Technical Papers
Mar 6, 2019

Deformation Analysis of Geodetic Networks by Applying Msplit Estimation with Conditions Binding the Competitive Parameters

Publication: Journal of Surveying Engineering
Volume 145, Issue 2

Abstract

In this paper, the use of the parameter estimation method in a split functional model in the analysis of geodetic network deformation is presented. Special attention is drawn to the situation when competitive parameters fulfill certain independent conditions in the systems of observation equations. It is also proposed that the so-called reversal-point effect can be eliminated from the Msplit estimation using conditional equations binding the competitive parameters. It is shown that the introduced extension of the Msplit estimation method does not deprive the studied method of its qualities, including its robustness.

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References

Amiri-Simkooei, A. R., S. M. Alaei-Tabatabaei, F. Zangeneh-Nejad, and B. Voosoghi. 2017. “Stability analysis of deformation-monitoring network points using simultaneous observation adjustment of two epochs.” J. Surv. Eng. 143 (1): 04016020. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000195.
Bakuła, M., and R. Kaźmierczak. 2017. Technology of rapid and ultrarapid static GPS/GLONASS surveying in urban environments. In Proc., 2017 Baltic Geodetic Congress, 1–7. New York: IEEE.
Berber, M., and S. Hekimoglu. 2003. “What is the reliability of conventional outlier detection and robust estimation in trilateration networks?” Surv. Rev. 37 (290): 308–318. https://doi.org/10.1179/sre.2003.37.290.308.
Błaszczak-Bąk, W., A. Janowski, W. Kamiński, and J. Rapiński. 2015. “Application of the Msplit method for filtering airborne laser scanning data-sets to estimate digital terrain models.” Int. J. Remote Sens. 36 (9): 2421–2437. https://doi.org/10.1080/01431161.2015.1041617.
Caspary, W. F. 1988. Concepts of network and deformation analysis. Kensington, Australia: Univ. of New South Wales.
Caspary, W. F., and H. Borutta. 1987. “Robust estimation in deformation models.” Surv. Rev. 29 (223): 29–45. https://doi.org/10.1179/sre.1987.29.223.29.
Chang, X.-W., and Y. Guo. 2005. “Huber's M-estimation in relative GPS positioning: Computational aspects.” J. Geod. 79 (6–7): 351–362. https://doi.org/10.1007/s00190-005-0473-y.
Chen, Y. Q. 1983. “Analysis of deformation surveys: A generalized method.” Technical Rep. No. 94. Fredericton, Canada: Univ. of New Brunswick.
Duchnowski, R., and Z. Wiśniewski. 2011. “Shift-Msplit estimation.” Geod. Cartogr. 60 (2): 79–97. https://doi.org/10.2478/v10277-012-0009-6.
Duchnowski, R., and Z. Wiśniewski. 2012. “Estimation of the shift between parameters of functional models of geodetic observations by applying Msplit estimation.” J. Surv. Eng. 138 (1): 1–8. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000062.
Duchnowski, R., and Z. Wiśniewski. 2014. “Comparison of two unconventional methods of estimation applied to determine network point displacement.” Surv. Rev. 46 (339): 401–405. https://doi.org/10.1179/1752270614Y.0000000127.
Duchnowski, R., and Z. Wiśniewski. 2017a. “Accuracy of the Hodges-Lehmann estimates computed by applying Monte Carlo simulations.” Acta Geod. Geophys. 52 (4): 511–525. https://doi.org/10.1007/s40328-016-0186-0.
Duchnowski, R., and Z. Wiśniewski. 2017b. “MP and Msplit estimation. A wider range of robustness.” In Proc., Environmental Engineering 10th Int. Conf. Vilnius, Lithuania: Vilnius Gediminas Technical University.
Durdag, U. M., S. Hekimoglu, and B. Erdogan. 2015. “Outlier detection by using fault detection and isolation techniques in geodetic networks.” Sur. Rev. 48 (351): 400–408. https://doi.org/10.1179/1752270615Y.0000000038.
Filipiak-Kowszyk, D., and W. Kamiński. 2016. The use of free adjustment and Msplit estimation for determination of the vertical displacements in unstable reference system. In Proc., 2016 Baltic Geodetic Congress (BGC Geomatics), 257–262. Gdańsk, Poland: IEEE.
Ge, Y., Y. Yuan, and N. Jia. 2013. “More efficient methods among commonly used robust estimation methods for GPS coordinate transformation.” Surv. Rev. 45 (330): 229–234. https://doi.org/10.1179/1752270612Y.0000000028.
Gökalp, E., and L. Tasçi. 2009. “Deformation monitoring by GPS at embankment dams and deformation analysis.” Surv. Rev. 41 (311): 86–102. https://doi.org/10.1179/003962608X390021.
Gong, X., and Z. Li. 2017. “A robust weighted total least-squares solution with Lagrange multipliers.” Surv. Rev. 49 (354): 176–185. https://doi.org/10.1080/00396265.2016.1150088.
Hekimoglu, S., and K. R. Koch. 2000. “How can reliability of the test for outliers be measured?” Allgemeine Vermessungs-Nachr. 107 (7): 247–253.
Huber, P. J. 1964. “Robust estimation of location parameter.” Ann. Math. Stat. 43 (4): 1041–1067. https://doi.org/10.1214/aoms/1177703732.
