A generalisation of the least-squares method for the adjustment of free networks

Summary The system of normal equations for the adjustment of a free network is a singular one. Therefore, a number of coordinates has to be fixed according to the matrix. The mean square errors and the error ellipses of such an adjustment are dependent on this choice. This paper gives a simple, direct method for the adjustment of free networks, where no coordinates need to be fixed. This is done by minimizing not only the sum of the squares of the weighted errorsV ^T PV=minimun but also the Euclidean norm of the vectorX and of the covariance matrixQ X ^T X=minimum trace (Q)=minimum This last condition is crucial for geodetic problems of this type.