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Coordinate transformation by the use of a matrix covariance estimated by least square collocation

Moisés Ferreira Costa, Marcelo Carvalho dos Santos, Luiz Danilo Damasceno Ferreira


Least Squares Collocation has been used in Geodesy mostly for the modelling
of the Earth’s gravity field. This investigation makes use of Least Squares
Collocation dealing with coordinate transformation between two realizations
of the South American Datum (SAD-69) in Brazil. The similarity
transformation in the tri-dimensional space, involving translations, rotations
and scale, is the model adopted for the parameter estimation. In the present
methodology, 200 points of the Brazilian Geodetic System have been tested.
The effect of correlation was established by means of a Gaussian covariance
function modelled from the data. The assessment of the results is carried out
by comparison of differences between coordinates estimated using Least
Squares Adjustment and Least Squares Collocation and reference values, i.e.,
known values. This involved all 200 points, used individually in each test. At
each test, one of the 200 points is removed and used as a test point. The tests
show how much results traditionally supplied by Least Squares Adjustment
can be improved by using a covariance function appropriate to correlated


Least Squares Collocation; Coordinate Transformation; Correlation; Colocação por Mínimos Quadrados; Transformação de Coordenadas; Correlação