Precomputing Influences of Observation for a Network
Publication: Journal of Surveying Engineering
Volume 126, Issue 1
Abstract
Formulae for judging a priori the influences of individual observations on the unknown parameters and the mean network precision are presented. The influences of an observation on the parameters and the mean network precision are measured by the influence index and the percentage share, respectively. The larger the redundancy number, or the smaller the parameter number of the observation, the smaller the influence index will be and hence the less influence the observation will have on the estimate of an unknown parameter vector. A larger parameter number ensures a high percentage share in the mean network precision. The numerical example of the first-order leveling network of Taiwan seems to indicate that a better weighting scheme tends to produce more homogeneities among the individual parameter numbers and their corresponding influence numbers.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baarda, W. (1968). A testing procedure for use in geodetic network. Netherlands Geodetic Commission, Publications on Geodesy, New Series, 2(5), Rijkscommissie voor Geodesie, Delft, The Netherlands.
2.
Cook, R. D. (1977). “Detection of influential observation in linear regression.” Technometrics, 19(1), 15–18.
3.
Cook, R. D. (1979). “Influential observations in linear regression.” J. Am. Statistical Assoc., 74(365), 169–174.
4.
Draper, N. (1981). Applied regression analysis, 2nd ed., Wiley, New York, 169–176.
5.
Heller, E. (1955). Entwicklung und Genauigkeit des neuen Deutschen Haupthöhennetzes. Deutsche Geodätische Kommission, München, Germany, Reihe B, Heft Nr. 17, 11.
6.
Hsu, R. (1994). “Adjustments of the first order leveling network of Taiwan using IAUE.” Bull. of College of Engrg., National Taiwan University, Taipei, Taiwan, 61, 49–59.
7.
Hsu, R. (1996a). “Application of statistical techniques to the first order leveling network of Taiwan for detecting remained non-random effects.” Survey Rev., 33(259), 316–324.
8.
Hsu, R. (1996b). “Convergence of the variance of unit weight in a leveling network adjustment.” Survey Rev., 33(260), 404–410.
9.
Lucas, J. R. (1985). “A variance component estimation method for sparse matrix application.” NOAA Tech. Rep., NOS 111 NGS 33, Rockville, Md.
10.
Lucht, H. ( 1983). “Neighbourhood correlations among observations in levelling networks.” Precise Levelling, 38 Contributions to the Workshop on Precise Levelling, Ferd. Dümmlers Verlag, Hannover, Germany, 315–326.
11.
Theil, H. (1963). “On the use of incomplete prior information in regression analysis.” J. Am. Statistical Assoc., 58, 401–414.
12.
Uotila, U. (1978). “Sequential solution with observation equations.” Dept. of Geodetic Sci., Ohio State University, Columbus, Ohio.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 126 • Issue 1 • February 2000
Pages: 8 - 17
History
Received: Mar 15, 1999
Published online: Feb 1, 2000
Published in print: Feb 2000
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.