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2015 Fiscal Year Annual Research Report

Combining different types of data for geophysical inverse problems: Theory and applications

Research Project

Project/Area Number 25400449
Research InstitutionKyoto University

Principal Investigator

徐 培亮  京都大学, 防災研究所, 助教 (10293961)

Project Period (FY) 2013-04-01 – 2016-03-31
Keywordserrors-in-variables / discrete tomography / variance components
Outline of Annual Research Achievements

This research project has been focused on inverse problems to estimate the unknown parameters in errors-in-variables (EIV), multiplicative noise and discrete tomography models by combining different types of data. We have achieved a number of new results and published 9 papers in international journals and one book chapter. The applicant has been invited to report the achieved results at several international conferences/symposia. More specifically, we have developed new least-squares (LS)-based estimators to reconstruct multiplicative error models and conducted quality evaluation of lattice
basis reduction for discrete tomography. We found that quality of lattice basis reduction can be directly affected by
the probability distribution of the reduced Gram-Schmidt coefficients. We have proposed bias-corrected weighted LS and
N-calibrated estimators to estimate the unknown parameters in an EIV model. The advantages of these new estimators are
that they can be as good as total LS, but require much less computation. By assuming that data are of different types
and of different accuracy, we have proved for the first time that the variance components in an EIV model cannot be estimable under certain conditions. If they are estimable, they can be unstable. Unless prior subjective information is assumed, we can hardly obtain the correct weighting factors for different types of data. Thus, we have also investigated how EIV can affect the parameter estimation and the determination of weighting factors for different types of data.

  • Research Products

    (9 results)

All 2016 2015

All Journal Article (3 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results,  Acknowledgement Compliant: 3 results) Presentation (5 results) (of which Int'l Joint Research: 4 results,  Invited: 3 results) Book (1 results)

  • [Journal Article] The effect of errors-in-variables on variance component estimation2016

    • Author(s)
      Xu PL
    • Journal Title

      Journal of Geodesy

      Volume: 90 Pages: 1-21

    • DOI

      10.1007/s00190-016-0902-0

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Alternative formulae for parameter estimation in partial errors-in-variables models2015

    • Author(s)
      Shi Y, Xu PL, Liu JN, Shi C
    • Journal Title

      Journal of Geodesy

      Volume: 89 Pages: 13-16

    • DOI

      10.1007/s00190-014-0756-2

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Comparing the estimates of the variance of unit weight in multiplicative error models2015

    • Author(s)
      Shi Y, Xu PL
    • Journal Title

      Acta Geod Geophys

      Volume: 50 Pages: 353-363

    • DOI

      10.1007/s40328-014-0096-y

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] A Review of Integer Estimation Methods for GPS2015

    • Author(s)
      Xu PL
    • Organizer
      Asian-Pacific GNSS
    • Place of Presentation
      Japan, Kyoto
    • Year and Date
      2015-11-16 – 2015-11-19
    • Int'l Joint Research
  • [Presentation] Mathematical foundations for the next generation of global gravity models from satellite gravity missions of CHAMP/GRACE types2015

    • Author(s)
      Xu PL
    • Organizer
      International Union of Geodesy and Geophysics
    • Place of Presentation
      Czech, Prague
    • Year and Date
      2015-06-21 – 2015-07-01
    • Int'l Joint Research
  • [Presentation] Quality evaluation of lattice basis reduction2015

    • Author(s)
      Xu PL
    • Organizer
      Chinese Satellite Navigation Conference
    • Place of Presentation
      China, Xi'an
    • Year and Date
      2015-05-13 – 2015-05-15
    • Invited
  • [Presentation] Zero initial partial derivatives of satellite orbits with respect to force parameters nullify the mathematical basis of the numerical integration method for the determination of standard gravity models from space geodetic measurements2015

    • Author(s)
      Xu PL
    • Organizer
      European Geoscience Union
    • Place of Presentation
      Austria, Vienna
    • Year and Date
      2015-04-12 – 2015-04-17
    • Int'l Joint Research / Invited
  • [Presentation] Least-squares-based adjustment of geodetic measurements with multiplicative random errors2015

    • Author(s)
      Xu PL
    • Organizer
      European Geoscience Union
    • Place of Presentation
      Austria, Vienna
    • Year and Date
      2015-04-12 – 2015-04-17
    • Int'l Joint Research / Invited
  • [Book] Mixed integer linear models2015

    • Author(s)
      Xu PL
    • Total Pages
      47
    • Publisher
      Springer

URL: 

Published: 2017-01-06  

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