Multi-epoch deformation analysis with geodetic datum invariance

[EN] Multiple epochs of geodetic deformation observations in 1D, 2D or 3D with their covariance matrices can be adjusted using the least-squares method and tested for deformation hypotheses, using the author’s hypothesis constrained multi-epoch analysis method. The method estimates deformations of a subfield relative to points in one or more other subfields. Therefore, the method is invariant for the choice of geodetic datum and does not require stable points. Here it is shown how the geodetic datum is defined at two levels. At the first level position, orientation, size and form of the point field are fixed to enable the use of coordinates (or heights). At the second level the position, orientation, size and form within any epoch interval are fixed, if they cannot be fixed from the observations in the adjustment model. This enables the comparison of epochs that have no predefined points that are stable in the epoch intervals. The stochastic test of the comparison is invariant for the choice of geodetic datum at these two levels. A procedure is described how to find the best deformation hypothesis, taking account of all available statistical information. It is shown that the proposed method is a powerful tool to find the best deformation hypothesis based on geodetic observations and their full stochastic information. It is thus usable for a broad scope of applications of geodetic deformation analysis.