The Investigation of General Solution in Free Datum Networks

Abstract

The datum of survey control networks sometimes cannot be defined because there is no position of fixed points is provided. In these types of networks the solution can be obtained by what is known as general solution of free datum networks. Actually, the datum in free networks is defined by additional datum constraints to solve the problem of singularity of the normal equations matrix. To solve the problem of datum defect, the unknown parameters of the datum are required to be fixed. These constraints can be established for a part or all points of the network to define the reference frame of the control network in several ways. The adjustment obtained using full datum constraints is called free or relative datum adjustment. In this research, the various forms of datum constraints are established and investigated in order to distinguish between them. More than one solution models applied individually as different cases to be compared with others. Conclusions drawn that the optimum solution with minimum norm and minimum trace is that the general solution using full constraints matrix, it gives the same coordinate differences obtained by others. Then it can be widely used in solution of survey control networks used in many types of networks such as these applied in deformation monitoring field.  Another conclusion is that the suitability of the general solution form for all other chosen datums. Any fixed datum solution can be obtained from the general solution by adding a scalar calculated from height(s) of the reference fixed point(s).