RTCM coördinaat transformatie berichten

7/31/2019 RTCM cordinaat transformatie berichten

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Motivation RTCM Transformations Questions

RTCM coordinate transformationand Projection messages

Hydrographic Society BeNeLux

Alain Muls & Peter Fardeau

Royal Military Academy

Department ofCommunications, Information, System & Sensors

[email protected]@rma.ac.be

A. Muls, P. Fardeau, RMACISS, RMA Mai 2012 RTCM Transformation & Projection Messages


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Motivation RTCM Transformations Questions Surveyors needs Schematics

Motivation of RTCM MT 10211027

Surveyors and Geodetic Datums RTCM basics

GNSS-RTK positioning is based on RTCM messages 10011004 Evolution from single base station to network approach Coordinates derived from RTCM GNSS-RTK measurements are

determined in the Coordinate Reference System (CRS) of the GNSSservice provider

surveyor needs to transform these coordinates to another local/nationalhorizontal and vertical datum



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Surveyors and Geodetic Datums

RTCM basics GNSS-RTK positioning is based on RTCM messages 10011004 Evolution from single base station to network approach Coordinates derived from RTCM GNSS-RTK measurements are

determined in the Coordinate Reference System (CRS) of the GNSSservice provider

surveyor needs to transform these coordinates to another local/nationalhorizontal and vertical datum

Coordinate transformations are a necessity currently transformation parameters, or a model, are calculated and

manually transferred to GNSS receivers simpler and more convenient method needed

RTCM messages that contain

transformation data information about the Coordinate Reference Systems parameters for the local projection system

allow the users of the RTK service to obtain their results in the desireddatum without any manual operations

allow for both horizontal and vertical local datum



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M

X

Y

Z

M

h

M(X, Y, Z) M(, , h)

M

N

E

M(E, N) and H

M

X

Y

Z

M

h

M(X, Y, Z) M(, , h)

M

N

E

M(E, N) and H

geocentriccoordinates

geographiccoordinates

plane projection

inverseprojection

direct

projection

(, , h) (X, Y, Z)

(X, Y, Z)

(, , h)

Target Datum T

Source Datum S

transformation3D Helmert

regression) transformationMolodenski (or

transformationdirect 2D/H

55

60

65

70

75

140

150

145

135

130

h= H+ N

H= h N



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Transformation from ECEF Coordinate System (CS) Local CS Datum transformation : cartesian (X,Y,Z)

S

cartesian (X,Y,Z)

T

Coordinate conversion : cartesian (X,Y,Z) geographic (, , h)

Cartographic projection : geographic (, ) plane coordinates (E,N)

Height transformation : ellipsoidal h orthometric H


C Q S S


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Transformation from ECEF Coordinate System (CS) Local CS Datum transformation : cartesian (X,Y,Z)

S

cartesian (X,Y,Z)T 7-parameter strict Helmert transformation

7-parameter linearised Helmert transformation

10-parameter linearised Molodenski-Badekas transformation

abridged Molodenski transformation

Coordinate conversion : cartesian (X,Y,Z) geographic (, , h) known procedure

Cartographic projection : geographic (, ) plane coordinates (E,N)

Lambert conformal projection

Mercator conformal projection

. . .

Height transformation : ellipsoidal h orthometric H

knowledge of geoid


M ti ti RTCM T f ti Q ti S d S h ti


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Transformation from ECEF Coordinate System (CS) Local CS Datum transformation : cartesian (X,Y,Z)S cartesian (X,Y,Z)T

7-parameter strict Helmert transformation

7-parameter linearised Helmert transformation

10-parameter linearised Molodenski-Badekas transformation

abridged Molodenski transformation

RTCM MT 1021 & 1022

Coordinate conversion : cartesian (X,Y,Z) geographic (, , h) known procedure

classical procedures Cartographic projection : geographic (, ) plane coordinates (E,N)

Lambert conformal projection

Mercator conformal projection

. . .

