the pai approach of the surveying administration brandenburg frank gielsdorftu berlin eckhardt...

The PAI Approach of the Surveying Administration

Brandenburg

Frank Gielsdorf TU BerlinEckhardt Seyfert Surveying Administration Brandenburg

http://www.tu-berlin.de/

http://www.geobasis-bb.de/LGB1/main/main_index.htm

Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg 2

Overview

• Why is PAI an adjustment problem?

• Why is PAI a topological problem?

• The process of geometrical updating

• Pilot project Brandenburg




Principle of Adjacent Points

0 x

d1 d2 d3 d4 d5 d6 d7 d8 d9

Error Propagation

Tllxx FCFC

29

28

27

26

25

24

23

22

21

111111111

11111111

1111111

111111

11111

1111

111

11

1

d

d

d

d

d

d

d

d

d

ll

CF

Absolute Accuracy (sigma x)

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

1 2 3 4 5 6 7 8 9




Absolute and Relative Accuracy

1 1 1 1 1 1 1 1 1

1 2 2 2 2 2 2 2 2

1 2 3 3 3 3 3 3 3

1 2 3 4 4 4 4 4 4

1 2 3 4 5 5 5 5 5

1 2 3 4 5 6 6 6 6

1 2 3 4 5 6 7 7 7

1 2 3 4 5 6 7 8 8

1 2 3 4 5 6 7 8 9

Covariance Matrix of x-ValuesCxx

Standard Deviation of d8

Wrong Approach

m87.3

87

8

28

278

d

xxd

Right Approach

m1

1487

),cov(2

8

8728

278

d

xxd xx




Adjustment Neglecting the Correlations

Point x GIS x GPS

1 105

2 107 105,65

3 113

4 122

5 124

6 134

7 139

8 143 143,53

9 145

10 154

11 163

12 166 165,13

m02.0

m3

GPS

GISObservations: GPS Coordinates

GIS Coordinates

0

1 2 3 4 5 6 7 8 9 10 11 12 x

GPSGPS GPS

! ! !

Violation of Neighborhood Relationships

Resulting Standard Deviations

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

100,00 110,00 120,00 130,00 140,00 150,00 160,00 170,00




Differences of Similiarity Transformation and Proximity Fitting

Observations = Local coordinatese.g. Helmert (4PT) oder Affine (6PT)

Observations = Coordinate differences(performed by Delaunay triangulation)

Transformation parameters

Adjustment Neglecting the Correlations




Observations: GPS coordinates GIS coordinate differences (pseudo observations)

Adjustment Considering the Correlations

Point X GPS DX GIS

1 -

2 105,65 2

3 6

4 7

5 4

6 10

7 5

8 143,53 4

9 2

10 9

11 9

12 165,13 3

Standard Deviations of Coordinates

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

100,00 110,00 120,00 130,00 140,00 150,00 160,00 170,00

1 2 3 4 5 6 7 8 9 10 11 12 x

GPSGPS GPS

d56

Standard Deviations of Coordinates

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

100,00 110,00 120,00 130,00 140,00 150,00 160,00 170,00




Example for PAI Adjustment




Integration of Geodesic Measurements

Collinear

Orthogonal

Parallel

Circle Continuities

Global Coordinates

Local Coordinates

Distances

28.37

35.2221.46

17.12

12.14

7.88

4.76

10.95

Membrane Triangles- 14.36 - - 20.08 -




Geometry and TopologyNeglected Topology

Neg

lect

edC

orre

latio

n




The Role of Point Identifiers

shapepoint 1

point n

pointx

y

point x

y

point_id

no direct accessredundancy

object disappearsif moved

just one reference frame

point

reference frame

is coordinatedx

y

(1,*)

(1,*)




Topology of Pseudo Observations

Distance weighted interpolation Delaunay Triangulation

Observation Topology




Ausgangslage Homogenisierung

The proximity fitting approach




Federal Country Brandenburg

Brandenburg Germany

Area 29 477 km2 357 020 km2

Population 2.6 Mio 82.2 Mio

Population Density

88 230




Pilot Project Fredersdorf

Federal StateBrandenburg

DistrictUckermark

ComunityFredersdorf

Points: 30.000, Area: 50 km2

Primary data acquisition for ALK is finished

Observations: GPS coordinates, cadastral field books




Temporal Partitioning of PAI

Primary Data Observations

View Coordinates

l0 xi

1

0

l

l

2

1

0

l

l

l

nl

l

l

l

2

1

0

xi+1

xi+2

xi+n

copy

adjustment

adjustment

adjustment

Status at time i

view 1

view 2

view n

1. update

2. update

n. update

time




Spatial Partitioning of PAI

A

B

C

Pi K1 K2

K3

K4

K5

P1 P2 P3

P4

P5

P6

Pj

Pk Pl

Updating Blocks1. Adjustment

2. Adjustment

3. Adjustment




Control Viewof PAI Process

primary acquisitioncompleted

mappingx0 --> l0

x and l areconsistent

adding ofobservations

x and l areinconsistent

checking ofupdating criteria

updatenecessary

update notnecessaryXOR

check-out ofupdating blocks

updating blockslocked

adjustment

adjustmentrealised

check-in ofupdating blocks




Data View of PAI Process

blocks points

blockboundaries

bound end

belong

(2,2)

(3,*)

(2,2)

(0,*)

(3,*) (1,*)

observations

connect

(1,*)

(1,*)

adjustment

calculate

(0,*)

(1,*)




Data Flow

ALK-GIAP

GEOgraf

SYSTRA

GEOgraf

ALK-GIAP

EDBS

EDBS

coordinates

coordinates

Observations

No identifiers for all pointsNo topology

Generation of topologyDefinition of update blocksPoint identifier

Adjustment calculationsAcquisition and management of observations

Moving the points




Unique Point Identifier

Federal State 12Cadastral District (Gemarkung): 1175Cadastral Section (Flur): 002Number: 23

P12316000700023Point Identifier

Rule On block boundaries obtain the lower point number

Organisation Structures

Important: prefix of point ID is datum independent – no coordinate grid!




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




PAI Test Project of OS

Links PRE-POST as Point Identities

Moving vectors = Local residuals

Links PRE-CUST as Point Identities




Thank you for your attention!

[email protected]



the pai approach of the surveying administration brandenburg frank gielsdorftu berlin eckhardt...

Documents

pai approach

pai adjustment slide

correlation slide

point n point x y x

pt observations

adjustment problem

covariance matrix of

correlations pointx