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<big>'''JSG T.23: High-rate GNSS'''</big>
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<big>'''JSG T.23: Spherical and spheroidal integral formulas of the potential theory for transforming classical and new gravitational observables'''</big>
  
Chair: ''Mattia Crespi (Italy)''<br>
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Chair: ''Michal Šprlák (Czech Republic)''<br>
Affiliation:''Commissions 1, 3 4 and GGOS''
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Affiliation:''Commission 2 and GGOS''
  
 
__TOC__
 
__TOC__
 
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<nowiki>Insert non-formatted text here</nowiki>
 
===Introduction===
 
===Introduction===
  
Global Navigation Satellite Systems (GNSS) have become for a long time an indispensable tool to get accurate and reliable information about positioning and timing; in addition, GNSS are able to provide information related to physical properties of media passed through by GNSS signals. Therefore, GNSS play a central role both in geodesy and geomatics and in several branches of geophysics, representing a cornerstone for the observation and monitoring of our planet.
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The gravitational field represents one of the principal properties of any planetary body. Physical quantities, e.g., the gravitational potential or its gradients (components of gravitational tensors), describe gravitational effects of any mass body. They help indirectly in sensing inner structures of planets and their (sub-)surface processes. Thus, they represent an indispensable tool for understanding inner structures and processes of planetary bodies and for solving challenging problems in geodesy, geophysics and other planetary sciences.
 
 
So, it is not surprising that, from the very beginning of the GNSS era, the goal was pursued to widen as much as possible the range in space (from local to global) and time (from short to long term) of the observed phenomena, in order to cover the largest possible field of applications, both in science and in engineering; two complementary, but primary as well, goals were, obviously, to get these information with the highest accuracy and in the shortest time.  
 
 
 
The advances in technology and the deployment of new constellations, after GPS (in the next years will be completed the European Galileo, the Chinese Beidou and the Japanese QZSS) remarkably contributed to transform this three-goals dream in reality, but still remain significant challenges when very fast phenomena have to be observed, mainly if real-time results are looked for.
 
 
 
Actually, for almost 15 years, starting from the noble birth in seismology, and the very first experiences in structural monitoring, high-rate GNSS has demonstrated its usefulness and power in providing precise positioning information in fast time-varying environments. At the beginning, high-rate observations were mostly limited at 1 Hz, but the technology development provided GNSS equipment (in some cases even at low-cost) able to collect measurements at much higher rates, up to 100 Hz, therefore opening new possibilities, and meanwhile new challenges and problems.
 
  
So, it is necessary to think about how to optimally process this potential huge heap of data, in order to supply information of high value for a large (and likely increasing) variety of applications, some of them listed hereafter without the claim to be exhaustive: better understanding of the geophysical/geodynamical processes mechanics; monitoring of ground shaking and displacement during earthquakes, also for contribution to tsunami early warning; tracking the fast variations of the ionosphere; real-time controlling landslides and the safety of structures; providing detailed trajectories and kinematic parameters (not only position, but also velocity and acceleration) of high dynamic platforms such as airborne sensors, high-speed terrestrial vehicles and even athlete and sport vehicles monitoring.
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Various measurement principles have been developed for collecting gravitational data by terrestrial, marine, airborne or satellite sensors. From a theoretical point of view, different parameterizations of the gravitational field have been introduced. To transform observable parameters into sought parameters, various methods have been introduced, e.g., boundary-value problems of the potential theory have been formulated and solved analytically by integral transformations.
  
Further, due to the contemporary technological development of other sensors (hereafter referred as ancillary sensors) related to positioning and kinematics able to collect data at high-rate (among which MEMS accelerometers and gyros play a central role, also for their low-cost), the feasibility of a unique device for high-rate observations embedding GNSS receiver and MEMS sensors is real, and it opens, again, new opportunities and problems, first of all related to sensors integration.
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Transforms based on solving integral equations of Stokes, Vening-Meinesz and Hotine have traditionally been of significant interest in geodesy as they accommodated gravity field observables in the past. However, new gravitational data have recently become available with the advent of satellite-to-satellite tracking, Doppler tracking, satellite altimetry, satellite gravimetry, satellite gradiometry and chronometry. Moreover, gravitational curvatures have already been measured in laboratory. New observation techniques have stimulated formulations of new boundary-value problems, equally as possible considerations on a tie to partial differential equations of the second order on a two-dimensional manifold. Consequently, the family of surface integral formulas has considerably extended, covering now mutual transformations of gravitational gradients of up to the third order.
  
