Technical Papers
Mar 9, 2016

Shift-Msplit* Estimation in Deformation Analyses

Publication: Journal of Surveying Engineering
Volume 142, Issue 4

Abstract

This paper presents an estimation method allowing direct and robust outlier assessment of parameter shifts in functional models of geodetic observations. The systems adopted in the discussion refer to functional models used in geodetic network deformation analysis. The proposed method is a robustness-oriented development of Shift-Msplit estimation. The problem of robustness is solved using an additional random variable with realizations that are outliers. The paper shows that the application of this variable also facilitates the selection of the appropriate number of competitive models in Msplit(q) estimation. Two numerical examples explain the manner of Shift-Msplit estimation performance and indicate the basic properties of the determined estimates.

Get full access to this article

View all available purchase options and get full access to this article.

References

Aydin, C., and Demirel, H. (2007). “Effect of estimated variance components for different gravity meters on analysis of gravity changes.” Festschrift zum 65. Geburstag von Prof. Dr. Ing. Carl, Erhard Gerstenecker, Technische Univ. Darmstadt, Darmstadt, Germany, 1–11.
Baarda, W. (1968). “A testing procedure for use in geodetic network.” Publications on Geodesy, Vol. 2, Netherlands Geodetic Commission, Amersfoort, Netherlands.
Camp, M., and Francis, O. (2007). “Is the instrumental drift of superconducting gravimeters a linear or exponential function of time?” J. Geod., 81(5), 337–344
Caspary, W. F. (1988). Concepts of network and deformation analysis, Univ. of New South Wales, Kensington, Australia.
Chen, Y. Q. (1983). “Analysis of deformation surveys—A generalized method.” Technical Rep. No. 94, Univ. of New Brunswick, Fredericton, Canada, 54–72.
Chen, Y. Q., Chrzanowski, A., and Secord, J. M. (1990). “A strategy for the analysis of the stability of reference points in deformation surveys.” CISM J. ACSGC, 44(2), 141–149.
Clerici, E., and Harris, M. W. (1983). “A review of the premium-protection method and its possible application in detection of displacements.” Bull. Géod., 57(1–4), 1–9.
Cross, P. A., and Price, D. R. (1985). “A strategy for the distinction between single and multiple gross errors in geodetic network.” Manuscr. Geod., 10, 172–178.
Doma, M. I. A. (2013). “A comparison of two different measures of precision into geodetic deformation monitoring networks.” Arab. J. Sci. Eng., 39(2),695–704
Duchnowski, R. (2008). “R-estimation and its application to the LS adjustment.” Boll. Geod. Sci. Affini., 67, 17–32.
Duchnowski, R. (2009). “Geodetic application of R-estimation—Levelling network examples.” Tech. Sci., 12(1), 135–144
Duchnowski, R. (2010). “Median-based estimates and their application in controlling reference mark stability.” J. Surv. Eng., 47–52.
Duchnowski, R. (2011). “Robustness of strategy for testing levelling mark stability based on rank tests.” Surv. Rev., 43(323), 687–699.
Duchnowski, R. (2013). “Hodges–Lehmann estimates in deformation analyses.” J. Geod., 87(10–12), 873–884.
Duchnowski, R., and Wiśniewski, Z. (2011). “Shift-Msplit estimation.” Geod. Cartog., 60(2), 79–97.
Duchnowski, R., and Wiśniewski, Z. (2012). “Estimation of the shift between parameters of functional models of geodetic observations by applying Msplit estimation.” J. Surv. Eng., 1–8.
Duchnowski, R., and Wiśniewski, Z. (2014). “Comparison of two unconventional methods of estimation applied to determine network point displacement.” Sur. Rev., 46(339), 401–405.
Erenoglu, R. C., and Hekimoglu, S. (2010). “Efficiency of robust methods and tests for outliers for geodetic adjustment models.” Acta. Geod. Geoph. Hung., 45(4), 426–439.
