This Stone method is a method for data reconciliation. It adjusts data in order to satisfy a set of linear constraints. The adjustments made to the data are as small as necessary to remove all discrepancies. In adjusting the initial data the method of Stone uses information on the relative reliabilities of the initial data, in particular a covariance matrix. Data that are considered most reliable are modified least and vice versa. The Stone method yields a set of fully reconciled data, with minimum variance.
The method of Stone translates the reconciliation problem into a mathematical optimisation problem. From a mathematical perspective, the method of Stone is a weighted quadratic optimisation problem under linear conditions. The formulation of this problem is relatively easy to understand.
The solution of the model includes the reconciled data as well as its covariance matrix. Analytical expressions can be derived for both results.
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