The Algorithm for Determining the Coordinates of a Point in Three-Dimensional Space by Using the Auxiliary Point

Open access


During the process of satellite navigation, and also in the many tasks of classical positioning, we need to calculate the corrections to the initial (or approximate) location of the point using precise measurement of distances to the permanent points of reference (reference points). In this paper the authors have provided a way of developing Hausbrandt's equations, on the basis of which the exact coordinates of the point in two-dimensional space can be determined by using the computed correction to the coordinates of the auxiliary point. The authors developed generalised equations for threedimensional space introducing additional fixed point and have presented proof of derived formulas.

Banachiewicz T. Rachunek krakowianowy, PWN, Warszawa. 1959.

Ciecko A., Oszczak B., Oszczak S.. Drive-by DTM: GPS and GSM Power Cost-Effective Terrain Modeling. Vol. 17., GPS World, 2006.

Felski A., Urbański J. Satelitarne systemy nawigacji i bezpieczeństwa żeglugi, AMW, Gdynia 1997.

Gleason, Scott and Demoz Gebre-Egziabher. GNSS Applications and Methods. Boston. Artitech House, 2009.

Groves P.D. Principles of GNSS, inertial, and multi-sensor integrated navigation systems. Second Edition, Artech House, 2013.

Hausbrandt S. Rachunek wyrównawczy i obliczenia geodezyjne, Tom I. Państwowe Przedsiębiorstwo Wydawnictw Kartograficznych, Warszawa, 1970.

Hofmann-'Wellenhof B., Lichtenegger H., Wasle E. GNSS Global Navigation Satellite Systems, GPS, Glonass, Galileo&more, SpringerWienNewYork, 2008.

Hoffmann-Wellenhof B., Lichtenegger H., Collins J. Global Positioning System. Theory and Practise. SpringerWienNewYork, 2001.

B. P. Lukas. Robust Indoor Positioning through Adaptive Collaborative Labeling of Location Fingerprints. ETH, Zurich, 2011.

NMEA 0183. National Marine Electronics Association. Standard for Interfacing Marine Electronics Devices, 2002.

Oszczak B. New algorithm for GNSS positioning Using System of Linear Equations, ION GNSS+ 2013 CD-ROM Proceedings, November, 2013.

Oszczak B.. Methods of Point Indicators, manuscript, unpublished, Olsztyn, 2011.

Rueger J.M. Electronic Distance Measurement, Springer-Verlag, Berlin, 1996.

Specht C. System GPS, Wydawnictwo Bernardinum, Pelplin, 2007.

Susi M., Borio D., Lachapelle G. Accelerometer signal features and classification algorithms for positioning applications. Proceedings of the 2011 Int. Technical Meeting of the Institute of Navigation. Web, 2011.

J.B. Tsui. Basic equations for finding user position. Fundamentals of Global positioning system receivers. A software approach. Ed. John Wiley & Sons, 2000, pp. 10-11.

Artificial Satellites

The Journal of Space Research Centre of Polish Academy of Sciences

Journal Information

CiteScore 2017: 0.71

SCImago Journal Rank (SJR) 2017: 0.302
Source Normalized Impact per Paper (SNIP) 2017: 0.703


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 103 103 17
PDF Downloads 14 14 2