ON THE APPLICATION OF FULLY ANALYTICAL SOLUTION FOR THE COMBINED-ORDER DESIGN PROBLEM OF FREE GEODETIC NETWORKS

Free geodetic networks are still very popular in geodesy, surveying and mapping mainly due
to their unique property of being independent of errors in external data. The free “floating”
network is a network in which only the internal shape is given by measurements of relative nature
(Schmitt, 1982). In such a case, the corrections solution vector to the approximate coordinates is
derived by selecting the best coordinate system. In other words, the term free network refers to a
network whose adjustment is made free from any kind of external constraints. This means that the
network can freely translate, rotate or undergo scale change in space. Optimization means
minimizing or maximizing an objective function which represents the criteria adopted to define the
“quality of a network”. Generally the quality of a control network is characterized by its precision,
reliability, strength and economy (Seemkooei, 2001; Kaplan, 2004). In this paper we focus on
designing an optimal network configuration and optimum observing plan (Combined-Order
Design Problem) in the sense that they will satisfy the present network quality requirement at a
minimum cost. A small free geodetic network are simulated and its optimal design is solved by
nonlinear programming method. The obtained results are discussed and analyzed.