Recursive identification of gross errors in linear data reconciliation

In the reconciliation of measurements of flows and concentrations so that they conform to conservation laws and other constraints, any gross errors in the measurements must be identified in order that they can be either corrected or deleted. A new method is derived for the recursive prediction of the changes in the objective function, and of the statistical tests for the measurements, which would result from the deletion of suspect measurements. Inverses of large matrices are not required and the reconciliation can also be easily calculated for any set of deletions. It is shown that the decrease in the objective function caused by deletion of a single measurement equals the square of the corresponding maximum power measurement statistic, calculated prior to that deletion. An algorithm for the detection of suspect sets of gross errors, whose deletion leads to acceptable values of all statistical tests and process flow rates, is proposed and illustrated.