Computing Helmert transformations

Alistair Watson

    Research output: Contribution to journalArticlepeer-review

    84 Citations (Scopus)


    The Helmert transformation is used in geodesy. It transforms a set of points into another by rotation, scaling and translation. When both sets of points are given, then least squares can be used to solve the inverse problem of determining the parameters. In particular, the parameters of the so-called seven-parameter transformation can be obtained by standard methods. In this note, it is shown how a Gauss–Newton method in the rotation parameters alone can easily be implemented to determine the parameters of the nine-parameter transformation (when different scale factors for the variables are needed).
    Original languageEnglish
    Pages (from-to)387-394
    Number of pages8
    JournalJournal of Computational and Applied Mathematics
    Issue number2
    Publication statusPublished - 2006


    • Helmert transformation
    • Least squares
    • Gauss-Newton method


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