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VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy pp 273–279Cite as

Variance Component Estimation by the Method of Least-Squares

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Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 132))

Abstract

Motivated by the fact that the method of least-squares is one of the leading principles in parameter estimation, we introduce and develop the method of least-squares variance component estimation (LS-VCE). The results are presented both for the model of observation equations and for the model of condition equations. LS-VCE has many attractive features. It provides a unified least-squares framework for estimating the unknown parameters of both the functional and stochastic model. Also, our existing body of knowledge of least-squares theory is directly applicable to LS-VCE. LS-VCE has a similar insightful geometric interpretation as standard least-squares. Properties of the normal equations, estimability, orthogonal projectors, precision of estimators, nonlinearity, and prior information on VCE can be easily established. Also measures of inconsistency, such as the quadratic form of residuals and the w-test statistic can directly be given. This will lead us to apply hypotheses testing to the stochastic model.

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Author information

Authors and Affiliations

  1. Delft institute of Earth Observation and Space systems (DEOS), Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands

    P.J.G. Teunissen & A.R. Amiri-Simkooei

Authors
  1. P.J.G. Teunissen
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  2. A.R. Amiri-Simkooei
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Editor information

Editors and Affiliations

  1. Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan

    Peiliang Xu (Dr.) (Dr.)

  2. GNSS Engineering Res. Center, Wuhan University, 430079 Wuhan, China

    Jingnan Liu (Professor) (Professor)

  3. Department of Geodesy & Surveying, Aristotle University of Thessaloniki, University Box 503, 54124 Thessaloniki, Greece

    Athanasios Dermanis (Professor) (Professor)

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Teunissen, P., Amiri-Simkooei, A. (2008). Variance Component Estimation by the Method of Least-Squares. In: Xu, P., Liu, J., Dermanis, A. (eds) VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy. International Association of Geodesy Symposia, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74584-6_45

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