Transcript Document

The PAI Approach of the
Surveying Administration
Brandenburg
Frank Gielsdorf
Eckhardt Seyfert
TU Berlin
Surveying Administration Brandenburg
Overview
• Why is PAI an adjustment problem?
• Why is PAI a topological problem?
• The process of geometrical updating
• Pilot project Brandenburg
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
2
Principle of Adjacent Points
d1
d2
d3
d4
d5
d6
d7
d8
d9
0
x
Absolute Accuracy (sigma x)
Error Propagation
T
C3,50

F

C

F
xx
ll
3,00
1
2,50

1 1
2,00
1 1
1,50
1 1
F  1,00
1 1
0,50
1 1

1 1
0,00
1 1

1 1
1
1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
  d21




 d2 2







 C 
ll




1


1 1


4
5
1 2 1 1 3



1 1 1 1

 d23
 d2 4
 d25
 d26
 d27
6
7
8
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
9  d28













2 
 d9 
3
Absolute and Relative Accuracy
Covariance Matrix of x-Values
Cxx
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
Standard Deviation of d8
Wrong Approach
 d 8   x27   x28  7  8
 d 8   3.87m
Right Approach
 d 8   x27   x28  2 cov(x7 , x8 )
 7  8  14
 d 8   1m
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Adjustment Neglecting the Correlations
Resulting Standard Deviations
Point
x GIS
1,40 1
105
2
107
3
113
1,00 4
122
5
124
0,80 6
134
7
139
8
143
0,40 9
145
10
0,20
11
154
0,0012
100,00
166
1,20
0,60
Observations: GPS Coordinates
GIS Coordinates
x GPS
105,65
Violation of Neighborhood Relationships
143,53
163
165,13
110,00
120,00
130,00
140,00
GPS
1
0
 GIS   3m
 GPS   0.02m
160,00
GPS
2
!
150,00
3
4
5
6
7
8
170,00
GPS
9
10
11
!
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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x
!
5
Adjustment Neglecting the Correlations
Differences of
Similiarity Transformation and Proximity Fitting
Observations = Local coordinates
e.g. Helmert (4PT) oder Affine (6PT)
Observations = Coordinate differences
(performed by Delaunay triangulation)
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Adjustment Considering the Correlations
X GPS
Point
DX Standard
GIS
Deviations of Coordinates
Standard Deviations
of CoordinatesGPS
Observations:
1
0,90
1,00
105,65
2
2
0,90
0,80
3
6
0,80
0,70
4
7
0,70
0,60
5
4
0,60
0,50
6
10
0,50
0,40
0,40
0,30
0,30
0,20
0,20
7
5
0,10
0,10
coordinates
GIS coordinate differences
(pseudo observations)
-
143,53
8
4
9
2
10
9
11
9
165,13
0,00 12
0,00
100,00
100,00
3
110,00
110,00
120,00
120,00
130,00
130,00
140,00
140,00
GPS
1
150,00
150,00
160,00
160,00
GPS
2
3
4
5
6
7
8
170,00
170,00
GPS
9
10
11
12
x
d56
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Example for PAI Adjustment
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Integration of Geodesic Measurements
Membrane Triangles
- 14.36 -
- 20.08 -
Collinear
Orthogonal
Parallel
Circle Continuities
Global Coordinates
Local Coordinates
Distances
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Geometry and Topology
Topology
Correlation
Neglected
Neglected
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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The Role of Point Identifiers
point 1
shape
point n
no direct access
redundancy
point
(1,*)
x
point
y
object disappears
if moved
x
is coordinated
y
(1,*)
point_id
point
x
reference frame
just one
reference frame
y
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Observation Topology
Topology of Pseudo Observations
Distance weighted interpolation
Delaunay Triangulation
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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The proximity fitting approach
Ausgangslage
Homogenisierung
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Federal Country Brandenburg
Brandenburg
Germany
Area
29 477 km2
357 020 km2
Population
2.6 Mio
82.2 Mio
Population
Density
88
230
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Pilot Project Fredersdorf
Federal State
Brandenburg
District
Uckermark
Comunity
Fredersdorf
Points: 30.000, Area: 50 km2
Primary data acquisition for ALK is finished
Observations: GPS coordinates, cadastral field books
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Temporal Partitioning of PAI
l0
copy
Primary Data
Observations
xi
Status at
time i
View
Coordinates
time
1. update
l0 
 
 l1 
adjustment
xi+1
view 1
2. update
l0 
 
 l1 
l 
 2
adjustment
xi+2
view 2
n. update
l0 
 
 l1 
l 
 2
M
 
ln 
adjustment
xi+n
view n
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Spatial Partitioning of PAI
Updating Blocks
1. Adjustment
2. Adjustment
A
P4
K3
P1
K1
K2
P2
P3
Pi
Pj
K4
P5
B
C
Pk
K5
P6
Pl
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
3. Adjustment
17
primary acquisition
completed
mapping
x0 --> l0
Control View
of PAI Process
x and l are
consistent
adding of
observations
x and l are
inconsistent
checking of
updating criteria
XOR
update not
necessary
update
necessary
check-out of
updating blocks
updating blocks
locked
adjustment
adjustment
realised
check-in of
updating blocks
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Data View of PAI Process
block
boundaries
(2,2)
(2,2)
bound
end
(3,*)
blocks
(0,*)
(3,*)
belong
(1,*)
points
(0,*)
(1,*)
calculate
connect
(1,*)
(1,*)
adjustment
observations
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Data Flow
ALK-GIAP
No identifiers for all points
No topology
EDBS
GEOgraf
Generation of topology
Definition of update blocks
Point identifier
coordinates
Observations
SYSTRA
coordinates
GEOgraf
Adjustment calculations
Acquisition and management
of observations
Moving the points
EDBS
ALK-GIAP
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Unique Point Identifier
Federal State
Cadastral District (Gemarkung):
Cadastral Section (Flur):
Number:
Point Identifier
Rule
12
1175
002
23
Organisation
Structures
P12316000700023
On block boundaries obtain the
lower point number
Important: prefix of point ID is datum independent –
no coordinate grid!
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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PAI Test Project of OS
Links PRE-POST
transformed as Point Identities
PRE: Old Geobase data
POST: New Geobase data
Links PRE-CUST
generated as Point Identities
CUST: Customer data
No geometrical constraints as wanted
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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PAI Test Project of OS
Moving vectors = Local residuals
Links PRE-POST as Point Identities
Links PRE-CUST as Point Identities
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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Thank you for your attention!
[email protected]
Frank Gielsdorf, Eckhardt Seyfert: The PAI Approach of the Surveying Administration Brandenburg
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