A theoretical random-error-propagation model for weakly constrained angular networks

Summary Idealized angular networks are considered which cover a two dimensional plane area. The networks consist of a multitude of identical elementary figures for which complete angular information can be deduced from the observations. Rather particular assumption have been made concerning the shape of the elementary figures and the covariance pattern of the observations. It is however believed that varying these assumptions would not alter the qualitative behavior of the theoretically derived error bounds. As the number n of points in such a network increases, the worst point error grows not less than a constant times √n. An upper bound for its growth is given by a constant times ℚnℓn(n). These results hold for completely free networks as well as in the case of a small number of fixed points.