All in all, it is clear that high-rate GNSS (and ancillary sensors) observations represent a great resource for future investigations in Earth sciences and applications in engineering, meanwhile stimulating a due attention from the methodological point of view in order to exploit their full potential and extract the best information. This is the why it is worth to open a focus on high-rate (and, if possible, real-time) GNSS within ICCT.
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In light of numerous efforts in extending the apparatus of integral transforms, many theoretical and numerical issues still remain open. Within this JSG, open theoretical questions related to existing surface integral formulas, such as stochastic modelling, spectral combining of various gradients and assessing numerical accuracy, will be addressed. We also focus on extending the apparatus of spheroidal integral transforms which is particularly important for modelling gravitational fields of oblate or prolate planetary bodies.
  
 
===Objectives===
 
===Objectives===
  
* To realize the inventories of:
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* Study noise propagation through spherical and spheroidal integral transforms.
** the available and applied methodologies for high-rate GNSS, in order to highlight their pros and cons and the open problems,
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* Propose efficient numerical algorithms for precise evaluation of spherical and spheroidal integral transformations.
** the present and wished applications of high-rate GNSS for science and engineering, with a special concern to the estimated quantities (geodetic, kinematic, physical), in order to focus on related problems (still open and possibly new) and draw future challenges
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* Develop mathematical expressions for calculating the distant-zone effects for spherical and spheroidal integral transformations.
** the technology (hw, both for GNSS and ancillary sensors, and sw, possibly FOSS), pointing out what is ready and what is coming, with a special concern for the supplied observations and for their functional and stochastic modeling with the by-product of establishing a standardized terminology
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* Study mathematical properties of differential operators in spheroidal coordinates which relate various functionals of the gravitational potential.
* To address known (mostly cross-linked) problems related to high-rate GNSS as (not an exhaustive list): revision and refinement of functional and stochastic models; evaluation and impact of observations time-correlation; impact of multipath and constellation change; outliers detection and removal; issues about GNSS constellations interoperability; ancillary sensors evaluation, cross-calibration and  integration
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* Formulate and solve spheroidal gradiometric and spheroidal curvature boundary-value problems.
* To address the new problems and future challanges arised from the inventories
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* Complete the family of spheroidal integral transforms among various types of gravitational gradients and to derive corresponding integral kernel functions.
* To investigate about the interaction with present real-time global (IGS-RTS, EUREF-IP, etc.) and regional/local positioning services: how can these services support high-rate GNSS observations and, on reverse, how can they benefit of high-rate GNSS observations
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* Investigate optimal combination techniques of various gravitational gradients for gravitational field modelling at all scales.
  
 
===Program of activities===
 
===Program of activities===
  
* To launch a questionnaire for the above mentioned inventory of methodologies, applications and technologies.
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* Presenting findings at international geodetic or geophysical conferences, meetings and workshops.
* To open a web page with information concerning high-rate GNSS and its wide applications in science and engineering, with special emphasis on exchange of ideas, provision and updating bibliographic list of references of research results and relevant publications from different disciplines.
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* Interacting with IAG Commissions and GGOS.
* To launch the proposal for two (one science and the other engineering oriented) state-of-the-art review papers in high-rate GNSS co-authored by the JSG Members.
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* Monitoring research activities of JSG members and other scientists whose research interests are related to scopes of this JSG.
* To organize a session at the forthcoming Hotine-Marussi symposium.
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* Organizing a session at the Hotine-Marussi Symposium 2022.
* To promote sessions and presentation of the research results at international symposia both related to Earth science (IAG/IUGG, EGU, AGU, EUREF, IGS) and engineering (workshops and congresses in structural and geotechnical engineering).
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* Providing a bibliographic list of publications from different branches of the science relevance to scopes of this JSG.
  
 
===Members===
 
===Members===
  
'' '''Mattia Crespi (Italy), chair''' <br /> Juan Carlos Baez (Chile) <br /> Elisa Benedetti (United Kingdom) <br /> Geo Boffi (Switzerland) <br /> Gabriele Colosimo (Switzerland) <br /> Athanasios Dermanis (Greece) <br /> Roberto Devoti (Italy) <br /> Jeff Freymueller (USA) <br /> Joao Francisco Galera Monico (Brazil) <br /> Jianghui Geng (Germany) <br /> Kosuke Heki (Japan) <br /> Melvin Hoyer (Venezuela) <br /> Nanthi Nadarajah (Australia) <br /> Yusaku Ohta (Japan) <br /> Ruey-Juin Rau (Taiwan) <br /> Eugenio Realini (Italy) <br /> Chris Rizos (Australia) <br /> Nico Sneeuw (Germany) <br /> Peiliang Xu (Japan) <br />''
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'' '''Michal Šprlák (Czech Republic), chair''' <br /> Sten Claessens (Australia) <br /> Mehdi Eshagh (Sweden) <br /> Ismael Foroughi (Canada) <br /> Peter Holota (Czech Republic) <br /> Juraj Janák (Slovakia) <br /> Otakar Nesvadba (Czech Republic) <br /> Pavel Novák (Czech Republic) <br /> Vegard Ophaug (Norway) <br /> Martin Pitoňák (Czech Republic) <br /> Michael Sheng (Canada) <br /> Natthachet Tangdamrongsub (USA) <br /> Robert Tenzer (Hong Kong) <br />''
 
