Investigating support by minimal detectable displacement in confidence region determination and significance test of displacements

Abstract

AbstractThe Minimal Detectable Displacement (MDD) is an important measure of monitoring networks sensitivity to displacements. In addition to the accuracy criteria, it is used as a detectability criterion in the optimal design of such networks. The paper examines whether the MDD provides grounds for verifying the correctness of the confidence, and the significance thresholds applied in the analyses of the determined displacements. According to our knowledge, the task so formulated has not yet been the subject of research presented in the literature in the field of geodetic determination of displacements. Hence, the approach presented here can be regarded as a new proposal extending the application area of the MDD. The investigations are focused on a probabilistic aspect of combining confidence and detectability as well as significance and detectability by the superimposition of the corresponding ellipsoids and their joint analysis. An initial research result is the diagrams showing a significance index and a non-centrality parameter as functions of the rank of the covariance matrix for displacements and also of system redundancy for specified values of Type I and Type II error probabilities. The diagrams, together with the theoretical basis created within the research, made it possible to analyse and evaluate the support by Minimal Detectable Displacement in confidence region determination and significance test of displacements. Based on the analysis of MDD support, two options of modifying the confidence and significance thresholds related to single point displacements are proposed for practical use.