G. Schmitt

Second Order Design

A very simple example as introduction in the SOD with respect to criterion matrices is demonstrated in figure 1. A network shall be densified by a new point 10; as observations three distances from or to the fixed points 1, 2 and 3 are planned. The accuracy postulation is given by a circle with the radius 1 cm as error ellipse. This postulation is represented by the identity matrix as criterion matrix

Review of Network Designs: Criteria, Risk Functions, Design Ordering

\text{Q}_\text{x} = \text{E} = \left( {\begin{array}{*{20}c} 1 & 0 \\ 0 & 1 \\ \end{array} } \right)

GPS probes the kinematics of the Vrancea Seismogenic Zone

and a standard deviation of the weight unit σ0 = 1 cm. The connexion between the normal equations and the criterion matrix as ideal variance-covariance matrix is

Third Order Design

\text{N} = \text{A}^\text{T} \text{PA} = \text{Q}_\text{x}^{ - 1} = \text{E}\text{.}

Ausgleichsrechnung - Theorie und aktuelle Anwendungen aus der Vermessungspraxis

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Monitoring horizontal motions in a local network at Caneva in Friuli, Italy

SummaryA numerically efficient solution strategy is developed for the second-order design of a free distance network. It is based on the fact that the direct (non-canonical) way has a regular least-squares solution. A flow chart illustrates the direct construction of the final equations, using a list of point coordinates and a list of projected distances as input. Results are shown for an actual network (11 points, 47 distances), considering different types of criterion matrices: Taylor-Karman structure with homogeneous-isotropic point error ellipses and special Taylor-Karman structure with isotropic relative error ellipses. Finally, the construction of a criterion-matrixQx is briefly discussed in the case that a certain number of quantities shall be derived from the network.