IJPAM: Volume 60, No. 1 (2010)

APPROXIMATE SOLUTION TO THE OVERDETERMINED
TWO-DIMENSIONAL RESECTION PROBLEM

Gunnar Thorbergsson
4, Krummaholar, Reykjavik, 111, ICELAND
e-mail: gunnarthorb.gmail.com


Abstract.In surveying a resection is the observation of directions or lines of sight from a station to three or more targets with known (fixed or previously computed) coordinates and the computation of the station coordinates from these observations alone. In this article we shall minimize the sum of squares of the distances from the targets to the corresponding lines of sight. This will result in a set of equations linear in the station coordinates (and quadratic in a trigonometric function). Apart from exceptional cases, one of the solutions to the equations gives good approximate values for the station coordinates.

Received: January 11, 2010

AMS Subject Classification: 93E24

Key Words and Phrases: resection, overdetermined, two-dimensional

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 1