACE RL06 monthly gravity field time series. This study provides an insight into the processing strategy of GFZ RL06 which has been considerably changed with respect to previous GFZ GRACE releases, and modifications relative to the precursor GFZ RL05a are described. The quality of the RL06 gravity field models is analyzed and discussed both in the spectral and spatial domain in comparison to the RL05a time series. All results indicate significant improvements of about 40% in terms of reduced noise. It is also shown that the GFZ RL06 time series is a step forward in terms of consistency, and that errors of the gravity field coefficients are more realistic. These findings are confirmed as well by independent validation of the monthly GRACE models, as done in this work by means of ocean bottom pressure in situ observations and orbit tests with the GOCE satellite. Thus, the GFZ GRACE RL06 time series allows for a better quantification of mass changes in the Earth system.DFG, FOR 2736, New Refined Observations of Climate Change from Spaceborne Gravity Missions (NEROGRAV)BMBF, 03F0654A, GRACE-FO - Projektmanagement, Aufbau eines wissenschaftlichen Auswertesystems und Aufbau eines GRACE-FO Projektbüro

Symmetries of perturbed conformal field theories

The symmetries of perturbed conformal field theories are analysed. We explain which generators of the chiral algebras of a bulk theory survive a perturbation by an exactly marginal bulk field. We also study the behaviour of D-branes under current-current bulk deformations. We find that the branes always continue to preserve as much symmetry as they possibly can, i.e. as much as is preserved in the bulk. We illustrate these findings with several examples, including permutation branes in WZW models and B-type D-branes in Gepner models.Comment: 30 pages, 3 figures. V2: Small error in eq. (2.14) correcte

The influence of the Earth's magnetic field on strapdown inertial gravimetry using Q-Flex accelerometers: static and dynamic experiments

In recent strapdown airborne and shipborne gravimetry campaigns with servo accelerometers of the widely used Q-Flex type, results have been impaired by heading-dependent measurement errors. This paper shows that the effect is, in all likelihood, caused by the sensitivity of the Q-Flex type sensor to the Earth’s magnetic field. In order to assess the influence of magnetic fields on the utilised strapdown IMU of the type iMAR iNAV-RQH-1003, the IMU has been exposed to various magnetic fields of known directions and intensities in a 3-D Helmholtz coil. Based on the results, a calibration function for the vertical accelerometer is developed. At the example of five shipborne and airborne campaigns, it is outlined that under specific circumstances the precision of the gravimetry results can be strongly improved using the magnetic calibration approach: The non-adjusted RMSE at repeated lines decreased from 1.19 to 0.26 mGal at a shipborne campaign at Lake Müritz, Germany. To the knowledge of the authors, a significant influence of the Earth’s magnetic field on strapdown inertial gravimetry is demonstrated for the first time

COST-G: towards a new GRACE and GRACE-FO combination

The combination service for time-variable gravity fields (COST-G) provides the full time-series of monthly GRACE gravity fields: COST-G GRACE RL01, combined in reprocessing mode, and a steadily growing time-series of monthly GRACE-FO gravity fields: COST-G GRACE-FO RL01 OP, combined on an operational basis. Both time-series are currently considered for re-combination. In case of GRACE, new high-quality time-series from Chinese analysis centers are available for combination. In case of GRACE-FO, a revision of the weighting scheme, developed in the frame of the Horizon2020 project Global Gravity-based Groundwater Product (G3P), and the availability of reprocessed GRACE-FO time-series from AIUB, CSR, GFZ, and JPL, lead to a significant improvement of the combined gravity fields. We present the preliminary re-combined GRACE and GRACE-FO time-series and quantify the differences with respect to the COST-G RL01 series in terms of signal and noise content

Branes: from free fields to general backgrounds

Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection coefficients for bulk fields on the disk; and second, a choice of an automorphism $\omega$ of the fusion rules that preserves conformal weights. Non-trivial automorphisms $\omega$ correspond to D-brane configurations for arbitrary conformal field theories. The choice of the fusion rule automorphism $\omega$ amounts to fixing the dimension and certain global topological features of the D-brane world volume and the background gauge field on it. We present evidence that for fixed choice of $\omega$ the boundary conditions are classified as the irreducible representations of some commutative associative algebra, a generalization of the fusion rule algebra. Each of these irreducible representations corresponds to a choice of the moduli for the world volume of the D-brane and the moduli of the flat connection on it.Comment: 56 pages, LaTeX2e. Typos corrected; two references adde