Titlebook: Generalized Gaussian Error Calculus; Michael Grabe Book 2010 Springer-Verlag Berlin Heidelberg 2010 Gaussian error calculus.Generalized er

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宴会

Means and Means of MeansWe shall confine ourselves to unweighted and weighted arithmetic means as issued by the method of least squares.

Insubordinate

Functions of Erroneous VariablesTo assess the influence of measurement errors propagated via functions, we confine ourselves to linearized series expansions. From there, we expect the functions to behave sufficiently smooth throughout a neighborhood of the expansion point. Also, the measuring errors themselves should not exceed reasonable sizes.

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Method of Least SquaresThe method of least squares controls the flow of errors via the elements of the design matrix. Hence, assuming linear systems with differing design matrices aiming at the same set of unknowns, the adjustment’s uncertainties would differ even if the uncertainties of the input data were the same.

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PreliminariesThe fitting of straight lines is based on data pairs

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Straight Lines: Case (ii)Case (ii), Table 12.1 assumes correct abscissas and repeatedly measured ordinates. As now the empirical variances of the ordinates are directly accessible the scattering of the random errors may vary from ordinate to ordinate.