Optimization of observation plan based on the stochastic characteristics of the geodetic network

Wojciech Pachelski, Paweł Postek

Abstract


Optimal design of geodetic network is a basic subject of many engineering projects. An observation plan is a concluding part of the process. Any particular observation within the network has through adjustment a different contribution and impact on values and accuracy characteristics of unknowns. The problem of optimal design can be solved by means of computer simulation. This paper presents a new method of simulation based on sequential estimation of individual observations in a step-by-step manner, by means of the so-called filtering equations. The algorithm aims at satisfying different criteria of accuracy according to various interpretations of the covariance matrix. Apart of them, the optimization criterion is also amount of effort, defined as the minimum number of observations required.

A numerical example of a 2-D network is illustrated to view the effectiveness of presented method. The results show decrease of the number of observations by 66% with respect to the not optimized observation plan, which still satisfy the assumed accuracy.


Keywords


optimization; observation plan; horizontal network; cost; accuracy; covariance matrix; sequential adjustment

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References


Adamczewski, Z. (2007). Rachunek Wyrównawczy w 15 wykładach, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa.

Baran, W. (1982). Some new procedures of the sequential adjustment. Int. Symp. of Geodetic Networks and Computations, Deutsche Geodatische Kommission, Munich, VIII:69-79.

Bernè, J. L. & Baselga, S. (2004). First-order design of geodetic networks using the simulated annealing method, Journal of Geodesy 78:47-54.

Caspary, W. F. (1987). Concepts of network and deformation analysis, Monograph 11, The University of New South Wales, Australia.

Chang, Y. M., Chen, C. H. & Chen, C. S. (1996). Optimal observation design of surveying network using artificial neural network. Geomat Res Aust 64:1-16.

Cross, P. A. (1985). Numerical Methods in Network Design, Springer – Verlag Berlin Heidelberg.

Grafarend, E. (1974). Optimization of geodetic network, Boll Geod. Sci. Aff. 33: 351-406.

Hausbrandt, S. (1971). Rachunek Wyrównawczy i Obliczenia Geodezyjne, Tom II, Państwowe Przedsiębiorstwo Wydawnictw Kartograficznych, Warszawa.

Lee, R. C. K. (1964). Optimal Estimation, Identification and Control, Research Monograph, M.I.T. Press, Cambridge.

Nickerson, B. G. (1979). Horizontal network design using interactive computer graphics, MScEng Thesis, University of New Brunswick, Canada.

Nowak, E. (1985). Interactive network design analysis based on successive modifications of covariance matrix. 7th International Symposium on Geodetic Computations IUGG, Zesz. Nauk. AGH Geodezja 90/1985, Kraków.

Pachelski, W. (1972). Teoria równań filtrujących i ich zastosowanie do opracowania obserwacji według metody najmniejszych kwadratów, Państwowe Wydawnictwo Naukowe, Warszawa.

Pachelski, W. (1981). Macierze kowariancji geodezyjnych obserwacji satelitarnych, Zakład Geodezji Planetarnej Centrum Badań Kosmicznych PAN, Warszawa.

Prószyński, W. (1980). Podstawy analiz dokładnościowych w geodezyjnych pomiarach realizacyjnych, Geodezja Inżynieryjna Tom II, Wydawnictwo PWK.

Prószyński, W. & Kwaśniak, M. (2006). Podstawy geodezyjnego wyznaczania przemieszczeń. Pojęcia i elementy metodyki, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa.

Quatrani, T. (2003). Introduction to the Unified Modeling Language, IBM Rational Software.




DOI: http://dx.doi.org/10.1515/rgg-2016-0018

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