dfhbf 5.0 -a new integrated geodesy approach for ...dfhbf.de/files/dfhrs_5.0.pdf3 4 trimble vrsnow 4...
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Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
DFHBF 5.0 DFHBF 5.0 -- A New Integrated Geodesy Approach A New Integrated Geodesy Approach for Regional Gravity Field Modelling and Height for Regional Gravity Field Modelling and Height
Reference Surface ComputationReference Surface Computation --Prof. Dr.-Ing. Reiner Jäger
Hochschule Karlsruhe Technik und Wirtschaft (HSKA) - University o Applied SciencesFaculty for Informationsmanagement and Media (IMM)
Dean of Master Study Programmes Geomatik&Geomatics (MSc)
Head of Institute of Geomatics and Projectleader at Institute for Applied Research (IAF)RaD
www.dfhbf.de , www.goca.info, www.monika.ag , www.geozilla.de , www.moldpos.euwww.navka.de , www.e-volo.com
Honorary Professor of the Sibirian State Academy of Geo desy (SSGA)
Email: [email protected]
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Study Programmes of the Faculty IMM with Study Programmes of the Faculty IMM with Contents related to Geodesy and NavigationContents related to Geodesy and Navigation
((www.hswww.hs --karlsruhe.dekarlsruhe.de ))Research Oriented (BSc Research Oriented (BSc –– MSc MSc –– PhD)PhD)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
HeightHeight System and System and
Height ReferenceHeight Reference Surface TypesSurface Types
((QGeoid/Geoid)QGeoid/Geoid)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Height System Types for Physical Heights H
HH
GeoidGeoid =: W= W=: W= W00Ideal Height Reference Ideal Height Reference
SurfaceSurface (HRS)(HRS)
hhNN
22
2),,,,,(
),,(),,( pzdydxd
zyxzyxl
zyxzyxWW
Erde
P ⋅+′⋅′⋅′′′′
′′′== ∫∫∫
ωρ
APoP WWC −= i
E
AiAP ngCC ∆⋅+= ∑
P
PorthP
P
PNormalP g
CHbzw
CH == ,, .
γ
GepotentialNumber C
Levelling andund Gravity Terrestrial HRS Realisation
H=constH=const . . Small areasSmall areas~ ~ „Constant„ConstantWaterlevel“Waterlevel“
EUROPE DHHN‘92EUROPE DHHN‘92
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
)(cosP)msinSmcosC(r
a1(
r
MGV nmnmnm
n
2n
n
0mϑ⋅λ⋅+λ⋅⋅
+⋅⋅= ∑ ∑∞
= =
Gravity Potential W of the Earth at Point P(r, λ, )
ZVW +=ϑ⋅⋅ω= 22
2sinr
2Z
Gravitationpotential of Earth (Masses)
Centrifugalpotenzial due to Eartrotation
Hg
NN QGG ⋅γ
γ−+=
Q-Geoid- Normal Heights
Geoid (W=W o) - Orthometric Heights)
ϑ
Spherical Harmonics asals Carrierfunctions and
Parameters
HBFHBF
Q
80GRSOG
)u,ß,(U),,r(W),,r(N
γλ−ϑλ=ϑλ
Height Reference System Types for Physical Heights H
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Precise Precise GNSSGNSS PositioningPositioning ServicesServices
Regional => GlobalRegional => GlobalDGNSS => Absolute GNSSDGNSS => Absolute GNSS
Paradigma Change: LowCost Paradigma Change: LowCost Hardware Hardware –– High Cost AlgorithmsHigh Cost Algorithms
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GNSS GNSS -- SystemsSystems
GNSS GNSS -- GlobalGlobal Navigation Satellite SytemsNavigation Satellite Sytems
GPSGPS
GALILEO GALILEO 20162016
GLONASSGLONASS COMPASSCOMPASS
Space Segment
User Segment Control Segment
~~ 50 50 (2013)(2013)
105! 105! (2016)(2016)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
12
3
4
TRIMBLE VRSNOW
RegionalRegional PrecisePrecise GNSSGNSS--PositioningPositioning Services Services e.ge.g. Germany. Germany
(B,L,h) ITRF-relatedAccuracy: 1-3 cm!!!
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
2
3
4
TRIMBLE VRSNOW
4 RTCM Services: 1-3 cm Horizontal and HeightGeodetic Infrastructures for GNSS-Services (GIPS) :
www.moldpos.eu
1
SRPOS SRPOS SiberiaSiberia
RegionalRegional PrecisePrecise GNSSGNSS--PositioningPositioning Services Services -- WorldwideWorldwide
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
•• SSRSSR--basedbased : Abs. : Abs. PrecPrec . OPPP. OPPP•• Starfire™GPSStarfire™GPS --CorrectionsCorrections•• StarfireStarfire Receiver (Receiver ( leftleft ))•• Global Global AccuracyAccuracy : „dm“: „dm“
OSR (= Observation-)related: Networked, scalabe („dm – cm“ ) DGNSS RTCM Correction (VRS-Concept)
• RTCM-Standard =>Open for any Rover- and Software-Type
Abs. GNSS = „Non-DGNSS “No Reference-Stations
But : NAVCOM Roverclients!
