Skip to main content

2015 | OriginalPaper | Buchkapitel

Multiparameter Regularization in Downward Continuation of Satellite Data

verfasst von : Shuai Lu, Sergei V. Pereverzev

Erschienen in: Handbook of Geomathematics

Verlag: Springer Berlin Heidelberg

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This chapter discusses the downward continuation of the spaceborne gravity data. We analyze the ill-posed nature of this problem and describe some approaches to its treatment. This chapter focuses on the multiparameter regularization approach and show how it can naturally appear in the geodetic context in the form of the regularized total least squares or the dual regularized total least squares, for example. The numerical illustrations with synthetic data demonstrate that multiparameter regularization can indeed produce a good accuracy approximation.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Bauer F, Pereverzev SV (2006) An utilization of a rough approximation of a noise covariance within the framework of multi-parameter regularization. Int J Tomogr Stat 4:1–12MathSciNetMATH Bauer F, Pereverzev SV (2006) An utilization of a rough approximation of a noise covariance within the framework of multi-parameter regularization. Int J Tomogr Stat 4:1–12MathSciNetMATH
Zurück zum Zitat Bauer F, Mathé P, Pereverzev SV (2007) Local solutions to inverse problems in geodesy: the impact of the noise covariance structure upon the accuracy of estimation. J Geod 81:39–51CrossRefMATH Bauer F, Mathé P, Pereverzev SV (2007) Local solutions to inverse problems in geodesy: the impact of the noise covariance structure upon the accuracy of estimation. J Geod 81:39–51CrossRefMATH
Zurück zum Zitat Beck A, Ben-Tal A, Teboulle M (2006) Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares. SIAM J Matrix Anal Appl 28:425–445MathSciNetCrossRefMATH Beck A, Ben-Tal A, Teboulle M (2006) Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares. SIAM J Matrix Anal Appl 28:425–445MathSciNetCrossRefMATH
Zurück zum Zitat Boumann J (2000) Quality assessment of satellite-based global gravity field models. PhD dissertation, Delft University of Technology Boumann J (2000) Quality assessment of satellite-based global gravity field models. PhD dissertation, Delft University of Technology
Zurück zum Zitat Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer, DordrechtCrossRefMATH Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer, DordrechtCrossRefMATH
Zurück zum Zitat Freeden W (1999) Multiscale modeling of spaceborne geodata. B.G. Teubner, LeipzigMATH Freeden W (1999) Multiscale modeling of spaceborne geodata. B.G. Teubner, LeipzigMATH
Zurück zum Zitat Freeden W, Pereverzev SV (2001) Spherical Tikhonov regularization wavelets in satellite gravity gradiometry with random noise. J Geod 74:730–736CrossRefMATH Freeden W, Pereverzev SV (2001) Spherical Tikhonov regularization wavelets in satellite gravity gradiometry with random noise. J Geod 74:730–736CrossRefMATH
Zurück zum Zitat Freeden W, Schneider F, Schreiner M (1997) Gradiometry – an inverse problem in modern satellite geodesy. In: Engl HW, Louis AK, Rundell W (eds) GAMM-SIAM symposium on inverse problems in geophysical applications. Fish Lake, Yosemite, pp 179–239 Freeden W, Schneider F, Schreiner M (1997) Gradiometry – an inverse problem in modern satellite geodesy. In: Engl HW, Louis AK, Rundell W (eds) GAMM-SIAM symposium on inverse problems in geophysical applications. Fish Lake, Yosemite, pp 179–239
Zurück zum Zitat Golub GH, Hansen PC, O’Leary DP (1999) Tikhonov regularization and total least squares. SIAM J Matrix Anal Appl 21:185–194MathSciNetCrossRefMATH Golub GH, Hansen PC, O’Leary DP (1999) Tikhonov regularization and total least squares. SIAM J Matrix Anal Appl 21:185–194MathSciNetCrossRefMATH
Zurück zum Zitat Klees R, Ditmar P, Broersen P (2003) How to handle colored observation noise in large least-squares problems. J Geod 76:629–640CrossRef Klees R, Ditmar P, Broersen P (2003) How to handle colored observation noise in large least-squares problems. J Geod 76:629–640CrossRef
Zurück zum Zitat Kunisch K, Zou J (1998) Iterative choices of regularization parameters in linear inverse problems. Inverse Probl 14:1247–1264MathSciNetCrossRefMATH Kunisch K, Zou J (1998) Iterative choices of regularization parameters in linear inverse problems. Inverse Probl 14:1247–1264MathSciNetCrossRefMATH
Zurück zum Zitat Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J Geod 76:359–368CrossRef Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J Geod 76:359–368CrossRef
