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Least squares collocation and statistical testing

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Abstract

The authors address the issue of statistical testing in least squares collocation (LSC) in two stages. The first stage concerns the extension and focusing of theLSC equations to the task of statistical testing. The second stage deals with statistical testing titself and is introduced in the second portion of the paper. The paper commences with an overview of the development ofLSC and its relationship to least squares adjustment (LSA). Expressions for the various random variables and their corresponding covariance matrices are derived and in some instances are gleaned from the literature for the following quantities: (i) corrections to the unknown parameters with a priori covariance information; (ii) estimated signal at both the observation and computation points; and (iii) the noise at the observation points. Some of the needed covariance matrices are either obscurely hidden in the literature or not available at all, but, nevertheless are given in the paper. Also given are expressions for the estimated variance factor which forms the basis of various statistical tests. The paper closes with an overview and enumeration of possible statistical tests for detection of outliers in the observations.

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Authors and Affiliations

  1. Department of Surveying Engineering, The University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Edward J. Krakiwsky & Zoltán F. Biacs

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  1. Edward J. Krakiwsky
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  2. Zoltán F. Biacs
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Krakiwsky, E.J., Biacs, Z.F. Least squares collocation and statistical testing. Bull. Geodesique 64, 73–87 (1990). https://doi.org/10.1007/BF02530616

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