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

Research Project

Project/Area Number 25400449
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Solid earth and planetary physics
Research InstitutionKyoto University

Principal Investigator

Xu Peiliang  京都大学, 防災研究所, 助教 (10293961)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywordsparameter estimation / inverse problems / errors-in-variables / multiplicative noise / integer estimation / variance components / discrete tomography / satellite gravity / tomography / ill-posed
Outline of Final Research Achievements

This project focuses 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 achieve a number of new results and publish 9 papers in international journals. The applicant is invited to report the achieved results at several international conferences. We develop new LS-based estimators to reconstruct multiplicative error models and conduct quality evaluation of lattice basis reduction for discrete tomography, which can be directly affected by the probability distribution of the reduced Gram-Schmidt coefficients. We propose bias-corrected LS and N-calibrated estimators to estimate the EIV parameters, which are as good as total LS, but require much less computation. We prove that the variance components in an EIV model can be inestimable and unstable. We investigate how EIV can affect the parameter estimation and the weighting factors for different types of data.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 2013

All Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 8 results,  Acknowledgement Compliant: 5 results) Presentation (8 results) (of which Int'l Joint Research: 4 results,  Invited: 6 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 Issue: 8 Pages: 1-21

    • DOI

      10.1007/s00190-016-0902-0

    • Related Report
      2015 Annual Research Report
    • 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 Issue: 1 Pages: 13-16

    • DOI

      10.1007/s00190-014-0756-2

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • 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 Issue: 3 Pages: 353-363

    • DOI

      10.1007/s40328-014-0096-y

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Effects of errors-in-variables on weighted least squares estimation2014

    • Author(s)
      Peiliang Xu, Jingnan Liu, Wenxian Zeng, Yunzhong Shen
    • Journal Title

      Journal of Geodesy

      Volume: 88 Issue: 7 Pages: 705-716

    • DOI

      10.1007/s00190-014-0716-x

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Variance components in errors-in-variables models: estimability, stability and bias analysis2014

    • Author(s)
      Peiliang Xu, Jingnan Liu
    • Journal Title

      Journal of Geodesy

      Volume: 88 Issue: 8 Pages: 719-734

    • DOI

      10.1007/s00190-014-0717-9

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Adjustment of Measurements with Multiplicative Errors: Error Analysis, Estimates of the Variance of Unit Weight, and Effect on Volume Estimation from LiDAR-Type Digital Elevation Models2014

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

      Sensors

      Volume: 14 Issue: 1 Pages: 1249-1266

    • DOI

      10.3390/s140101249

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Experimental quality evaluation of lattice basis reduction methods for decorrelating low-dimensional integer least squares problems2013

    • Author(s)
      Xu PL
    • Journal Title

      EURASIP Journal on Advances in Signal Processing

      Volume: 2013 Issue: 1

    • DOI

      10.1186/1687-6180-2013-137

    • NAID

      120005347124

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Adjustment of geodetic measurements with mixed multiplicative and additive random errors2013

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

      Journal of Geodesy

      Volume: 87 Issue: 7 Pages: 629-643

    • DOI

      10.1007/s00190-013-0635-2

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [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
    • Related Report
      2015 Annual Research Report
    • 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
    • Related Report
      2015 Annual Research Report
    • 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
    • Related Report
      2015 Annual Research Report
    • 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
    • Related Report
      2015 Annual Research Report
    • 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
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Experimental quality evaluation of lattice basis reduction methods for discrete tomography2014

    • Author(s)
      Xu PL
    • Organizer
      American Mathematical Society Joint Meeting
    • Place of Presentation
      Baltimore, アメリカ
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Fast integer estimation methods for GPS ambiguity resolution: review and improvement2013

    • Author(s)
      Xu PL
    • Organizer
      European Geoscience Union General Assembly
    • Place of Presentation
      Vienna, Austria
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Variance components in errors-in-variables models: estimability, stability and bias analysis2013

    • Author(s)
      Xu PL
    • Organizer
      Hotine-Marussi International Symposium
    • Place of Presentation
      Rome, Italy
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] Mixed integer linear models2015

    • Author(s)
      Xu PL
    • Total Pages
      47
    • Publisher
      Springer
    • Related Report
      2015 Annual Research Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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