Ge, Y., Yuan, Y., and Jia, N. (2013). “More efficient methods among commonly used robust estimation methods for GPS coordinate transformation.” Sur. Rev., 45(330), 229–234.
Gökalp, E., and Taşçi, L. (2009). “Deformation monitoring by GPS at embankment dams and deformation analysis.” Surv. Rev., 41(311), 86–102.
Grodecki, J. (1999). “Generalized maximum-likelihood estimation of variance components with inverted gamma prior.” J. Geod., 73(7), 367–374.
Grodecki, J. (2001). “Generalized maximum-likelihood estimation of variance–covariance components with non-informative prior.” J. Geod., 75(2–3), 157–163.
Gui, Q., Gong, Y., Li, G., and Li, B. (2007). “A Bayesian approach to the detection of gross errors based on posterior probability.” J. Geod., 81(10), 651–659.
Gui, Q., and Zhang, J. (1998). “Robust biased estimation and its applications in geodetic adjustment.” J. Geod., 72(7), 430–435.
Guo, J., Ou, J., and Wang, H. (2010). “Robust estimation for correlated observation: Two local sensitivity-based downweighting strategies.” J. Geod., 84(4), 243–250.
Guo, J., Ou, J., and Yuan, Y. (2011). “Reliability analysis for a robust M-estimator.” J. Surv. Eng., 9–13.
Hampel, F. R. (1974). “The influence curve and its role in robust estimation.” J. Am. Stat. Assoc., 69(346), 383–397.
Hampel, F. R., Ronchetti, E. M., Rousseuw, P. J., and Stahel, W. A. (1986). Robust statistics: The approach based on influence functions, Wiley, New York.
Hekimoglu, S., Demirel, H., and Aydin, C. (2002). “Reliability of conventional deformation analysis methods for vertical networks.” Proc., XXII FIG General Assembly, International Federation of Surveyors, København, Denmark.
Hekimoglu, S., Erdogan, B., and Butterworth, S. (2010). “Increasing the efficacy of the conventional deformation analysis methods: Alternative strategy.” J. Surv. Eng., 53–62.
Hodges, J. L., and Lehmann, E. L. (1963). “Estimates of location based on rank tests.” Ann. Math. Stat., 34(2), 598–611.
Hoyland, A. (1965). “Robustness of the Hodges-Lehmann estimate for shift.” Ann. Math. Stat., 36(1), 174–197.
Huber, P. J. (1964). “Robust estimation of location parameter.” Ann. Math. Stat., 35(1), 73–101.
Huber, P. J. (1981). Robust statistics, Wiley, New York.
Janicka, J., and Rapinski, J. (2013). “Msplit transformation of coordinates.” Surv. Rev., 45(331), 269–274.
Janowski, A., and Rapinski, J. (2013). “M-Split estimation in laser scanning data modeling.” J. Indian Soc. Remote Sens., 41(1),15–19.
Kadaj, R. (1984). “Die Methode der besten Alternative: Ein Ausgleichungsprinzip für Beobachtungssysteme.” Z. Vermessungswesen, 113(4), 157–166 (in German).
Katambi, S. S., Guo, J., and Kong, X. (2002). “Applications of graph theory to gross error detection for GPS geodetic control networks.” Geo. Inf. Sci., 5(4), 26–31.
Koch, K. R. (1986). “Maximum likelihood estimate of variance components.” Bull. Géod., 60(4), 329–338.
Koch, K. R. (1987). “Bayesian inference for variance components.” Manuscr. Geod., 12, 309–313.
Koch, K. R. (1996). “Robuste Parameterschätzung.” Allg. Vermess. Nach., 103(11), 1–18.
Krarup, T., and Kubik, K. (1983). “The Danish method; experience and philosophy.” Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften, München, Reihe A, Heft Nr 7, 131–134.
Kubáčkowá, L., and Kubáček, L. (1991). “Optimum processing of measurements from a group of instruments affected by drift.” Manuscr. Geod., 16, 148–154
Nowel, K. (2015). “Investigating efficacy of robust M estimation of deformation from observation differences.” Surv. Rev., 47(346), 21–30.
Nowel, K., and Kamiński, W. (2014). “Robust estimation of deformation from observation differences for free control networks.” J. Geod., 88(8), 749–764.
Pope, J. (1976). “The statistics of residuals and detection of outliers.” NOAA Technical Rep. Nos. 66, NGS1, National Geodetic Survey, Rockville, MD.
Prószyński, W. (1994). “Criteria for internal reliability of linear least squares models.” Bull. Géod., 68(3), 162–167.