RTCM MT 1025, 1026 & 1027

RTCM MT 1023 & 1024 Height transformation : ellipsoidal h orthometric H

knowledge of geoid

RTCM MT 1023 & 1024A. Muls, P. Fardeau, RMACISS, RMA Mai 2012 RTCM Transformation & Projection Messages

Motivation RTCM Transformations Questions MT 1021 & 1022 MT 1023 & 1024 MT 1025 & 1026 & 1027


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RTCM Transformation Messages

3-D Coordinate Transformation Formulas Generalities

Y

X

Z

MZt

G

Xt

Yt

Zs

Ys

O

yx

Xs

z

7 parameters needed for 3Dsystem transformation

3 translation parameters(X,Y,Z)

3 rotation parameters (X, Y, Z) 1 scaling parameter

S= 1 + 106




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Y

X

Z

MZt

G

Xt

Yt

Zs

Ys

O

yx

Xs

z




S= 1 + 106

RTCM Datum Transformations Linearised Helmert transformation (

X

, Y

, Z

)

XYZ

T

=

XYZ

+ (1 + 106)

1 z yz 1 xy x 1

XYZ

S




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Y

X

Z

MZt

G

Xt

Yt

Zs

Ys

O

yx

Xs

z




S= 1 + 106

RTCM Datum Transformations Linearised Helmert transformation (X, Y , Z)

XYZ

T

=

XYZ

+ (1 + 106)

1 z yz 1 xy x 1

XYZ

S

Helmert strict formula if not (X, Y , Z )




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3-D Coordinate Transformation Formulas RTCM Datum Transformations

Molodenski-Badekas transformation with local rotation point (XP,YP,ZP)(X, Y , Z )

XYZ

T

=

XYZ

+ (1 + 106)

1 z yz 1 xy x 1

XXPYYPZZP

+

XPYPZP




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3-D Coordinate Transformation Formulas RTCM Datum Transformations

Molodenski-Badekas transformation with local rotation point (XP,YP,ZP)(X, Y , Z )

XYZ

T

=

XYZ

+ (1 + 106)

1 z yz 1 xy x 1

XXPYYPZZP

+

XPYPZP

Abridged Molodenski Transformation

based on difference between ellipsoids (da, df) determines corrections on geodetic coordinates (d, d)




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3-D Coordinate Transformation Formulas

RTCM MT 1021/1022 structure




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3-D Coordinate Transformation Formulas RTCM MT 1021/1022 structure




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3-D Coordinate Transformation Formulas RTCM Computation Indicator (DF150)

determines which datum transformation formula to apply

room for new procedures RTCM Height Indicator (DF151)




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3-D Coordinate Transformation Formulas RTCM Computation Indicator (DF150)

determines which datum transformation formula to apply

room for new procedures RTCM Height Indicator (DF151)

determines whether height result is geometric (ellipsoidal) or physical(orthometric)

geoid model applied either on target or source datum grid interpolation technique used




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RTCM Residual Messages

Generation of transformation messages service provider calculates the transformation parameters based on a

grid of n= 16 points centered around the rover position

RTCM MT 1023 based on (, )

RTCM MT 1024 based on (E,N)




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grid of n= 16 points centered around the rover positionRTCM MT 1023 based on (, )

RTCM MT 1024 based on (E,N) Two grid concepts

Static grid reference transformation of a country (or service area) applied to N points of source & target datum with N n obtain 7 (10) parameters & N residuals vector extract n= 16 grid out of national grid centered around rover position sent to rover




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Static grid reference transformation of a country (or service area) applied to N points of source & target datum with N n obtain 7 (10) parameters & N residuals vector extract n= 16 grid out of national grid centered around rover position sent to rover

Dynamic grid

dynamically generate n= 16 grid around rover position obtain 7 (10) parameters & n residual vectors sent to rover




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Static grid

reference transformation of a country (or service area) applied to N points of source & target datum with N n obtain 7 (10) parameters & N residuals vector extract n= 16 grid out of national grid centered around rover position sent to rover

Dynamic grid

dynamically generate n= 16 grid around rover position obtain 7 (10) parameters & n residual vectors sent to rover

