SCALAR RISK FUNCTIONS AS CRITERIA FOR DATUM DEFINITION IN GEODETIC NETWORKS

SCALAR RISK FUNCTIONS AS CRITERIA FOR DATUM DEFINITION IN GEODETIC NETWORKS

[ Mehdi Eshagh ] - Islamic Azad University, Shahr-e-Rey branch, Tehran , Iran

abstract

The first step designing a geodetic network is Zero order design, in which a suitable datum is defined The problem of datum is a mathematical problem and it refers to projection concepts. In precision point of view, the cofactor matrix of the net point coordinates can be a good means for datum definition .But how can this matrix be used for datum definition? Different functions can be defined in this way; one can consider one of the trace, determinant , norm , difference between maximum and minimum latent roots and maximum latent root of this matrix as a criteria. These criteria can be regarded as scalar risk functions. But do the criteria introduce the same datum for a geodetic network? In this paper criteria are investigated and our numerical results show good agreement among them. Of course this result cannot be a general answer but the maximum latent root, norm, and trace criteria are more suitable for datum definition.

keywords

Adjustment, Scalar risk function, constraint, criterion, and datum