Least squares adjustment and collocation |
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Authors: | K -R Koch |
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Institution: | 1. Institut für Theoretische Geod?sie der Universit?t, Bonn.
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Abstract: | Summary For the estimation of parameters in linear models best linear unbiased estimates are derived in case the parameters are random
variables. If their expected values are unknown, the well known formulas of least squares adjustment are obtained. If the
expected values of the parameters are known, least squares collocation, prediction and filtering are derived. Hence in case
of the determination of parameters, a least squares adjustment must precede a collocation because otherwise the collocation
gives biased estimates. Since the collocation can be shown to be equivalent to a special case of the least squares adjustment,
the variance of unit weight can be estimated for the collocation also. This estimate gives the scale factor for the covariance
matrices being used in the collocation. In addition, the methods of testing hypotheses and establishing confidence intervals
for the parameters of the least squares adjustment may be applied to the collocation. |
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