Second‐Order Design: Shooting for Maximum Reliability

Abstract

In general, the purpose of geodetic network optimization is to solve for both a network configuration, i.e., the point location, and an observational plan, i.e., the types of observations together with the precisions of the measurements to be made, which are optimal in the sense of good precision, high reliability and low cost. Precision describes how a network propagates random errors, and the reliability of a geodetic network refers to the ability of the network to resist gross errors in the observations. This paper concentrates on the solution of an observational plan of a geodetic network, assuming its configuration was fixed, which is optimal in the sense of highest reliability. General precision requirements are incorporated in the solution model in the form of inequality constraints. The developed mathematical model is of practical significance, especially for geodetic networks established for deformation monitoring purposes; in this case, high reliability of the network is the key to the successful detection of outliers in the observations in order to avoid misinterpreting the systematic errors or gross errors as deformation phenomenon. An illustrative example is included.