Optimal design and adjustment of geodetic networks. (Optimal’noe proektirovanie i uravnivanie geodezicheskikh setej.) (Russian) Zbl 0771.90103

Gerasimenko, M. D.

Moskva: Nauka. 161 p. (1992).

Summary: Algorithms of optimal design and adjustment of geodetic networks based on the method of least squares are presented. From the theoretical point of view there are some reasons for the appearance of ill-conditioned systems of normal equations. New stable methods of adjustment are proposed. A procedure for the choice of the most stable method of adjustment with preliminary evaluation of the condition number is recommended. The book provides a review of the state of the art in network design and optimization. Analytical expression for the derivation of most of the typical risk functions are derived and a numerically efficient method for solving the second order design problem is provided. The major theoretical conclusions and practical recepies are illustrated with numerical examples. Some conclusions on optimal design of geodetic networks are given.

MSC:

90C90

Applications of mathematical programming

Keywords:

optimal design; geodetic networks