Applies also to the height component using geoid model



C f


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3-D Coordinate Transformation Formulas Example : Parc du Cinquantenaire Brussels



RTCM T f i M


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Common points: Source coordinates | Target coordinates

23g11 4016764.5458 310230.5629 4928203.5147 | 4016698.0708 310135.8128 4928208.1822

31b14 4022786.4028 299909.2424 4924003.9429 | 4022719.6595 299814.9517 4924008.7406

31d07 4022324.9114 314447.7170 4923485.5479 | 4022258.2780 314352.7590 4923490.4010

31d13 4023385.2314 318752.8584 4922380.0632 | 4023318.5904 318657.6998 4922384.9681

31g17 4026579.7847 308408.9864 4920442.3940 | 4026512.9663 308314.2949 4920447.3406

31g18 4027340.7332 309092.6684 4919783.1311 | 4027273.8977 308997.9441 4919788.1083

31u16 4024002.7098 307108.2089 4922578.6215 | 4023935.9703 307013.5839 4922583.4869

32d02 4022194.0961 312028.9645 4923754.1773 | 4022127.4508 311934.1179 4923759.0140

Gravity center on source system

Gravity 4023172.3019 309997.4011 4923078.9241 50.849514580 4.406104202 111.989

Parameters of Affine Helmert Transform

Translation [m]

-66.6914

-94.7556

4.8561

Scale factor [-]

0.999957827Rotations [rad] [arcsec]

-0.000002759 -0.569153

0.000001616 0.333348

0.000005497 1.133788

Standard Deviation [m]

0.02414



RTCM T f ti M


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Source datum: WGS84

Target datum: BD72

Common points

Source coordinates X [m] Y [m] Z [m]

Target coordinates X [m] Y [m] Z [m]

Transformed coords X [m] Y [m] Z [m]

delta dX [m] dY [m] dZ [m]

------------------------------------------------------------

31d07 4022324.9114 314447.7170 4923485.5479

4022258.2780 314352.7590 4923490.4010

4022258.2796 314352.7773 4923490.3978

0.0016 0.0182 -0.0032

31u16 4024002.7098 307108.2089 4922578.6215

4023935.9703 307013.5839 4922583.4869

4023935.9683 307013.5720 4922583.4921

-0.0020 -0.0119 0.0052

..... ............ ........... ............

All points

Source X [m] Y [m] Z [m] Latitude [d] Longitude [d] EllH [m]

Target X [m] Y [m] Z [m] Latitude [d] Longitude [d] EllH [m]

----------------------------------------------------------------------------------------------------31d07 402232 4.9114 314 447.717 0 49 23485.5 479 50.855 311041 4.4 700413 89 11 1.374

4022258.2796 314352.7773 4923490.3978 50.856658001 4.468770965 127.586

31u16 402400 2.7098 307 108.208 9 49 22578.6 215 50.842 443447 4.3 643012 06 10 7.334

4023935.9683 307013.5720 4922583.4921 50.843789967 4.363033603 131.593

PRK02 402400 8.6759 309 089.371 7 49 22469.7 554 50.840 729840 4.3 923391 10 12 2.182

4023941.9452 308994.6515 4922474.6361 50.842076685 4.391070879 116.767

PRK03 402402 6.0866 309 083.452 7 49 22456.0 371 50.840 534133 4.3 922363 97 12 2.221

4023959.3552 308988.7327 4922460.9184 50.841880986 4.390968173 116.729

PRK07 402400 9.4592 308 997.542 3 49 22471.5 276 50.840 783468 4.3 910384 14 11 9.609

4023942.7279 308902.8259 4922476.4080 50.842130300 4.389770212 119.339

..... ............ ........... ............ ............ ........... ........



RTCM P j ti M


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RTCM Projection Messages

From geocentric to plane state coordinates MT1025 projection parameters other than Lambert Conic Conformal

with 2 standard parallels and Oblique Mercator MT1026 Lambert Conic Conformal with 2 standard parallels MT1027 Oblique Mercator


Motivation RTCM Transformations Questions


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Questions ?


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RTCM coördinaat transformatie berichten