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Michael Grabe
A new Formalism for the Estimation of Measurement Uncertainties – Least Squares Adjustment
In two preceding papers, we have discussed an error model being alternative to that of the ISO-Guide. In the current paper, we transfer this model to the method of least squares. We show that the minimized sum of squared residuals loses its conventionally assumed statistical properties, the Gauß-Markoff theorem breaks down and, in consequence thereof, the method of least squares is no longer in a position to provide so-called “optimal estimators”.
The paper presents an formalism which reliably localizes the true values of the measurands. The couplings of the adjustment’s estimators are due to random as well as to systematic errors. Consequently, a new class of geometric solids stemming from systematic errors has to be put alongside the conceptually known confidence ellipsoids expressing the influence of random errors. The author terms the new bodies security polytopes.
tm – Technisches Messen, Oldenbourg Wissenschaftsverlag
Print ISSN: 0171-8096
Volume: 72, 09/2005
Pages: 531 - 540