Prószyński, W. (1997). “Measuring the robustness potential of the least squares estimation: geodetic illustration.” J. Geod., 71(10), 652–659.
Prószyński, W. (2010). “Another approach to reliability measures for systems with correlated observations.” J. Geod., 84(9), 547–556.
Rousseeuw, P. J. (1984). “Least median of squares regression.” J. Am. Stat. Assoc., 79(388), 871–880.
Schaffrin, B. (1989). “An alternative approach to robust collocation.” Bull. Géod., 63(4), 395–404.
Schaffrin, B., and Wang, Z. W. (1994). “Multiplicative outlier search using homBLUP and an equivalence theorem.” Manuscr. Geod., 20(1), 21–26.
Serfling, R. (1980). Approximation theorems of mathematical statistics, Wiley, New York.
Setan, H., and Singh, R. (2001). “Deformation analysis of a geodetic monitoring network.” Geomatica, 55(3), 333–346.
Shaorong, Z. (1990). “On separability for deformations and gross errors.” Bull. Géod., 64(4), 383–396.
Teunissen, P. J. G. (1990). “Nonlinear least squares.” Manuscr. Geod., 15, 137–150.
Wiśniewski, Z. (1989). “Estimation of local variance coefficients in adjustment of geodetic networks.” Boll. Geod. Sci. Affini., 48(2), 165–180.
Wiśniewski, Z. (1996). “Estimation of the third and fourth order central moments of measurement errors from sums of powers of least squares adjustment residuals.” J. Geod., 70(5), 256–262.
Wiśniewski, Z. (2009). “Estimation of parameters in a split functional model of geodetic observations (Msplit estimation).” J. Geod., 83(2), 105–120.
Wiśniewski, Z. (2010). “Msplit(q) estimation: Estimation of parameters in a multi split functional model of geodetic observations.” J. Geod., 84(6), 355–372.
Wiśniewski, Z. (2014). “M-estimation with probabilistic models of geodetic observations.” J. Geod., 88(10), 941–957.
Yang, Y. (1991). “Robust Bayesian estimation.” Bull. Géod., 65(3), 145–150.
Yang, Y. (1994). “Robust estimation for dependent observation.” Manuscr. Geod., 19, 10–17.
Yang, Y. (1997). “Estimators of covariance matrix at robust estimation based on influence functions.” Z. Vermessungswesen, 122, 166–174.
Yang, Y., Song, L., and Xu, T. (2002). “Robust estimator for correlated observations based on bifactor equivalent weights.” J. Geod., 76(6), 353–358.
Youcai, H., and Mertikas, S. P. (1995). “On the design of robust regression estimators.” Manuscr. Geod., 20, 145–160.
Zhong, D. (1997). “Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights.” J. Geod., 71(9), 552–561.
Zienkiewicz, M. H. (2015). “Application of Msplit estimation to determine control points displacements in networks with unstable reference system.” Surv. Rev., 47(342), 174–180.
Zienkiewicz, M. H., and Bałuta, T. (2013). “Example of robust free adjustment of horizontal network covering detection of outlying points.” Tech. Sci., 16(3), 179–192.
Zienkiewicz, M. H., and Baryła, R. (2015). “Determination of vertical indicators of ground deformation in the Old and Main City of Gdansk area by applying unconventional method of robust estimation.” Acta Geodyn. Geomater., 12(3), 249–257.

Information & Authors

Information

Published In

Go to Journal of Surveying Engineering
Journal of Surveying Engineering
Volume 142Issue 4November 2016

History

Received: Apr 30, 2015
Accepted: Jan 13, 2016
Published online: Mar 9, 2016
Discussion open until: Aug 9, 2016
Published in print: Nov 1, 2016

Permissions

Request permissions for this article.

Authors

Affiliations

Z. Wiśniewski [email protected]
Professor, Institute of Geodesy, Univ. of Warmia and Mazury, 1 Oczapowskiego St., 10-957 Olsztyn, Poland. E-mail: [email protected]
M. H. Zienkiewicz [email protected]
Assistant, Chair of Geodesy and Oceanography, Gdynia Maritime Univ., 19 Sędzickiego St., 81-374 Gdynia, Poland (corresponding author). E-mail: [email protected]

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share