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ISPRS Int. J. Geo-Inf. 2014, 3(2), 817-852; doi:10.3390/ijgi3020817
Article

The Sequential Generation of Gaussian Random Fields for Applications in the Geospatial Sciences

 and
*
Sensor Geopositioning Center, National Geospatial-Intelligence Agency (contractors), 7500 GEOINT Dr, Springfield, VA 22150, USA
“Approval number” assigned by authors’ organization: PA case #14-350
* Author to whom correspondence should be addressed.
Received: 8 February 2014 / Revised: 21 May 2014 / Accepted: 26 May 2014 / Published: 16 June 2014

Abstract

This paper presents practical methods for the sequential generation or simulation of a Gaussian two-dimensional random field. The specific realizations typically correspond to geospatial errors or perturbations over a horizontal plane or grid. The errors are either scalar, such as vertical errors, or multivariate, such as , , and  errors. These realizations enable simulation-based performance assessment and tuning of various geospatial applications. Both homogeneous and non-homogeneous random fields are addressed. The sequential generation is very fast and compared to methods based on Cholesky decomposition of an a priori covariance matrix and Sequential Gaussian Simulation. The multi-grid point covariance matrix is also developed for all the above random fields, essential for the optimal performance of many geospatial applications ingesting data with these types of errors.
Keywords: geospatial; random field; errors; sequential; simulation; covariance matrix; strictly positive definite correlation function geospatial; random field; errors; sequential; simulation; covariance matrix; strictly positive definite correlation function
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Dolloff, J.; Doucette, P. The Sequential Generation of Gaussian Random Fields for Applications in the Geospatial Sciences. ISPRS Int. J. Geo-Inf. 2014, 3, 817-852.

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