Robust Testing Procedure for Detection of Multiple Blunders
Publication: Journal of Surveying Engineering
Volume 118, Issue 1
Abstract
Blunder detection is a topic of great interest to surveyors and mappers because undetected blunders significantly distort the solution. Therefore, a robust testing procedure has been developed for the detection and identification of multiple blunders in survey data. In the method, the theories of robust estimation and statistical hypothesis testing are successfully integrated to provide a reliable and unified testing process. The method can be applied to the case of multiple blunders and can greatly improve the detection and isolation of blunders as compared to the statistical testing of estimated residuals from a conventional least‐squares process. The conventional least‐squares procedure tends to smooth the blunder into good observations, whereas the proposed method does not. Two numerical examples are given to test and illustrate the performance of the proposed method for cases of single and multiple blunders.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Andrews, D. F. (1974). “A robust method for multiple linear regression.” Technometrics, 16(4), 523–531.
2.
Baarda, W. (1968). “A test procedure for use in geodetic networks.” New Series 2, Netherland Geodetic Commission, Delft, The Netherlands, 5.
3.
Biacs, Z. F. (1989). “Estimation and hypothesis testing for deformation analysis in special purpose networks.” UCSE Report No. 20032, The Univ. of Calgary, Dept. of Surveying Engrg., Calgary, Alberta, Canada.
4.
Caspary, W., and H. Borutta (1987). “Robust estimation in deformation models.” Survey Review, 29(233).
5.
Ebong, M. B. (1984). “The least sum adjustment of a geodetic levelling network.” Manuscripta Geodetica, 10.
6.
Fuchs, H. (1980). “Untersuchungen zur ausgleichung durch minimieren der absolut summe der verbesserungen,” thesis presented to Technical University Graz in Austria, in partial fulfillment of the requirements for the degree of Doctor of Philosophy (in German).
7.
Fuchs, H. (1983). “Contribution to the adjustment by minimizing the sum of absolute residuals, Manuscripta Geodaetica, Vol. 7.
8.
Hampel, F. R. (1968). “Contributions to the theory of robust estimation,” thesis presented to the University of California, at Berkeley, California, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
9.
Heck, B. (1980). Statistische ausreisserkriterien zur kontrolle geodaetischer beobachtungen. B‐10, VIII Int. Kurs fur Ingenieursvermessung, Zurich, Switzerland (in German).
10.
Huber, P. J. (1964). “Robust estimation of a location parameter.” Ann. Math. Statist., 36, 73–101.
11.
Huber, P. J. (1980). Robust statistics. John Wiley & Sons, New York.
12.
Koch, K. R. (1988). Parameter estimation and hypothesis testing in linear models. Springer‐Verlag, New York, N.Y.
13.
Kok, J. J. “On data snooping and multiple outlier testing,” NOAA Technical Report NOS NGS 30, National Ocean Service, National Geodetic Survey, US Department of Commerce, Rockville, MD.
14.
Kubik, K. K. (1983). “The Danish method: Experience and philosophy.” DGK, Reihe A 98, Munich, Germany.
15.
Lueuberger, D. G. (1989). Linear and Nonlinear Programming, Second Ed., Addison‐Wesley Publishing Co.
16.
Meissl, P. (1980). “Adjustment of levelling networks by minimizing the sum of absolute residuals.” 2nd Int. Symp. on Problems Related to the Redefinition of the North American Geodetic Network, Ottawa, Canada.
17.
Mikhail, E. M. (1976). Observations and least squares. Univ. Press of America, New York, N.Y.
18.
Pope, A. J. (1976). “The statistics of residuals and the detection of outliers.” NOAA Technical Report NOS 65, NGS 1, U.S. Dept. of Commerce, Rockville, Md.
19.
Somogyi, J., and Zavoti, J. (1989). “—norm estimation for similarity transformations.” —normás becslések hasonlósági transzformációkhoz) Geodézia és Kartográfia, 41(5), 329–334 (in Hungarian).
20.
Stefanovie, P. (1978). “Blunders and least squares.” ITC, 1.
21.
Tukey, J. W. (1960). “A survey of sampling from contaminated distributions.” Contributions of probability and statistics, I. Olkin, ed., Stanford Univ. Press, Stanford, Calif.
22.
Vanicek, P., and Krakiwsky, E. J. (1986). Geodesy: The concepts. North‐Holland, Amsterdam, The Netherlands.
23.
Zarembka, P., ed. (1974). Frontiers in econometrics. Academic Press, New York, N.Y.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 118 • Issue 1 • February 1992
Pages: 11 - 23
Copyright
Copyright © 1992 ASCE.
History
Published online: Feb 1, 1992
Published in print: Feb 1992
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.