An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions but must be computed numerically by means of Monte Carlo. This paper provides the first results on the Monte Carlo-based critical value inserted into different scenarios of correlation between outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, over-identifications and statistical overlap associated with IDS in the presence of a single outlier. On the basis of such probability levels, we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for cases in which IDS is in play. The MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances in which the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection but the lower the rates of outlier identification. In such a case, the larger the Type I Error, the larger the ratio between the MIB and MDB. We also highlight that an outlier becomes identifiable when the contributions of the measures to the wrong exclusion rate decline simultaneously. In this case, we verify that the effect of the correlation between outlier statistics on the wrong exclusion rate becomes insignificant for a certain outlier magnitude, which increases the probability of identification.

One of the main challenges in the quality control of geodetic measurements is the reliable identification of multiple outliers. Within this context, the goal of this paper is to present a procedure designated here as Sequential Likelihood Ratio Tests for Multiple Outliers (SLRTMO). To verify its performance, a levelling network was simulated involving one, two and three (simultaneous) outliers. Also a GNSS network involving one and two (simultaneous) outliers was analysed. Results showed that SLRTMO is efficient for single and multiple outliers, simulated with magnitude greater than five standard deviations, with a mean success rate of 79.6% for these cases. Furthermore, the maximum number of outliers to be tested has to be defined according to the redundancy of the network so as to ensure the performance of SLRTMO.

An Attempt to Analyse Baarda’s Iterative Data Snooping Procedure based on Monte Carlo Simulation