dc.contributor.author Palancz, Bela dc.contributor.author Awange, Joseph dc.contributor.author Grafarend, Erik dc.date.accessioned 2017-01-30T11:38:03Z dc.date.available 2017-01-30T11:38:03Z dc.date.created 2009-03-05T00:56:49Z dc.date.issued 2007 dc.identifier.citation Palancz, Bela and Awange, Joseph and Grafarend, Erik. 2007. Computer Algebra Solution of GPS N-points Problem. GPS Solutions. dc.identifier.uri http://hdl.handle.net/20.500.11937/13584 dc.identifier.doi 10.1007/s10291-007-0066-8 dc.description.abstract 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 (http://www.ngs.noaa.gov/gps-toolbox/exist.htm) website or the Wolfram Information Center (http://library.wolfram.com/infocenter/MathSource/6629/). dc.publisher John Wiley and Sons, Inc. dc.subject Algebra dc.subject Positioning dc.subject CAS dc.subject GPS dc.title Computer Algebra Solution of GPS N-points Problem dc.type Journal Article dcterms.source.issn 15211886 dcterms.source.title GPS Solutions curtin.accessStatus Fulltext not available curtin.faculty Department of Spatial Sciences curtin.faculty Faculty of Science and Engineering curtin.faculty WA School of Mines
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