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    Resultant optimization of the three-dimensional intersection problem

    20302_downloaded_stream_290.pdf (287.3Kb)
    Access Status
    Open access
    Authors
    Awange, Joseph
    Fukuda, Y.
    Date
    2007
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Awange, Joseph and Fukuda, Yoichi. 2007. Resultant optimization of the three-dimensional intersection problem. Survey Review 39 (304): 100-108.
    Source Title
    Survey Review
    DOI
    10.1179/003962607X165050
    Faculty
    Division of Resources and Environment
    Department of Spatial Sciences
    Remarks

    Copyright 2007 Maney Publishing. All rights reserved

    URI
    http://hdl.handle.net/20.500.11937/45238
    Collection
    • Curtin Research Publications
    Abstract

    Resultant approach is here employed to optimize the dimensionless space angles to solve in a closed form the over-determined three-dimensional intersection problem. The advantages of the resultant optimization approach are the non-requirement of the approximate initial starting values, non iterative and does not rely on linearization during its operation, save for the nonlinear variance-covariance/error propagation to generate the weight matrix. Resultant method, a branch of abstract algebra, is employed to compute the combinatorial scatters, which are then optimized to offer a closed form solution. Using the test network Stuttgart Central as an example, it is demonstrated that the resultant optimization approach can be applied as an alternative approach to conventional methods such as least squares for point positioning within the over-determined intersection framework, especially when the approximate starting values for linearization and iterative approaches are not known as may happen in Photogrammetry, Machine Vision or in Robotics.

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