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    Direct polynomial approach to nonlinear distance (ranging) problems

    Access Status
    Fulltext not available
    Authors
    Awange, Joseph
    Grafarend, E.
    Fukuda, Y.
    Takemoto, S.
    Date
    2003
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Awange, Joseph and Grafarend, Erik and Fukuda, Yoichi and Takemoto, Shuzo. 2003. Direct polynomial approach to nonlinear distance (ranging) problems. Earth, Planets and Space 55: pp. 231-241.
    Source Title
    Earth, Planets and Space
    Additional URLs
    http://www.terrapub.co.jp/journals/EPS/pdf/2003/5505/55050231.pdf
    ISSN
    13438832
    Faculty
    Department of Spatial Sciences
    Faculty of Science and Engineering
    WA School of Mines
    URI
    http://hdl.handle.net/20.500.11937/40047
    Collection
    • Curtin Research Publications
    Abstract

    In GPS atmospheric sounding, geodetic positioning, robotics and photogrammetric (perspective center and intersection) problems, distances (ranges) as observables play a key role in determining the unknown parameters. The measured distances (ranges) are however normally related to the desired parameters via nonlinear equations or nonlinear system of equations that require explicit or exact solutions. Procedures for solving such equations are either normally iterative, and thus require linearization or the existing analytical procedures require laborious forward and backward substitutions. We present in the present contribution direct procedures for solving distance nonlinear system of equations without linearization, iteration, forward and backward substitution. In particular, we exploit the advantage of faster computers with large storage capacities and the computer algebraic softwares of Mathematica, Maple and Matlab to test polynomial based approaches. These polynomial (algebraic based) approaches turn out to be the key to solving distance nonlinear system of equations. The algebraic techniques discussed here does not however solve all general types of nonlinear equations but only those nonlinear system of equations that can be converted into algebraic (polynomial) form.

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