Multidimensional Statistical Tests for Imprecise Data

The total uncertainty budget of geodetic data usually comprises two main types of uncertainty: random variability which reflects uncontrollable effects during observation and data processing, and imprecision which is due to remaining systematic errors between data and model. Whereas random variability can be treated by means of stochastics, it is more adequate to model imprecision using Fuzzy-theory. Hence, it is necessary to extend the classical techniques of geodetic data analysis such as parameter estimation and statistical hypothesis testing in a suitable way in order to take imprecision into account.The study focuses on imprecise vector data and on the consistent extension of a multidimensional hypothesis test which is based on a quadratic form. Within the considered approach it is also possible to introduce fuzzy regions of acceptance and rejection in order to model linguistic uncertainties. For the final decision the crisp degree of rejectability for the null hypothesis is computed. Whereas in the one-dimensional case this is straightforward, in the multidimensional case the so-called α-cut optimization technique has to be applied. The global test in outlier detection and the congruence test of static deformation analysis are considered as application examples.