Data reconciliation and gross error diagnosis based on regression

In this article we show that the linear reconciliation problem can be represented by a standard multiple linear regression model. The appropriate criteria for redundancy, determinability and gross error detection are shown to follow in a straightforward manner from the standard theory of linear least squares. The regression approach suggests a natural measure of the redundancy of an observation. This approach yields also an explicit expression for the probability of detecting a gross error in an observation, which depends on its redundancy. The criterion for the detection of gross errors derived from the regression model is shown to yield the maximum probability of correct outlier identification. We consider two examples analyzed in the literature to demonstrate how our approach allows a complete understanding of the main data features.