| Summary: | Within deformation monitoring there are often determined horizontal displacements of points situated on the surveyed object. These movements between two epochs expressed by ()1/22ÂY2ÂXiÂp+=ipÂas stochastic quantities can be tested using a conveniently formulated forrmulated hypothesis Ho about significancy behaviour of .In the actual case Ho, expressed the assumption, the time different two positions of a certain point will lie in the area bordered by a time related confidence ellipse. Also, if the displacement vector estimate Âwill be found inside the ellipse, the corresponding point Pipi can be treated with risk as a statistically significant unmoved point, i.e. as stabil point:; if will exceed the ellipse boundary, the test interpretation is opposite. ¿ipÂFor a such decide it can be used various numerical tests from the test group of the linear hypothesis of parameters in linear models of estimation theory as e.g. tests of congruency and tests for the detection of outliers. Besides them, there are applicable graphical tests too, before all the htime relative confidence ellipsesh. Their mathematical background is derived from the tests of congruency. A time related confidence ellipse defines a 2D random space, that with probability (confidence ) ¿−1 covers the coordinate estimate vector  of the unknown displacement vector (connecting the physical positions of the point Pipi ) between epochs t and tL.In case of various significance level (confidence level 1-¿¿) one can obtain for the same ellipses with different sizes. Using this testing method it is therefore necessary to introduce for the results or the level of the confidence as well..
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