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    Explicit solution of the overdetermined three-dimensionalresection problem

    Access Status
    Fulltext not available
    Authors
    Awange, Joseph
    Grafarend, E.
    Date
    2003
    Type
    Journal Article
    
    Metadata
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    Citation
    Awange, J. L. and Grafarend, E. W 2003. Explicit solution of the overdetermined three-dimensionalresection problem. Journal of Geodesy 76: pp. 605-616.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s00190-002-0287-0
    ISSN
    09497714
    Faculty
    Department of Spatial Sciences
    Faculty of Science and Engineering
    WA School of Mines
    Remarks

    The original publication is available at : www.springerlink.com

    URI
    http://hdl.handle.net/20.500.11937/12246
    Collection
    • Curtin Research Publications
    Abstract

    Several procedures for solving in a closed form the three-dimensional resection problem have already been presented. In the present contribution, the over determined three-dimensional resection problem is solved in a closed form in two steps. In step one a combinatorial minimal subset of observations is constructed which is rigorously converted into station coordinates by means of the Groebner basis algorithm or the multipolynomial resultant algorithm. The combinatorial solution points in a polyhedron are then reduced to their barycentric in step two by means of their weighted mean. Such a weighted mean of the polyhedron points in R3 is generated via the Error Propagation law/variance-covariance propagation. The Fast Nonlinear Adjustment Algorithm was proposed by C.F. Gauss, whose work was published posthumously, and C.G.I. Jacobi. The algorithm, here referred to as theGauss-Jacobi Combinatorial algorithm, solves the over determined three-dimensional resection problem in a closed form without reverting to iterative or linearization procedures. Compared to the actual values, the obtained results are more accurate than those obtained from the closed-form solution of a minimano of three known stations.

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