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Numeric - symbolic solution of GPS phase ambiguity problem with Mathematica
Author

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Revision date

2018-01-08
Description

The GPS phase ambiguity is a global, quadratic mixed integer programming problem, which should be computed online. To solve the problem, probably the most popular procedure is the so called LAMBDA method (see Teunissen et al, 1997). In this article we suggest an alternative algorithm, which can also satisfy this requirement. The algorithm utilizes the Mathematica's numeric - symbolic computation ability, first transforms the mixed problem into a pure integer one. Then the bounds of region of the global solution can be computed on the basis of maximum - minimum eigenvalues of the matrix of the bilinear form with the continuous solution as center of this region. Employing McCormic Envelopes the quadratic problem is linearized. As illustration of the method a simple example as well as a real world five - satellite problem are given.
Subject

*Engineering > Signal Processing
Keywords

Mixed Integer Programming, GPS phase ambiquity, McCormic Envelopes
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GPS_Phase_Ambiguity_Problem_Palancz.nb (1.1 MB) - Mathematica Notebook