DOI: 10.5593/sgem2017/22/S09.022


R. Chrzan, B. Oszczak, J. Cwiklak, K. Olek
Wednesday 13 September 2017 by Libadmin2017

References: 17th International Multidisciplinary Scientific GeoConference SGEM 2017, www.sgem.org, SGEM2017 Conference Proceedings, ISBN 978-619-7408-02-7 / ISSN 1314-2704, 29 June - 5 July, 2017, Vol. 17, Issue 22, 177-186 pp, DOI: 10.5593/sgem2017/22/S09.022


The aim of this paper was to analyze Bancroft positioning algorithm with comparison to the use of the uncorrelated reference point indicators, and present the results of experimental studies. Comparison of the results was Carried out in MATLAB, the source code is derived and the results are presented. The most popular method for a position determination in GNSS is to use autonomous positioning. This is the basic algorithm used in GPS systems. However users can use other positioning algorithms, depending on what they want to achieve. One of this is Bancroft positioning algorithm.
The Bancroft algorithm allows Obtaining a direct solution of the receiver position and the clock offset for four satellites, without requesting any "a priori" knowledge for the receiver location. Moreover, with redundant observations in the system of equations, the
least squares method can be used for symmetric matrix achievement, that is, normal
equations, thus the position can be computed for more satellites in view of the sky. Thus
it means that without approximate location of the receiver we can calculate its position and clock error of that receiver. On the other hand, the algorithm with use of uncorrelated reference point indicators give the opportunity to receive position faster
and the approximate position of user is not needed. If so, who wins? This is a good
thing at a time when the user loses the connection with the satellites and needs a fast,
but not necessarily exact position. For comparison of These algorithms was created a
computer program in MATLAB software which randomly generated constellation of
five satellites for one million cases. The geometry of the satellites was regular and good for receiver point position calculations. Pseudoranges were calculated from generated
satellites coordinates. Then GPS errors and biases were added to them randomly from 0 to 20 meters. Satellite constellation was created in based on geographical coordinates of Deblin. Unknown receiver coordinates was computed by using two positioning algorithms, which were programmed in MATLAB. The results of individual algorithms were shown in the graphs, relative to the real position of Deblin. The next step was
comparing the results of these selected algorithms on the common figure.

Keywords: Bancroft, GPS, algorithm, reference point indicators.