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Mathematical Frontier Research as Conceived in Space-Geodesy

Research Project

Project/Area Number 16540386
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Solid earth and planetary physics
Research InstitutionKyoto University

Principal Investigator

XU Pl  Kyoto Univ Disaster Prevention Res, Inst Joshu, 防災研究所, 助手 (10293961)

Co-Investigator(Kenkyū-buntansha) FUKUDA Y  Kyoto Univ Faculty of Sciences, Professor, 理学研究科, 教授 (30133854)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsSpace Geodesy / Mixed Integer Linear Models / Gravity Field / Ocean Bottom Deformation / Optimization / Integer Statistics / Voronoi Cells / Variance Components / space geodesy / mixed integer linear model / variance components / inverse problems / probabilistic bound / ocean bottom deformation / outliers / sing-constrained robust LS / least median of squares / repeated median / subjective breakdown point
Research Abstract

The major new results of this research project can be briefly summarized as follows : (i) We systematically discuss the estimation and hypothesis testing problems in a mixed integer linear model, which directly motivated by space geodesy and is the basis for precise GPS positioning. We have first mathematically solved the problem of constructing Voronoi cells for an arbitrary positive definite matrix associated with mixed integer linear models by using interval mathematics to eliminate an infinite number of redundant linear constraints. We have also provided spherical and ellipsoidal enclosures to bound the Voronoi cell. By re-formulating the problem of bounding the Voronoi cell as a mathematical programming model, we have successfully found the tightest possible bounds of the Voronoi cell from inside and outside, respectively. As a result, we are able to find the tightest possible probabilistic bounds. The error bound has been shown to perform much better than the one proposed by Shan … More non (1959). In fact, the hypothesis testing problem is, for the first time, addressed in this research project and published in IEEE Transactions on Information Theory. By combining GPS with acoustic technology, we have first shown that ocean-bottom crustal deformation could be measured at the accuracy of sub-centimeters in all the three components. This is also the first theoretical demonstration that ocean bottom crustal deformation could be measured as easily and routinely as on land ; (ii) We have proposed a new robust estimation method, which is named as sign-constrained robust least squares. The method has been shown to be able to tolerate up to 50 percent of outliers, and even much more than 50 percent when used iteratively. As a by-product, we have proved that neither the plus sign nor the square is responsible for the non-robustness of least squares, as otherwise has been claimed in the literature on robust estimation. We have further proved that both Huber's M-estimation and weighted L1 method are not robust if measurements are of different accuracy ; (iii) We have first proposed the bias-corrected estimation technique to estimate variance components in linear inverse ill-posed models and applied it to satellite gravity fields, together with our multiple parameter regularization method. We have also proved that not all the variance covariance components are estimable. Less

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (19 results)

All 2007 2006 2005 2004 Other

All Journal Article (19 results)

  • [Journal Article] Estimability Analysis of Variance and Covariance Components2007

    • Author(s)
      Xu, P.L., Liu, Y.M., Shen, Y.Z., Fukuda, Y.
    • Journal Title

      Journal of Geodesy 80(in press)

      Pages: 10-10

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Estimability of variance and covariance components2007

    • Author(s)
      Xu P.L., Liu Y, Shen Y., Fukuda Y.
    • Journal Title

      Journal of Geodesy (accepted)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Reply to the comments by KR Koch and K Kusche2007

    • Author(s)
      Xu P.L., Shen Y., Fukuda Y., Liu Y
    • Journal Title

      Journal of Geodesy (accepted)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Multiple Parameter Regularization : Numerical Solutions and Applications to the Determination of Geopotential from Precise Satellite Orbits2006

    • Author(s)
      Xu, P.L., Fukuda, Y., Liu, Y.M.
    • Journal Title

      Journal of Geodesy 80

      Pages: 17-27

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Variance Component Estimation in Inverse Ill-posed Linear Models2006

    • Author(s)
      Xu, P.L., Shen, Y.Z., Fukuda, Y., Liu, Y.M.
    • Journal Title

      Journal of Geodesy 80

      Pages: 69-81

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Voronoi Cells, Probabilistic Bounds and Hypothesis Testings in Mixed Integer Linear Models2006

    • Author(s)
      Xu, P.L.
    • Journal Title

      IEEE Transactions on Information Theory 52

      Pages: 3122-3138

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Probabilistic Bounds and Hypothesis Testings in Mixed Integer Linear Models2006

    • Author(s)
      Xu, P.L., Voronoi Cells
    • Journal Title

      IEEE Transactions on Information Theory 52

      Pages: 3122-3138

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Voronoi cells, probabilistic bounds and hypothesis testing2006

    • Author(s)
      Xu P.L.
    • Journal Title

      IEEE Transactions on Information Theory (accepted)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Multiple parameter regularization : numerical solutions and applications to the determination of geopotential2006

    • Author(s)
      Xu P.L., Fukuda Y., Liu Y.M.
    • Journal Title

      Journal of Geodesy (accepted)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Variance component estimation in inverse ill-posed models2006

    • Author(s)
      Xu P.L., Shen Y., Fukuda Y., Liu Y.
    • Journal Title

      Journal of Geodesy (accepted)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Sign- constrained Robust Least Squares, Subjective Breakdown Point and the Effect of Weights of Observations on Robustness2005

    • Author(s)
      Xu P. L.
    • Journal Title

      Journal of Geodesy 79

      Pages: 146-159

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Precise, Three-dimensional Seafloor Geodetic Deformation Measurements using Difference Techniques2005

    • Author(s)
      Xu, P.L., Ando, M., Tadokoro, K.
    • Journal Title

      Earth Planets Space 57

      Pages: 795-808

    • NAID

      10017470009

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Sign-constrained Robust Least Squares Subjective Breakdown Point and the Effect of Weights of Observations on Robustness2005

    • Author(s)
      Xu, P.L.
    • Journal Title

      Journal of Geodesy 79

      Pages: 146-159

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Three-dimensional Seafloor Geodetic Deformation Measurements using Difference Techniques2005

    • Author(s)
      Xu, P.L., Ando, M., Tadokoro, K., Precise
    • Journal Title

      Earth Planets Space 57

      Pages: 795-808

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Precise, three-dimensional measurement of ocean bottom deformation2005

    • Author(s)
      Xu P.L., Ando M., Todokoro K.
    • Journal Title

      Earth Planets Space 57

      Pages: 795-808

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness2005

    • Author(s)
      Xu P.L.
    • Journal Title

      Journal of Geodesy (accepted)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Determination of Stress Tensors from Fault-slip Data2004

    • Author(s)
      Xu P. L.
    • Journal Title

      Geophysical Journal International 157

      Pages: 1316-1330

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Determination of Stress Tensors from Fault-slip Data2004

    • Author(s)
      Xu, P.L.
    • Journal Title

      Geophysical Journal International 157

      Pages: 1316-1330

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Estimability Analysis of Variance and Covariance Components

    • Author(s)
      Xu, P.L., Liu, Y.M., Shen, Y.Z., Fukuda, Y.
    • Journal Title

      Journal of Geodesy DOI 10.1007/s00190-006-0122-0 (in press)

      Pages: 10-10

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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