{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T06:49:09Z","timestamp":1775544549583,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2014,6,16]],"date-time":"2014-06-16T00:00:00Z","timestamp":1402876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/ijgi3020817","type":"journal-article","created":{"date-parts":[[2014,6,16]],"date-time":"2014-06-16T11:52:47Z","timestamp":1402919567000},"page":"817-852","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The Sequential Generation of Gaussian Random Fields for Applications in the Geospatial Sciences"],"prefix":"10.3390","volume":"3","author":[{"given":"John","family":"Dolloff","sequence":"first","affiliation":[{"name":"Sensor Geopositioning Center, National Geospatial-Intelligence Agency (contractors), 7500 GEOINT Dr, Springfield, VA 22150, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Doucette","sequence":"additional","affiliation":[{"name":"Sensor Geopositioning Center, National Geospatial-Intelligence Agency (contractors), 7500 GEOINT Dr, Springfield, VA 22150, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chiles, J., and Delfiner, P. (1999). Geostatistics: Modeling Spatial Uncertainty, Wiley.","DOI":"10.1002\/9780470316993"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Christakos, G. (2005). Random Field Models in Earth Sciences, Dover.","DOI":"10.1093\/oso\/9780195174991.003.0042"},{"key":"ref_3","unstructured":"Cressie, N., and Wikle, C.K. (2011). Statistics for Spatio-Temporal Data, Wiley."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation, Oxford University Press.","DOI":"10.1093\/oso\/9780195115383.001.0001"},{"key":"ref_5","unstructured":"Schabenberger, O., and Gotway, C.A. (2005). Statistical Methods for Spatial Data Analysis, Chapman & Hall\/CRC. [1st ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dolloff, J. (2013). The full multi-state vector error covariance matrix: Why needed and its practical representation. Proc. SPIE.","DOI":"10.1117\/12.2015121"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Dolloff, J., Lofy, B., Sussman, A., and Taylor, C. (2006). Strictly positive definite correlation functions. Proc. SPIE, 6235.","DOI":"10.1117\/12.663967"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Doucette, P., Dolloff, J., Zuzelski, R., Lenihan, M., and Mosko, D. (2013). Evaluating conflation methods using uncertainty modeling. Proc. SPIE.","DOI":"10.1117\/12.2015321"},{"key":"ref_9","unstructured":"Doucette, P., Dolloff, J., and Spizler, A. (2014, January 8\u201311). Experiments with Fast Sequential Simulation for Assessment of Geospatial Algorithms. Proceedings of 11th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, East Lansing, MI, USA. in press."},{"key":"ref_10","unstructured":"Pebesma, E.J. Package \u201cGstat\u201d (Version 1.0-19). Available online:http:\/\/cran.r-project.org\/web\/packages\/gstat\/gstat.pdf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/j.cageo.2004.03.012","article-title":"Multivariable geostatistics in S: The gstat package","volume":"30","author":"Pebesma","year":"2004","journal-title":"Comput. Geosci."},{"key":"ref_12","unstructured":"Hansen, T.M. MGstat (Version 0.99);. Available online:http:\/\/mgstat.sourceforge.net\/mGstat.pdf."},{"key":"ref_13","unstructured":"Deutsch, C., and Journel, A. (1992). GSLIB: Geostatistical Software Library and User\u2019s Guide, Oxford University Press."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1016\/0098-3004(94)90069-8","article-title":"Improving variogram reproduction on dense simulation grids","volume":"20","author":"Tran","year":"1994","journal-title":"Comput. Geosci."},{"key":"ref_15","unstructured":"Bar-Shalom, Y., and Fortmann, T. (1988). Tracking and Data Association, Academic Press."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/3\/2\/817\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:12:31Z","timestamp":1760217151000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/3\/2\/817"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,16]]},"references-count":15,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,6]]}},"alternative-id":["ijgi3020817"],"URL":"https:\/\/doi.org\/10.3390\/ijgi3020817","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,16]]}}}