Author(s): Cherokee C. Johnson
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 17, Number 3
Pages: 308 - 324
Cite this article: Johnson, Cherokee C., "TRIANGULATION THEORY AND TECHNIQUES", NAVIGATION, Journal of The Institute of Navigation, Vol. 17, No. 3, Fall 1970, pp. 308-324.
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Abstract: THIS COMPENDIUM attempts to collate and coalesce those aspects of triangulation theory related to posit,ion-fix techniques employing lines-of-bearing. The author presents the discovery of the n-locus of a triangle, upon which lie several points of geometric interest. Formulae for the coordinates of various special forms of Least Squares Fits to a triangle are derived. The well known method of “resection by intersection” is examined, complemented by varia-Gons of the Technique. The m-Locus of a triangle is discovered, yielding the Classical Least Squares for triangulation theory. The m-locus dissolves the mystery surrounding the technique employing equi-angular adjustment to the triangulation measurements to reduce the error-triangle to a point. The treatise concludes with formulae for the direct calculation of the Classical Least Squares, bypassing the need of the vertices of the triangle of error and consequently the lengths of the sides of the triangle.