SECOND-ORDER DESIGN OF GEODETIC NETWORKS BY MEANS OF A STATISTICALLY PERFECTLY ISOTROPIC AND HOMOGENEOUS MEAN ERROR MATRIX

Abstract

Goals of second-order design of geodetic networks are considered, together with mathematical conditions of developing the proper homogeneous, perfectly isotropic variance-covariance matrices. In case of free networks, perfect isotropy will be shown to be possible exclusively for indefinite network scales. An adjustment method providing for perfect isotropy even in case of telemetry will be suggested, and so will be a simple measurement method to be combined with the suggested adjustment method for automatically safeguarding perfect isotropy. An optimization algorithm will be presented, to determine a system of measurement weight values resulting in a statistically homogeneous, perfectly isotropic weight coefficient matrix.