Huber, P. J. 1981. Robust statistics. New York: Wiley.
Janicka, J., and J. Rapiński. 2013. “Msplit transformation of coordinates.” Surv. Rev. 45 (331): 269–274. https://doi.org/10.1179/003962613X13726661625708.
Janowski, A. 2018. “The circle object detection with the use of Msplit estimation.” E3S Web Conf. 26: 00014. https://doi.org/10.1051/e3sconf/20182600014.
Janowski, A., and J. Rapiński. 2013. “M-split estimation in laser scanning data modeling.” J. Indian Soc. Remote Sens. 41 (1): 15–19. https://doi.org/10.1007/s12524-012-0213-8.
Koch, K. R. 1999. Parameter estimation and hypothesis testing in linear models. 2nd ed. Berlin: Springer.
Koch, K. R. 2018. “Monte Carlo methods.” GEM Int. J. Geomath. 9 (1): 117–143. https://doi.org/10.1007/s13137-017-0101-z.
Nowel, K. 2015. “Robust M-estimation in analysis of control network deformations: Classical and new method.” J. Surv. Eng. 141 (4): 04015002. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000144.
Nowel, K., and W. Kamiński. 2014. “Robust estimation of deformation from observation differences for free control networks.” J. Geod. 88 (8): 749–764. https://doi.org/10.1007/s00190-014-0719-7.
Teunissen, P. J. G. 1995. “The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation.” J. Geod. 70 (1–2): 65–82. https://doi.org/10.1007/BF00863419.
Ulam, S., R. D. Richtmyer, and J. von Neumann. 1990. “Statistical methods in neutron diffusion.” In Analogies between analogies: The mathematical reports of S. M. Ulam and his Los Alamos collaborators, edited by Stanislaw Ulam, A. R. Bednarek, and F. Ulam, 17–36. Berkeley, CA: University of California Press.
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. https://doi.org/10.1007/s001900050016.
Wiśniewski, Z. 2009. “Estimation of parameters in a split functional model of geodetic observations (Msplit estimation).” J. Geod. 83 (2): 105–120. https://doi.org/10.1007/s00190-008-0241-x.
Wiśniewski, Z. 2010. “Msplit(q) estimation: Estimation of parameters in a multi split functional model of geodetic observations.” J. Geod. 84 (6): 355–372. https://doi.org/10.1007/s00190-010-0373-7.
Wiśniewski, Z. 2014. “M-estimation with probabilistic models of geodetic observations.” J. Geod. 88 (10): 941–957. https://doi.org/10.1007/s00190-014-0735-7.
Wiśniewski, Z. 2016. Adjustment calculus in geodesy. [In Polish.] Olsztyn, Poland: University of Warmia and Mazury Publishing.
Wiśniewski, Z. 2017. “MP estimation applied to platykurtic sets of geodetic observations.” Geod. Cartogr. 66 (1): 117–135. https://doi.org/10.1515/geocart-2017-0001.
Wiśniewski, Z., and M. H. Zienkiewicz. 2016. “Shift-Msplit* estimation in deformation analyses.” J. Surv. Eng. 142 (4): 04016015. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000183.
Xu, P. 1989. “On robust estimation with correlated observations.” Bull. Géodésique 63 (3): 237–252. https://doi.org/10.1007/BF02520474.
Yang, Y. 1994. “Robust estimation for dependent observations.” Manuscr. Geod. 19: 10–17.
Yang, Y., W. Gao, and X. Zhang. 2010. “Robust Kalman filtering with constraints: A case study for integrated navigation.” J. Geod. 84 (6): 373–381. https://doi.org/10.1007/s00190-010-0374-6.
Yu, H., Y. Shen, L. Yang, and Y. Nie. 2017. “Robust M-estimation using the equivalent weights constructed by removing the influence of an outlier on the residuals.” Surv. Rev. 51 (364): 1–10. https://doi.org/10.1080/00396265.2017.1360436.
Zienkiewicz, M. H. 2014. “Application of Msplit estimation to determine control points displacements in networks with unstable reference system.” Surv. Rev. 47 (342): 174–180. https://doi.org/10.1179/1752270614Y.0000000105.
Zienkiewicz, M. H. 2017. “Selected theoretical and empirical properties of Msplit estimation.” [In Polish.] Ph.D. thesis, University of Warmia and Mazury in Olsztyn, Faculty of Geodesy, Geospatial and Civil Engineering.
Zienkiewicz, M. H., K. Hejbudzka, and A. Dumalski. 2017. “Multi split functional model of geodetic observations in deformation analyses of the Olsztyn Castle.” Acta Geodyn. Geomater. 14 (2): 195–204. https://doi.org/10.13168/AGG.2017.0003.

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Go to Journal of Surveying Engineering
Journal of Surveying Engineering
Volume 145Issue 2May 2019

History

Received: Dec 14, 2017
Accepted: Jul 25, 2018
Published online: Mar 6, 2019
Published in print: May 1, 2019
Discussion open until: Aug 6, 2019

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Authors

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M. H. Zienkiewicz [email protected]
Assistant Professor, Chair of Geodesy and Oceanography, Gdynia Maritime Univ., 19 Sędzickiego St., Gdynia 81-374, Poland. Email: [email protected]

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