ZOD - Zero Order Design of Geodetic Networks - free networks, - PowerPoint PPT Presentation

ZOD - Zero Order Design of Geodetic Networks - free networks, G-inverses, S-transformation - Fakultät Bau-, Geo-, Umwelt -Geodätisches Institut- Fakultät Bau-, Geo-, Umwelt -Geodätisches Institut- KIT – Universität des Landes Baden-Württemberg und www.kit.edu nationales Großforschungszentrum in der Helmholtz-Gemeinschaft

Zero Order Design - Free Network - - 1/2/3-dimensional geodetic networks - Observations : usually of geometrical nature - distances,directions, angles, zenith distances, height differences… - Parameters : coordinates 1D/2D resp. 3D funktional relationship between observations ↔ parameters: - GMM - adjustment by observation equations ⇒ - observations are of relative nature - they fix only the relative situation, that means the inner geometry - the position of the point field in plane/space is free ⇒ datum is free ! ZOD - Zero Order Design of Geodetic Networks 2 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - Free Network - visualising datum defects (Example: Reines Richtungsnetz; Niemeier 2008) datum fixing as a central component in network adjustment l x obserations parameters datum fixing ZOD - Zero Order Design of Geodetic Networks 3 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - Free Network - ZOD - Zero Order Design of Geodetic Networks 4 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - Free Network - H 1 H 2 H 3 H 4 -1 +1 -1 +1 -1 +1 +1 -1 -1 +1 Analyse und Planung Geodätischer Netze 5 Dr.-Ing. M. Illner Geodätisches Institut

Zero Order Design - Free Network - ZOD - Zero Order Design of Geodetic Networks 6 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - Free Network - ZOD - Zero Order Design of Geodetic Networks 7 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - Free Network - ZOD - Zero Order Design of Geodetic Networks 8 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 9 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 10 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 11 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 12 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 13 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 14 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 15 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - G - Inverses - ZOD - Zero Order Design of Geodetic Networks 16 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - inner solution - ZOD - Zero Order Design of Geodetic Networks 17 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - inner solution - ZOD - Zero Order Design of Geodetic Networks 18 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - inner solution - ZOD - Zero Order Design of Geodetic Networks 19 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - inner solution - ZOD - Zero Order Design of Geodetic Networks 20 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - trace minimization - ZOD - Zero Order Design of Geodetic Networks 21 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - trace minimization - Analyse und Planung Geodätischer Netze 22 Dr.-Ing. M. Illner Geodätisches Institut

structure of the G -matrices for 1D- and 2D-networks eigenvector components g i of the i-th point type of kind of free datum dimen- net- observations defect parameters translation rotation scale sion work about X Y Z height height 1 translation 1-D net- d=1 1 differences (vertical shift) work work distances and translations in 1 0 azimuths, d=2 Y- and X- 0 1 GNSS direction distances or 2 translations, 1 0 xi distances and d=3 rotation about plane 0 1 -y i directions Z-axis 2-D net- work directions, dis- 2 translations, 1 0 x i y i tance ratios or d=4 rotation about Z- 0 1 -y i x i as for d=3 with axis, scale scale ZOD - Zero Order Design of Geodetic Networks 23 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - nullspace G – structure of G -matrices for 3D-networks eigenvector components g i of the i-th point type of dimen- kind of free datum net- defect translation rotation scale sion observations parameters work about X Y Z translations in 1 0 0 GNSS d=3 X-, Y- and Z- 0 1 0 direction 0 0 1 translations in s i and z i or 1 0 0 -y i X-, Y- and Z- s i and r i and z i d=4 0 1 0 x i direction, rotation 0 0 1 0 about Z space r i and z i or 3 translations, 1 0 0 -y i x i 3-D network as in the case d=4 d=5 1 rotation, 0 1 0 x i y i with scale 1 scale 0 0 1 0 z i distances or dis- 3 translations, 1 0 0 0 z i -y i tances and d=6 rotations about 0 1 0 -z i 0 x i directions X-, Y- and Z-axis 0 0 1 y i -x i 0 3 translations, 1 0 0 0 z i -y i x i As in the case d=6 d=7 3 rotations, 0 1 0 -z i 0 x i y i with scale 1 scale 0 0 1 y i -x i 0 z i ZOD - Zero Order Design of Geodetic Networks 24 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - nullspace G - 3 translations 3 rotations scale ZOD - Zero Order Design of Geodetic Networks 25 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - S-transformation - ZOD - Zero Order Design of Geodetic Networks 26 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - S-transformation - ZOD - Zero Order Design of Geodetic Networks 27 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - S-transformation - ZOD - Zero Order Design of Geodetic Networks 28 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - 1D-network - ZOD - Zero Order Design of Geodetic Networks 29 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - 1D-network - ZOD - Zero Order Design of Geodetic Networks 30 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - 1D-network- ZOD - Zero Order Design of Geodetic Networks 31 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - elimination of orientation unknowns - 2 l 1 t 1,3 3 l 2 1 l 3 4 ZOD - Zero Order Design of Geodetic Networks 32 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut

Zero Order Design - elimination of orientation unknowns - ZOD - Zero Order Design of Geodetic Networks 33 Prof. Dr.-Ing. Dr.-Ing. E.h. Günter Schmitt Geodätisches Institut