MINISTERIO DE FOMENTO DIRECCIÓN GENERAL DEL INSTITUTO GEOGRÁFICO NACIONAL GRID ESTIMATION. APLICATION TO DATUM DISTORTION MODELLING Javier Glez. Matesanz

MINISTERIODE FOMENTO

DIRECCIÓN GENERALDEL INSTITUTOGEOGRÁFICONACIONAL

GRID ESTIMATION. APLICATION TO DATUM DISTORTION MODELLING

Javier Glez. Matesanz

Adolfo Dalda Mourón

Instituto Geográfico Nacional



National Network using Spatial Techniques

REGENTE

ED50-ETRS89 Differences

(Regidor 2001)



Low Order Network

Objective:– Predict datum

changes in the low order network



Objectives

OneOne transformation

Simple to applySimple to apply

Friendly for any spatial information data user

Efficient,Efficient, capable of transforming great amounts of data

SIG funcionality

Capable of imitate a re-adjustment of a network, changes in shape and systematic effects.

Removing distortions due to regional perturbations of local geodetic networks

(Collier 1992)



7Parameters transformation

Spatial Coord.

Geoidal model

Heterogeneity– 2 areas:

• NW

• rest

890

0

0

501

1

1

)1(

ETRSxy

xz

yz

EDZ

Y

X

Z

Y

X

Z

Y

X

890

0

0

501

1

1

)1(

ETRSxy

xz

yz

EDZ

Y

X

Z

Y

X

Z

Y

X

P

Z

YX

RX

RZ

RY

X

Z

Y

P

Z

YX

RX

RZ

RY

X

Z

Y



7 PARAMETER

Difficulties finding unique transformation

Simply to apply. Geoid

Efficient



Polynomial transformation

Real and complex variablesHeterogeneous behavior absorbingUnique transformationRegression models controls

...' 37

265

24321 CCCCCCC ...' 3

72

652

4321 CCCCCCC

...'''''''' 37

265

24321 CCCCCCC ...'''''''' 3

72

652

4321 CCCCCCC

n

j

jjj iiKKi

0

' ))((''

n

j

jjj iiKKi

0

' ))((''

Statisticscomputation

Regression of yover (x1,...xk)

Smallest t

Drop the variable

tmin>t

End

iiRkn

qst

ˆ

ˆ1

No

Yes

Statisticscomputation

Regression of yover (x1,...xk)

Smallest t

Drop the variable

tmin>t

End

iiRkn

qst

ˆ

ˆ1

No

Yes




Complex variable




Real variables



Polynomial transformationComparison– Truth “REGENTE”

– Complex V.– Real V.


DIRECCIÓN GENERALDEL INSTITUTOGEOGRÁFICONACIONAL Distortion modelling

BEST CONFORMALMODEL

Shape change

Systemchange

JOINTTRANSFORMATION

DISTORTIONMODELLING

Prediction



Distortion modelling

System A

TranslationRotation

System A

TranslationRotation



Longitude distortion



Latitude distortion



Minimum Curvature Surface method

• Metal plate behaviour • Soft surface



Minimum Curvature Surface method

D

P

y

w

yx

w

x

w

4

4

22

4

4

4 2D

P

y

w

yx

w

x

w

4

4

22

4

4

4 2

02

2

2

2

y

u

x

u

x0

2

2

2

2

y

u

x

u

x

020u)uuu8(u-

)uuu2(u

uuu

ji,1-ji,1ji,j1,-ij1,i

1-j1,-i1-j1,i1j1,-i1j1,i

2-ji,j2,-i2ji,,22,,2

jijiji uuu

020u)uuu8(u-

)uuu2(u

uuu

ji,1-ji,1ji,j1,-ij1,i

1-j1,-i1-j1,i1j1,-i1j1,i

2-ji,j2,-i2ji,,22,,2

jijiji uuu

Ie. NADCON



Rubber Sheeting method

T. Delaunay

Ie Great Britain

y

x

y

x

y

x

ED

ED

yyxx

yyxx

ETRS

ETRS

50

50

89

89

cossin

coscos

y

x

y

x

y

x

ED

ED

yyxx

yyxx

ETRS

ETRS

50

50

89

89

cossin

coscos



Rubber Sheeting method

T. Delaunay.Virtual points needed to allow linear behaviour out of the border



Least Squares Collocation method

d1

d5

d4

d3

d2

)5()4()3()2()1( dCdCdCdCdCCl

)0()54()53()52()51(

)45()0()43()42()41(

)35()34()0()32()31(

)25()24()23()0()21(

)15()14()13()12()0(

CdCdCdCdC

dCCdCdCdC

dCdCCdCdC

dCdCdCCdC

dCdCdCdCC

CD

54321

1DIP CC 1

DIP CC



Least Squares Collocation

Mmcc prediction

Signal estimation

Ax=K+s+n

Ie Australia, Canada

1DIP CC 1

DIP CC

2)/(2

12

0 ))/(2

11()(

dsedsCsC

2)/(2

12

0 ))/(2

11()(

dsedsCsC

Longitude Covariance



TEST AREA (Castilla La Mancha)

Readjustment of low order network in ETRS89

~1400 external points. Not taken into account to build the tree grids

(JSSobrino 2002)



Comparison

Test Castilla La Mancha

Overall goodness of fit

Method

MC

S

LSC

Rub

ber

S.

Goo

dnes

sof

fit

2iRGajG 2

iRGajG



Points < 25cm

MCS

LSC

Rubber Sheeting


DIRECCIÓN GENERALDEL INSTITUTOGEOGRÁFICONACIONAL Conclusions

ABSORBDISTORTION

SIMPLE

READJUSTMENT

UNIQUE

EFFICIENT

FRIENDLY

SIG

Documents

MINISTERIO DE FOMENTO DIRECCIÓN GENERAL DEL INSTITUTO GEOGRÁFICO NACIONAL GRID ESTIMATION. APLICATION TO DATUM DISTORTION MODELLING Javier Glez. Matesanz