 
  
 
===Bibliography===
 
===Bibliography===
 
[Biblioraphy [http://icct.kma.zcu.cz/index.php/JSG_0.10:_High-rate_GNSS_-_Bibliography]]
 

Latest revision as of 10:35, 10 June 2020

JSG T.23: Spherical and spheroidal integral formulas of the potential theory for transforming classical and new gravitational observables

Chair: Michal Šprlák (Czech Republic)
Affiliation:Commission 2 and GGOS

Insert non-formatted text here

Introduction

The gravitational field represents one of the principal properties of any planetary body. Physical quantities, e.g., the gravitational potential or its gradients (components of gravitational tensors), describe gravitational effects of any mass body. They help indirectly in sensing inner structures of planets and their (sub-)surface processes. Thus, they represent an indispensable tool for understanding inner structures and processes of planetary bodies and for solving challenging problems in geodesy, geophysics and other planetary sciences.

Various measurement principles have been developed for collecting gravitational data by terrestrial, marine, airborne or satellite sensors. From a theoretical point of view, different parameterizations of the gravitational field have been introduced. To transform observable parameters into sought parameters, various methods have been introduced, e.g., boundary-value problems of the potential theory have been formulated and solved analytically by integral transformations.

Transforms based on solving integral equations of Stokes, Vening-Meinesz and Hotine have traditionally been of significant interest in geodesy as they accommodated gravity field observables in the past. However, new gravitational data have recently become available with the advent of satellite-to-satellite tracking, Doppler tracking, satellite altimetry, satellite gravimetry, satellite gradiometry and chronometry. Moreover, gravitational curvatures have already been measured in laboratory. New observation techniques have stimulated formulations of new boundary-value problems, equally as possible considerations on a tie to partial differential equations of the second order on a two-dimensional manifold. Consequently, the family of surface integral formulas has considerably extended, covering now mutual transformations of gravitational gradients of up to the third order.

In light of numerous efforts in extending the apparatus of integral transforms, many theoretical and numerical issues still remain open. Within this JSG, open theoretical questions related to existing surface integral formulas, such as stochastic modelling, spectral combining of various gradients and assessing numerical accuracy, will be addressed. We also focus on extending the apparatus of spheroidal integral transforms which is particularly important for modelling gravitational fields of oblate or prolate planetary bodies.

Objectives

  • Study noise propagation through spherical and spheroidal integral transforms.
  • Propose efficient numerical algorithms for precise evaluation of spherical and spheroidal integral transformations.
  • Develop mathematical expressions for calculating the distant-zone effects for spherical and spheroidal integral transformations.
  • Study mathematical properties of differential operators in spheroidal coordinates which relate various functionals of the gravitational potential.
  • Formulate and solve spheroidal gradiometric and spheroidal curvature boundary-value problems.
  • Complete the family of spheroidal integral transforms among various types of gravitational gradients and to derive corresponding integral kernel functions.
  • Investigate optimal combination techniques of various gravitational gradients for gravitational field modelling at all scales.

Program of activities

  • Presenting findings at international geodetic or geophysical conferences, meetings and workshops.
  • Interacting with IAG Commissions and GGOS.
  • Monitoring research activities of JSG members and other scientists whose research interests are related to scopes of this JSG.
  • Organizing a session at the Hotine-Marussi Symposium 2022.
  • Providing a bibliographic list of publications from different branches of the science relevance to scopes of this JSG.

Members

Michal Šprlák (Czech Republic), chair
Sten Claessens (Australia)
Mehdi Eshagh (Sweden)
Ismael Foroughi (Canada)
Peter Holota (Czech Republic)
Juraj Janák (Slovakia)
Otakar Nesvadba (Czech Republic)
Pavel Novák (Czech Republic)
Vegard Ophaug (Norway)
Martin Pitoňák (Czech Republic)
Michael Sheng (Canada)
Natthachet Tangdamrongsub (USA)
Robert Tenzer (Hong Kong)

Bibliography