Gröbner bases, multipolynomial resultants and the Gauss-Jacobi combinatorial algorithms -adjustment of nonlinear GPS/LPS observations
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In this paper, the algebraic techniques of Grobner bases and Multipolynomial resultants are presented as efficient algebraic tools for solving the nonlinear geodetic problems.Abstract:
Die Methode der Grobner-Basen und Multipolynomialen Resultante wird als wirksames algebraische Hilfsmittel zur expliziten Losung nichtlinearer geodatischer Problem vorgestellt. Wir nutzen dir Grobner-Basen und Multipolynomialen Resultante als Rechenhilfsmittel bei der Losung des nichtlinearen Gauss-Markov Modells mit Hilfe des kombinatorischen Gauss-Jacobi-Algorithmus.
The algebraic techniques of Grobner bases and Multipolynomial resultants are presented as efficient algebraic tools for solving the nonlinear geodetic problems. The capability of the Grobner bases and the Multipolynomial resultants to solve explicitly nonlinear geodetic problems enables us to use them as the computational engine in the Gauss-Jacobi combinatorial algorithm to solve the nonlinear Gauss-Markov model.read more
Citations
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Nonlinear analysis of the three-dimensional datum transformation[conformal group C7(3)]
TL;DR: The problem of incorporating the stochasticity measures of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ7(3)] which is free of linearization and any iteration procedure can be considered to be solved.
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Nonlinear Adjustment of GPS Observations of Type Pseudo-Ranges
TL;DR: In this article, the Fast Nonlinear Adjustment Algorithm (FNon Ad Al) has been already proposed by Gauss whose work was published posthumously and Jacobi (1841), which solves the over-determined GPS pseudo-ranging problem without reverting to iterative or linearization procedure except for the second moment (Variance-Covariance propagation).
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A comparison of different solutions of the Bursa–Wolf model and of the 3D, 7-parameter datum transformation
J. Závoti,János Kalmár +1 more
TL;DR: Various methods for calculating the scale factor are discussed and solutions based on quaternion with those that are based on rotation matrix making use of skew-symmetric matrix are compared.
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Dixon resultant’s solution of systems of geodetic polynomial equations
TL;DR: In this article, the authors proposed the Dixon resultant as an alternative to Grobner basis or multipolynomial resultant approaches for solving systems of polynomial equations inherent in geodesy.
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Groebner-basis solution of the three-dimensional resection problem (P4P)
TL;DR: In this article, the Groebner basis is used to solve the nonlinear Grunert distance equation in a single step once the equations have been converted into algebraic form.
References
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TL;DR: The Cayley method of studying discriminants was used by Cayley as discussed by the authors to study the Cayley Method of Discriminants and Resultants for Polynomials in One Variable and for forms in Several Variables.