Modelling positional errors with isotropic random vector fields

João Casaca 1 and Ana Maria Fonseca 1
1 National Laboratory for Civil Engineering
Av. Brasil 101, 1700-066 Lisbon, Portugal
Tel.: + 351 21 844 3000; Fax: + 351 21 844 3026
jcasaca@lnec.pt; anafonseca@ lnec.pt

Abstract
Analysis of spatially distributed random multidimensional phenomena, such as positional errors, requires some generalization from the usual concepts of Geostatistics: random vector fields, associating random vectors to space positions, must be used instead of random scalar fields; covariance matrix functions, must replace scalar covariance functions; matrix variograms, must replace scalar variograms; etc. In the case of isotropic vector random fields, which are well suited to model space distribution of positional errors, multidimensional generalization is easier, allowing the construction of a scalar pseudo-variogram which may be used as an efficient tool to  partially estimate its autocovariance matrix functions. After a theoretical introduction, to present the concept of the scalar pseudo-variogram of an isotropic random vector field, the paper describes its application to the positional error vector of a geometrically corrected high resolution numeric image, acquired with the sensors of the Quickbird satellite.

Keywords: autocovariance function, isotropy, positional error vector, pseudo-variogram, vec- tor random field.

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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