Reliability Measures for Correlated Observations

Abstract

Following the pioneering work by W. Baarda, surveying engineers routinely inspect the Studentized residuals after an adjustment when high reliability is crucial. To detect outliers among uncorrelated observations, the relative magnitude between the cofactor of the residual and the corresponding (unadjusted) observation has to be checked. These ratios are commonly taken from a so-called “reliability matrix.” As other researchers have pointed out recently, the traditional approach breaks down in the case of correlated observations, and new measures of reliability have been proposed that, however, are not necessarily bounded. Therefore, we introduce a standardization procedure that guarantees our new reliability measures to fall between 0 and 1. We then show their behavior in a few simple examples, followed by a (simulated) global positioning system (GPS) application that allows these conclusions: (1) the “traditional” redundancy numbers give much too optimistic results for correlated observations; and (2) the ranking of observations according to previously recorded reliability measures may well be reversed after the standardization, making the “least-reliable” observations moderately reliable, and vice versa.