Some Theoretical Problems in the Adjustment of Free Networks

In this paper various approaches to the adjustment of free networks on the basis of the theory of generalized inverse are analyzed.It has been pointed out that the difference between them lies in the adoption of different least norm inverses.The nature of the residuals of free networks,and of the reference systems is also dealt with.It has been proved that the residuals thus obtained are the same as those obtained by the classical adjustment of free networks and are independent of the additional least norm condition.It was shown that the least norm condition determines the orientation of reference system of the network.The coordinates from these two types of adjustment can be converted with each other by means of these reference systems.