Improved Accuracy of Area Objects in a Geographic Information System Based on Helmert’s Variance Component Estimation Method
Publication: Journal of Surveying Engineering
Volume 135, Issue 1
Abstract
Helmert’s variance component estimation method based on a least-squares adjustment of condition equations is presented, in which the registered area and the coordinates of a cadastral parcel are assumed to be different and independent types of observations with errors in the cadastral parcel area adjustment. The Helmert method is employed for the estimation of variance components of these two types of observations, thus providing a determination of accurate weights between them. At the same time, inconsistencies between the registered and digitized areas of the parcels are adjusted through a least-squares adjustment. The mathematical models for adjusting the boundaries of the parcel areas are derived, incorporating both the area conditions and geometric conditions. An empirical test is conducted and the results are compared to those obtained from the conventional method, assuming that the digitized coordinates are treated as observations while the registered parcel areas are not. The analysis of the results demonstrates that the least-squares adjustment, when based on Helmert’s variance component estimates, refinds the weights of the observations more accurately, improves the accuracy of the adjusted coordinates in parcel digitization, and resolves the inconsistencies between the registered areas and digitized areas of the parcels more rigorously.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers thank the anonymous reviewers very much for the detailed and constructive comments, and clarifying this manuscript. The work described in this paper was substantially supported by the National Natural Science Foundation of China (Project No. NNSFC40771174), Program for New Century Excellent Talents in Universities (Project No. UNSPECIFIEDNCET-06-0381), Foundation of Shanghai Dawn Scholarship and Rising-star Program (Project Nos. UNSPECIFIED07SG24 and UNSPECIFIED08QH14022) and grants from the Doctoral Program of Higher Education of China (Project No. UNSPECIFIED20070247046).
References
Bolstad, P. V., Gessler, P., and Lillesand, T. M. (1990). “Positional uncertainty in manually digitized map data.” Int. J. Geogr. Inf. Syst., 4(4), 399–412.
Chen, Y. Q., Chrzanowski, A., and Kavouras, M. (1990). “Assessment of observations using minimum norm quadratic unbiased estimation.” CISM Journal ACSGC, 44(1), 39–46.
Chrisman, N. R., and Yandell, B. (1988). “Effects of point error on area calculations: A statistical model.” Surv. Mapp., 48(4), 241–246.
Förstner, W. (1979a). “Ein verfahren zur schätzung von varianz- und kovarianz-komponenten.” Allgemeine Vermessungs-Nachrichten, 86(11/12), 446–453 (in German).
Förstner, W. (1979b). “Konvergenzbeschleunigung bei der a posteriori varianzschätzung.” Zeitschrift für Vermessungswessen, 104(4), 149–156 (in German).
Grafarend, E. W., and Schaffrin, B. (1979). “Variance-covariance component estimation of Helmert type.” J. Surv. and Mapping Div., 39(3), 225–234.
Grodecki, J. (2001). “Generalized maximum-likelihood estimation of variance-covariance components with non-informative prior.” J. Geodesy, Berlin, 75(2), 157–163.
Hsu, R. (2001). “Helmert method as equivalent of iterated almost unbiased estimation.” J. Surv. Eng., 127(3), 79–89.
Keefer, B. J., Smith, J. L., and Gregoire, T. G. (1988). “Simulating manual digitizing error with statistical models.” Proc., GIS/LIS’88, American Society of Photogrammetry and Remote Sensing/American Congress on Surveying and Mapping, Falls Church, Va., 475–483.
Koch, K. R. (1986). “Maximum likelihood estimate of variance components.” Bull. Geod., 60(4), 329–338.
Kubik, K. (1970). “The estimation of weights of measured quantities within the method of least squares.” Bull. Geod., 44(1), 21–40.
Liu, D. J., Shi, W. Z., Tong, X. H., and Sun, H. C. (1999). Accuracy analysis and quality control of spatial data in GIS, Shanghai Science and Technology Documentation Press, Shanghai, China (in Chinese).
Lu, E. S., and Shih, T. Y. (2002). “Parcel boundary identification with computer—Assisted boundary overlay process for Taiwan.” Comput. Environ. Urban Syst., 26(5), 425–445.
Merrit, R., and Masters, E. (1999). “Digital cadastral upgrades—A progress report.” Proc., 1st Int. Symp. on Spatial Data Quality, W. Z. Shi, M. F. Goodchild, and F. Peter, eds., The Hong Kong Polytechnic University Press, Hong Kong, 180–188.
Mikhail, E. M., and Gracie, G. (1981). Analysis and adjustment of survey measurement, Van Nostrand Reinhold, New York.
Rao, C. R. (1971). “Estimation of variance and covariance components—MINQUE theory.” J. Multivariate Anal., 1(3), 257–275.
Rao, S. R. S. (1997). Variance components estimation: Mixed models, methodologies and applications, Chapman and Hall, London.
Schaffrin, B. (1983). Varianz-kovarianz-komponenten-Schätzung bei der ausgleichung heterogener wiederholungsmessungen, Deutsche Geodätische Kommission, Reihe C, Germany, Heft Nr 282 (in German).
Schaffrin, B., and Iz, H. B. (2001). “Integrating heterogeneous data sets with partial inconsistencies.” Proc., Gravity, geoid and geodynamics 2000, M. Sideris, ed., Springer, Berlin, 49–54.
Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance components, Wiley, New York.
Tamim, N., and Schaffrin, B. (1995). “A methodology to create a digital cadastral overlay through upgrading digitized cadastral data.” Surv. Land Inf. Sys., 55(1), 3–12.
Thapa, K., and Bossler, J. (1992). “Accuracy of spatial data used in geographic information systems.” Photogramm. Eng. Remote Sens., 58(6), 835–841.
Tong, X. H., and Liu, D. J. (2004). “Probability density function and estimation for error of digitized map coordinates in GIS.” J. Cent. S. Univ. Tech., 11(1), 69–74.
Tong, X. H., Liu, D. J., and Du, D. S. (2002). “Quality controls for development of a land and housing fundamental GIS database.” Proc., 5th Int. Symp. on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, G. Hunter and K. Lowell, eds., RMIT Univ., Melbourne, Australia, 282–288.
Tong, X. H., Shi, W. Z., and Liu, D. J. (2005). “A least-squares based method for adjusting the boundaries of area object.” Photogramm. Eng. Remote Sens., 71(2), 189–195.
Tong, X. H., and Xu, G. S. (2005). “Modeling cadastral spatial features based on geography markup language in GIS: A case study in Shanghai.” J. Environ. Inform., 6(2), 103–110.
Wolf, P. R., and Ghilani, C. D. (1997). Adjustment computations: Statistics and least-squares in surveying and GIS, Wiley, New York.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Aug 2, 2007
Accepted: Jul 23, 2008
Published online: Feb 1, 2009
Published in print: Feb 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.