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BANCROFT ALGORITHM COMPARISON TO THE REFERENCE POINT INDICATOR METHOD
Abstract
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.
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References3
Bancroft S.: An algebraic solution of the GPS equations. IEEE Transactions on Aerospace and Electronic Systems 21, 1985, pp. 56 59.
El-Rabbany A.: Introduction to GPS. The Global Positioning System. Artech House, 2006.
Oszczak B.: GNSS Positioning Algorithms Using Reference Point Indicators Method. ARTIFICAL SATELLITES, Vol. 49, No.1, 2014.
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