Print Email Facebook Twitter Extendable linearised adjustment model for deformation analysis Title Extendable linearised adjustment model for deformation analysis Author Velsink, H. Faculty Civil Engineering and Geosciences Department Geoscience and Remote Sensing Date 2015-11-30 Abstract This paper gives a linearised adjustment model for the affine, similarity and congruence transformations in 3D that is easily extendable with other parameters to describe deformations. The model considers all coordinates stochastic. Full positive semi-definite covariance matrices and correlation between epochs can be handled. The determination of transformation parameters between two or more coordinate sets, determined by geodetic monitoring measurements, can be handled as a least squares adjustment problem. It can be solved without linearisation of the functional model, if it concerns an affine, similarity or congruence transformation in one-, two- or three-dimensional space. If the functional model describes more than such a transformation, it is hardly ever possible to find a direct solution for the transformation parameters. Linearisation of the functional model and applying least squares formulas is then an appropriate mode of working. The adjustment model is given as a model of observation equations with constraints on the parameters. The starting point is the affine transformation, whose parameters are constrained to get the parameters of the similarity or congruence transformation. In this way the use of Euler angles is avoided. Because the model is linearised, iteration is necessary to get the final solution. In each iteration step approximate coordinates are necessary that fulfil the constraints. For the affine transformation it is easy to get approximate coordinates. For the similarity and congruence transformation the approximate coordinates have to comply to constraints. To achieve this, use is made of the singular value decomposition of the rotation matrix. To show the effectiveness of the proposed adjustment model total station measurements in two epochs of monitored buildings are analysed. Coordinate sets with full, rank deficient covariance matrices are determined from the measurements and adjusted with the proposed model. Testing the adjustment for deformations results in detection of the simulated deformations. Subject deformation analysisobservation equations with constraintsrank deficient covariance matrixaffinesimilarity and congruence transformation To reference this document use: http://resolver.tudelft.nl/uuid:0d27b595-d6e9-4851-a583-32741acb780d Publisher Maney Online ISSN 0039-6265 Source Survey Review, 47 (345), 2015 Part of collection Institutional Repository Document type journal article Rights (c) 2015 Survey Review LtdMORE OpenChoice articles are open access and distributed under the terms of the Creative Commons Attribution License 3.0 Files PDF 326199.pdf 402.75 KB Close viewer /islandora/object/uuid:0d27b595-d6e9-4851-a583-32741acb780d/datastream/OBJ/view