Zurück zum Zitat Lu S, Pereverzev SV, Tautenhahn U (2008) Dual regularized total least squares and multi-parameter regularization. Comput Methods Appl Math 8:253–262MathSciNetCrossRefMATH Lu S, Pereverzev SV, Tautenhahn U (2008) Dual regularized total least squares and multi-parameter regularization. Comput Methods Appl Math 8:253–262MathSciNetCrossRefMATH
Zurück zum Zitat Lu S, Pereverzev SV, Tautenhahn U (2009) Regularized total least squares: computational aspects and error bounds. SIAM J Matrix Anal Appl 31:918–941MathSciNetCrossRefMATH Lu S, Pereverzev SV, Tautenhahn U (2009) Regularized total least squares: computational aspects and error bounds. SIAM J Matrix Anal Appl 31:918–941MathSciNetCrossRefMATH
Zurück zum Zitat Nair MT, Pereverzev SV, Tautenhahn U (2005) Regularization in Hilbert scales under general smoothing conditions. Inverse Probl 2:1851–1869MathSciNetCrossRefMATH Nair MT, Pereverzev SV, Tautenhahn U (2005) Regularization in Hilbert scales under general smoothing conditions. Inverse Probl 2:1851–1869MathSciNetCrossRefMATH
Zurück zum Zitat Pereverzev SV, Schock E (1999) Error estimates for band-limited spherical regularization wavelets in an inverse problem of satellite geodesy. Inverse Probl 15:881–890MathSciNetCrossRefMATH Pereverzev SV, Schock E (1999) Error estimates for band-limited spherical regularization wavelets in an inverse problem of satellite geodesy. Inverse Probl 15:881–890MathSciNetCrossRefMATH
Zurück zum Zitat Rebhan H, Aguirre M, Johannessen J (2000) The gravity field and steady-state ocean circulation explorer mission-GOCE. ESA Earth Obs Q 66:6–11 Rebhan H, Aguirre M, Johannessen J (2000) The gravity field and steady-state ocean circulation explorer mission-GOCE. ESA Earth Obs Q 66:6–11
Zurück zum Zitat Rummel R, van Gelderen, Koop R, Schrama E, Sanso F, Brovelli M, Miggliaccio F, Sacerdote F (1993) Spherical harmonic analysis of satellite gradiometry. Publ Geodesy, New Series, 39. Netherlands Geodetic Commission, Delft Rummel R, van Gelderen, Koop R, Schrama E, Sanso F, Brovelli M, Miggliaccio F, Sacerdote F (1993) Spherical harmonic analysis of satellite gradiometry. Publ Geodesy, New Series, 39. Netherlands Geodetic Commission, Delft
Zurück zum Zitat Svensson SL (1983) Pseudodifferential operators – a new approach to the boundary value problems of physical geodesy. Manuscr Geod 8:1–40MathSciNetMATH Svensson SL (1983) Pseudodifferential operators – a new approach to the boundary value problems of physical geodesy. Manuscr Geod 8:1–40MathSciNetMATH
Zurück zum Zitat van Huffel S, Vanderwalle J (1991) The total least squares problem: computational aspects and analysis. SIAM PhiladelphiaCrossRef van Huffel S, Vanderwalle J (1991) The total least squares problem: computational aspects and analysis. SIAM PhiladelphiaCrossRef
Zurück zum Zitat Xu PL (1992) Determination of surface gravity anomalies using gradiometric observables. Goephys J Int 110:321–332CrossRef Xu PL (1992) Determination of surface gravity anomalies using gradiometric observables. Goephys J Int 110:321–332CrossRef
Zurück zum Zitat Xu PL, Rummel R (1992) A generalized regularization method with application in determination of potential fields. In: Holota P, Vermeer M (eds) Proceedings of 1st continental workshop on the geoid in Europe, Prague, pp 444–457 Xu PL, Rummel R (1992) A generalized regularization method with application in determination of potential fields. In: Holota P, Vermeer M (eds) Proceedings of 1st continental workshop on the geoid in Europe, Prague, pp 444–457
Zurück zum Zitat Xu PL, Rummel R (1994) A generalized ridge regression method with application in determination of potential fields. Manuscr Geod 20:8–20 Xu PL, Rummel R (1994) A generalized ridge regression method with application in determination of potential fields. Manuscr Geod 20:8–20
Zurück zum Zitat Xu PL, Fukuda Y, Liu YM (2006) Multiple parameter regularization: numerical solutions and applications to the determination of geopotential from precise satellite orbits. J Geod 80:17–27CrossRef Xu PL, Fukuda Y, Liu YM (2006) Multiple parameter regularization: numerical solutions and applications to the determination of geopotential from precise satellite orbits. J Geod 80:17–27CrossRef
Metadaten
Titel
Multiparameter Regularization in Downward Continuation of Satellite Data
verfasst von
Shuai Lu
Sergei V. Pereverzev
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-54551-1_27