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dc.contributor.authorPalancz, Bela
dc.contributor.authorAwange, Joseph
dc.contributor.authorGrafarend, Erik
dc.identifier.citationPalancz, Bela and Awange, Joseph and Grafarend, Erik. 2007. Computer Algebra Solution of GPS N-points Problem. GPS Solutions.

A computer algebra solution is applied here todevelop and evaluate algorithms for solving the basic GPS navigation problem: finding a point position using four ormore pseudoranges at one epoch (the GPS N-points problem).Using Mathematica 5.2 software, the GPS N-pointsproblem is solved numerically, symbolically, semi-symbolically,and with Gauss-Jacobi, on a work station. Forthe case of N > 4, two minimization approaches based onresiduals and distance norms are evaluated for the direct numerical solution and their computational duration iscompared. For N = 4, it is demonstrated that the symbolic computation is twice as fast as the iterative directnumerical method. For N = 6, the direct numerical solutionis twice as fast as the semi-symbolic, with the residual minimization requiring less computation time compared tothe minimization of the distance norm. Gauss-Jacobi requires eight times more computation time than the direct numerical solution.It does, however, have the advantage of diagnosing poor satellite geometry and outliers. Besides offering a complete evaluation of these algorithms, we have developed Mathematica 5.2 code (a notebook file)for these algorithms (i.e., Sturmfel's resultant, Dixon's resultants, Groebner basis, reduced Groebner basis and Gauss-Jacobi). These are accessible to any geodesist, geophysicist, or geoinformation scientist via the GPSToolbox ( website or the Wolfram Information Center (

dc.publisherJohn Wiley and Sons, Inc.
dc.titleComputer Algebra Solution of GPS N-points Problem
dc.typeJournal Article
dcterms.source.titleGPS Solutions
curtin.accessStatusFulltext not available
curtin.facultyDepartment of Spatial Sciences
curtin.facultyFaculty of Science and Engineering
curtin.facultyWA School of Mines

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