The combined geodetic network adjusted on the reference ellipsoid – a comparison of three functional models for GNSS observations

• Autorzy: Kadaj R.

Identyfikatory

DOI

10.1515/geocart-2016-0013

• Języki publikacji: EN

Abstrakty

EN

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

Słowa kluczowe

EN

combined geodetic network; hybrid geodetic network; GNSS vectors on ellipsoid; network adjustment on the ellipsoid

PL

sieć geodezyjna; elipsoida odniesienia; parametry geodezyjne

• Wydawca: Komitet Geodezji PAN
• Czasopismo: Geodesy and Cartography
• Rocznik: 2016
• Tom: Vol. 65, no. 2
• Strony: 229--257
• Opis fizyczny: Bibliogr. 25 poz., rys., tab., wykr.

Twórcy

autor

Kadaj R.

• Rzeszów University of Technology, Department of Geodesy and Geotechnics, 12 Al. Powstańców Warszawy, 35-959 Rzeszów, Poland

Bibliografia

• [1] Adam, J., Halmos, F. and Varga M. (1982). On the concepts of combination of Doppler Satellite and Terrestrial Geodetic Networks. Acta Geodaet., Geophys. et Montanist. Acad. Sci. Hung. Vol. 17(2).
• [2] Baeumker, M. (1984). Zur dreidimensionalen Ausgleichung von terrestrischen und Satellitenbeobachtungen. Wiss. Arbeiten der Fachrichtung Verm. d. Universität Hannover, 130.
• [3] Czarnecki, K. (1994). Geodezja współczesna w zarysie. Wydawnictwo Wiedza i Życie, ISBN 83-86805-67-6. Warszawa 1994.
• [4] Daxinger, W. and Stirling, R. (1995). Kombinierte Ausgleichung von terrestrischen und GPS – Messungen. Österreichische Zeitschrift für Vermessung und Geoinformation, 83, 48–55.
• [5]Deutsch R. (1965): Estimation Theory. Prentice-Hall, Inc. Englewood Cliffs, N.J.
• [6] Gajderowicz, I. (1979). Łączne wyrównanie sieci dopplerowskich i naziemnych. Z.N. ART w Olsztynie. Geodezja i Urządzenia Rolne, 8.
• [7] Gajderowicz, I. (1981). A theoretical basis for simultaneous adjustment of Doppler and terrestrial networks using a satellite reference ellipsoid. Artificial Satellites, 16(1).
• [8] Gajderowicz, I. (1997). Combination of classical observations with two-dimensional GPS vectors. Olsztyn University of Agriculture & Technology. Institute of Geodesy.
• [9] Gargula, T. (2010). GPS vector Network adjustment on the projection plane of local coordinate system. Polska Akademia Nauk, Oddział w Krakowie, Komisja Technicznej Infrastruktury Wsi. Nr 6/2010, 133–144.
• [10] Groten, E. (1977). Combination of geometrical satellite with terrestrial data. In (Eds. Halmos F. and Samogyi J.): Optimization of design and computation of control networks – International Symposium in Sopron, 4–10 July, 1977). Akademiai Kiado, Budapest, 95–104.
• [11] Hofmann-Wellenhof, B., Lichtenegger, H. and Wasle E. (2008). GNSS Global Navigation Satellite Systems. Springer-Verlag Wien.
• [12] Kadaj, R. (1997). Wyrównanie sieci wektorowej GPS i jej transformacja do układu odwzorowawczego elipsoidy Krasowskiego lub GRS-80 w programach systemu GEONET. Seminarium Komitetu Geodezji PAN: Zastosowanie technik kosmicznych w geodezji i geodynamice. Kraków 22–23 września 1997.
• [13] Kadaj, R. (1998). Models, methods and computation algorithms of kinematic network in geodetic deformations measurements. [In Polish: Modele, metody i algorytmy obliczeniowe sieci kinematycznych w geodezyjnych pomiarach przemieszczeń i odkształceń obiektów]. Wydawnictwa AR w Krakowie, 1988, ISBN 83-86524-37-5.
• [14] Kadaj R, (2008). New algorithms of GPS post-processing for multiple baseline models and analogies to classic geodetic networks. Geodesy and Cartography, Vol. 57, No 2, 61–79.
• [15] Krakiwsky, E.,J. and Thomson, D.B. (1974). Mathematical models for the combination of terrestrial and satellite Networks. The Canadian Surveyor, 28(5).
• [16] Mołodeńskij, M.S. (1954). Nowyj mietod reszenija geodeziczeskich zadacz (ros). Trudy CNIIGAiK, 103, Moskwa 1954.
• [17] Leick, A. (2004). GPS Satellite Surveying. John Wiley & Sonst, Inc. (Third Edition). ISBN 0-471-05930-7.
• [18] Strauss, R. and, Walter, H. (1993). Die Ausgleichung von GPS-Beobachtungen im System der Landeskoordinaten. AVN 6/1993, 207–212.
• [19] Strehle, J. (1996). Ermittlung von Landeskoordinaten aus GPS-Messungen. Mitteilungsblatt DVWBayern 41/1996, 623–645.
• [20] Szpunar, W. (1982). Fundamental of higher geodesy. [In Polish: Podstawy geodezji wyższej], PPWKWarszawa 1982.
• [21] Świątek, K. (1986). Wyrównanie łączne sieci naziemnej i doplerowskiej. Geodezja i Kartografia, XXXV, 3–4.
• [22] Świątek, K. (1988). Wyrównanie sieci geodezyjnych z wykorzystaniem pomiarów doplerowskich i analiza modeli transformacji. Acta Acad. Agricult. Ac. Technicae Olstenensis. Suplementum A. No. 17.
• [23] Thomson, D.B. (1976). Combination of Geodetic Networks. Technical Report No. 30, April 1976, Department of Surveying Engineering University of New Brunswick, Canada.
• [24] Warchałowski, E. (1952). Higher geodesy – mathematical part. [In Polish: Geodezja Wyższa – część matematyczna] PWN – Warszawa 1952.
• [25] Welsch, W.M. and Oswald, W. (1984). Kombinierte Ausgleichung von Doppler-Satellitennetzen und terrestrischen Netzen. In: Schödlbauer, A., Welsch, W. (Hrsg.) : Satelliten-Doppler-Messungen Beiträge zum Geodätischen Seminar 24/25. September 1984. Schriftenreihe des Wissenschaftlichen Studiengangs Vermessungswesen der Hochschule der Bundeswehr München, Heft 15, S. 155–191 ISSN: 0173-1009.