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

• Autor(a) principal: Costa, Moisés Ferreira
• Data de Publicação: 2008
• Outros Autores: Santos, Marcelo Carvalho dos, Ferreira, Luiz Danilo Damasceno
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Boletim de Ciências Geodésicas
• Texto Completo: https://revistas.ufpr.br/bcg/article/view/11274
• topic: Least Squares Collocation; Coordinate Transformation; Correlation; Colocação por Mínimos Quadrados; Transformação de Coordenadas; Correlação

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