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    Nonlinearity and Least-Squares.

    Access Status
    Fulltext not available
    Authors
    Teunissen, Peter
    Knickmeyer, E.H.
    Date
    1988
    Type
    Journal Article
    
    Metadata
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    Citation
    Teunissen, P.J.G. and Knickmeyer, E.H. 1988. Nonlinearity and least-squares. CISM Journal ACSGC. 42 (4): pp. 321-330.
    Faculty
    Department of Spatial Sciences
    URI
    http://hdl.handle.net/20.500.11937/47264
    Collection
    • Curtin Research Publications
    Abstract

    Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinearity on the first two moments of least squares estimators. Expressions for the moments of least squares estimators of parameters, residuals and functions derived from parameters, are given. The measures of nonlinearity are discussed both from a statistical and differential geometric point of view. Finally, our results are applied to the 2D symmetric Helmert transformation with a rotational invariant covariance structure.

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