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    Ranging algebraically with more observations than unknowns

    Access Status
    Fulltext not available
    Authors
    Awange, Joseph
    Fukuda, Y.
    Takemoto, S.
    Ateya, I.
    Grafarend, E.
    Date
    2003
    Type
    Journal Article
    
    Metadata
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    Citation
    Awange, Joseph and Fukuda, Yoichi and Takemoto, Shuzo and Ateya, Ismail and Grafarend, Erik. 2003. Ranging algebraically with more observations than unknowns. Earth, Planets and Space 55 (7): pp. 387-394.
    Source Title
    Earth, Planets and Space
    Additional URLs
    http://www.terrapub.co.jp/journals/EPS/pdf/2003/5507/55070387.pdf
    ISSN
    13438832
    Faculty
    Department of Spatial Sciences
    Faculty of Science and Engineering
    WA School of Mines
    URI
    http://hdl.handle.net/20.500.11937/28433
    Collection
    • Curtin Research Publications
    Abstract

    In the recently developed Spatial Reference System that is designed to check and control the accuracy of the three-dimensional coordinate measuring machines and tooling equipment (Metronom US., Inc., Ann Arbor: http://www.metronomus.com), the coordinates of the edges of the instrument are computed from distances of the bars. The use of distances in industrial application is fast gaining momentum just as in Geodesy and in Geophysical applications and thus necessitating efficient algorithms to solve the nonlinear distance equations. Whereas the ranging problem with minimum known stations was considered in our previous contribution in the same Journal, the present contribution extends to the case where one is faced with many distance observations than unknowns (overdetermined case) as is usually the case in practise. Using the Gauss-Jacobi Combinatorial approach, we demonstrate how one can proceed to position without reverting to iterative and linearizing procedures such as Newton's or Least Squares approach.

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