Optimization of Horizontal Direction Observations in Triangulation or Triangulateration Networks

Abstract

This paper deals with the modeling and solution of an optimal direction observation scheme in two‐dimensional triangulation or triangulateration networks under a given precision criterion matrix of the estimated coordinates. The difficulty in setting up appropriate criterion matrices for the orientation unknowns is overcome by eliminating the orientation unknowns from the adjustment model and equating the variance‐covariance matrix of the estimated coordinates with the given criterion matrix of coordinates. Based on the analysis of the given optimization examples, a two‐step optimization procedure is proposed, which may result in a most economic survey campaign. That is, the optimal solution of individual observational weights for all the possible directions in the network should be explored first, to delete those directions that obtained zero or close to zero optimal weights and therefore have insignificant contribution to the network accuracy. The solution of an optimal group weight for each station in the network is then sought for only those directions that obtained significant individual weights. The obtained optimal group weights of directions are used as a guideline in the choice of instrumentation and operational procedures.