A Generalized Least Squares Solution Hybrid Measuring Systems

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Abstract
The Helmert method of subjecting a least squares adjustment to rigorously enforced boundary conditions is shown to be a special case of a generalized concept, in which these conditions are allowed to contribute to the solution in accordance with the weights of the observations that generate them. All parameters entering the solution are treated uniformly as weighted observations with a range in weight from 0 to ∞. The generalized approach not only provides the necessary algorithm for the statistically correct treatment of hybrid measuring systems, but, at the same time, provides the means of obtaining optimum design of experiments.

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