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The quality of geodetic deformation analysis depends essentially on the adequate consideration of all uncertainties in the measurement and analysis process. Although the non reducible systematics during the measurement process (observation imprecision) play a decisive role in practice, only random variations (stochastics) are taken into account. In this study, the uncertainty budget of the observations is assumed to comprise both, stochasticity and observation imprecision, what leads to intervals or fuzzy intervals for their description. For this reason, it is necessary to extend the classical techniques of statistical hypothesis testing in a suitable way to check the accordance of the collected data with the assumptions met in the model. This requires oneand multidimensional hypothesis tests with imprecise extensions for outlier detections, global tests and congruence tests in least-squares adjustment. It is shown, that the consideration of observation imprecision is an independent extension of the classical test approach. The new hypothesis tests are based on the intervals or fuzzy intervals of the observations. As the main benefit, numerical examples demonstrate an improved interpretation of the observations and model parameters, e.g., in epoch comparison.

Congruence tests and outlier detection in deformation analysis with respect to observation imprecision