1. The PAI Approach of the Surveying Administration Brandenburg Frank GielsdorfTU Berlin Eckhardt SeyfertSurveying Administration Brandenburg

2. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg2 Overview Why is PAI an adjustment problem? Why is PAI a topological problem? The process of geometrical updating Pilot project Brandenburg

3. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg3 Principle of Adjacent Points 0 x d1d1 d2d2 d3d3 d4d4 d5d5 d6d6 d7d7 d8d8 d9d9 Error Propagation

4. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg4 Absolute and Relative Accuracy 111111111 122222222 123333333 123444444 123455555 123456666 123456777 123456788 123456789 Covariance Matrix of x-Values C xx Standard Deviation of d 8 Wrong Approach Right Approach

5. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg5 Adjustment Neglecting the Correlations Pointx GISx GPS 1105 2107105,65 3113 4122 5124 6134 7139 8143143,53 9145 10154 11163 12166165,13 Observations: GPS Coordinates GIS Coordinates 0 123456789101112 x GPS !!! Violation of Neighborhood Relationships

6. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg6 Differences of Similiarity Transformation and Proximity Fitting Observations = Local coordinates e.g. Helmert (4PT) oder Affine (6PT) Observations = Coordinate differences (performed by Delaunay triangulation) Transformation parameters Adjustment Neglecting the Correlations

7. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg7 Observations: GPS coordinates GIS coordinate differences (pseudo observations) Adjustment Considering the Correlations PointX GPSDX GIS 1- 2 105,652 36 47 54 610 75 8 143,534 92 109 119 12 165,133 123456789101112 x GPS d 56

8. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg8 Example for PAI Adjustment

9. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg9 Integration of Geodesic Measurements Collinear Orthogonal Parallel Circle Continuities Global Coordinates Local Coordinates Distances 28.37 35.22 21.46 17.12 12.14 7.88 4.76 10.95 Membrane Triangles - 14.36 - - 20.08 -

10. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg10 Geometry and Topology Neglected Topology Neglected Correlation

11. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg11 The Role of Point Identifiers shape point 1 point n point x y x y point_id no direct access redundancy object disappears if moved just one reference frame point reference frame is coordinated x y (1,*)

12. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg12 Topology of Pseudo Observations Distance weighted interpolationDelaunay Triangulation Observation Topology

13. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg13 Ausgangslage Homogenisierung The proximity fitting approach

14. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg14 Federal Country Brandenburg BrandenburgGermany Area29 477 km 2 357 020 km 2 Population2.6 Mio82.2 Mio Population Density 88230

15. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg15 Pilot Project Fredersdorf Federal State Brandenburg District Uckermark Comunity Fredersdorf Points: 30.000, Area: 50 km 2 Primary data acquisition for ALK is finished Observations: GPS coordinates, cadastral field books

16. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg16 Temporal Partitioning of PAI Primary Data Observations View Coordinates l 0 x i         1 0 l l           2 1 0 l l l                 n l l l l  2 1 0 x i+ 1 x 2 x i+n copy adjustment Status at time i view 1 view 2 view n 1. update 2. update n. update time

17. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg17 Spatial Partitioning of PAI Updating Blocks 1. Adjustment 2. Adjustment 3. Adjustment

18. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg18 Control View of PAI Process primary acquisition completed mapping x 0 --> l 0 x and l are consistent adding of observations x and l are inconsistent checking of updating criteria update necessary update not necessary XOR check-out of updating blocks locked adjustment realised check-in of updating blocks

19. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg19 Data View of PAI Process blocks points block boundaries boundend belong (2,2) (3,*) (2,2) (0,*) (3,*)(1,*) observations connect (1,*) adjustment calculate (0,*) (1,*)

20. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg20 Data Flow ALK-GIAP GEOgraf SYSTRA GEOgraf ALK-GIAP EDBS coordinates Observations No identifiers for all points No topology Generation of topology Definition of update blocks Point identifier Adjustment calculations Acquisition and management of observations Moving the points

21. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg21 Unique Point Identifier Federal State12 Cadastral District (Gemarkung):1175 Cadastral Section (Flur):002 Number:23 P12316000700023 Point Identifier RuleOn block boundaries obtain the lower point number Organisation Structures Important: prefix of point ID is datum independent – no coordinate grid!

22. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg22 PAI Test Project of OS PRE: Old Geobase data CUST: Customer data POST: New Geobase data Links PRE-POST transformed as Point Identities Links PRE-CUST generated as Point Identities No geometrical constraints as wanted

23. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg23 PAI Test Project of OS Links PRE-POST as Point Identities Moving vectors = Local residuals Links PRE-CUST as Point Identities

24. Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg24 Thank you for your attention! gielsdorf@fga.tu-berlin.de