„„ GlobalGlobal G(lobal“)NSS Precise PositioningG(lobal“)NSS Precise Positioning Services Services -- WorldwideWorldwide
1
2
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
International GNSS-Service (IGS) - Online SSR Models, since April 2013
„„ GlobalGlobal G(lobal“)NSS Precise PositioningG(lobal“)NSS Precise Positioning Services Services -- WorldwideWorldwide
3„RTS“: http://rts.igs.org/
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Low Cost High Precise GNSS
1.) „LowCost- High-Precise“ – „Software-Receiver“
3.) RTKLIB Open Source …. NAVKA-GNSS-Algorithms(www.navka.de)
=> GNSS + => GNSS + MEMS:MEMS: „Multisensor „Multisensor –– Platforms (NAVKA)“Platforms (NAVKA)“
2.) Online Precise Point Positioning (OPPP) „Absolute GNSS“
…. and Low -Cost GNSS -PositioningTrends
„Smartphone RTK“
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GeodeticGeodetic InfrastructuresInfrastructuresforfor
GNSS Positioning ServicesGNSS Positioning Services(GIPS)(GIPS)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
e.g www.moldpos.eu
www.dfhbf.de
www.monika.ag www.goca.info
Geodetic Infrastructures for GNSSGeodetic Infrastructures for GNSS –– Positioning Service (GIPS)Positioning Service (GIPS)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
DFLBF / DFLBF / DFHBFDFHBF
GIPS-3- RTCM-Transformationmessages (2007) - Former use of Reference Transformations on GNSS - Controllers
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
MOLDPOS- Project www.moldpos.eu• Karlsruhe University of Applied Sciences (HSKA)• Agency for Land Relations and Cadastre Moldova (ALRC)• Technical University of Moldova (TUM)
GIPS-3 - RTCM-Transformationmessages (2007) – Present use of Reference Transformations by GNSS Positioning Services Prov iders
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Area of validity for the 7PT Transformation (Origin,Ex tension and + 16 Gridpoints)
GIPS-3 - RTCM-Transformationmessages (2007) – Present use of Reference Transformations by GNSS Positioning Services Prov iders
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
RCTM-Messages 1021 or 1022
GridLocation&Size
7 Parameters
Ellipsoid Parameters
Source / Target
Geoid -QGeoid
Grid
GIPS-3 - RTCM-Transformationmessages (2007) – Present use of Reference Transformations by GNSS Positioning Services Prov iders
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
MessageMessage 10231023 Message 1024or
Height Indicator = 1 „dh i„ = Physical Heights‘ Residuals dH i
Height Indicator = 2 „dh i„ = Geoid / HRS Heights N i (dN i)
Residuals P 14
Residuals P 15
Residuals P 16
:: ::
GIPS-3 - RTCM-Transformationmessages (2007) – Present use of Reference Transformations by GNSS Positioning Services Prov iders
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPSGIPS--11
Continuous Datumtransformation Parameters between
SG95 and SC42 for
SRPOS GNSS Positioning Service(Novosibirsk Region)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS-1 Continuous Datumtransformation Paramet ers between SG95 and SC42 for SRPOS (Novosibirsk Region )
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS-1 Continuous Datumtransformation Paramet ers between SG95 and SC42 for SRPOS (Novosibirsk Region )
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPSGIPS--2 2
HeightHeight ReferenceReference SurfaceSurface
((QGeoidQGeoid//GeoidGeoid))
DFHBFDFHBF--Approach Version 4.0Approach Version 4.0
StageStage 11
„„GeometricalGeometrical Approach“Approach“
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS-2 DFHBF 4.0 - FEM Representation of HRS
( ) ( ) ( ) ( )
⋅⋅−=
−=
∆∆∆
∑∑=
−
=
l
i
il
j
ji
mijnijmnnm
nm
nm
xyaaxyNxyNxyN
y
x
0 0,,,
,
,
0
0
,,,,
0
0
, pp
3D difference at any point P(x,y) along the border SA_SE of themeshes m and n has to vanish
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
( ) ( )( ) ( )( ) ( ) ! 0tNxxtxyytyaa n,mj
sasesai
sasesal
0i
il
0jm,ijn,ij ≡∆=−⋅+⋅−⋅+⋅−∑
=∑−
=
( )
⋅⋅−=
∆ ∑=
∑−
=
l
0i
il
0j
jim,ijn,ijmn,
xyaa
0
0
N
0
0
( ) ! 00
2210, ≡⋅=⋅++⋅+⋅+=∆ ∑
=
l
k
kk
kknm tctctctcctN L
( ) l,0k ,0x,y;x,y;;c sesesasank ==ppm
( ) ( ) ( ) ( )
⋅⋅−=
−=
∆∆∆
∑∑=
−
=
l
i
il
j
ji
mijnijmnnm
nm
nm
xyaaxyNxyNxyN
y
x
0 0,,,
,
,
0
0
,,,,
0
0
, pp
GIPS-2 DFHBF 4.0 - FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Result: Continuous Height Reference Surface: NFEM(p)
( )
( )
∑ ∑ ⋅=⋅=
= =
−
=
nm2,1,0
l
0i
il
0jk
Tjik,ijk
FEM
;C
xyaNN
pp
pfp
GIPS 2 - DFHBF 4.0 - FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
EGG97 EuropeanGravimetric QGeoid 97
and othersNon-fitted Stokes-
based models
Mean- up to lang-wavedErrors
0.1 – 1.5 m !
Weak-Shapes of Classical
Gravimetric„Geoid“models
∫∫==Ψ
⋅⋅⋅∆−∆
+=π
α
ψ
αψψπγ
2
0Re
0
Re
)()(4
0
ddSgga
NN
f
f
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Tallinn Tallinn ExampleExample
EGG97-QGeoid
withoutDatum∂∂∂∂N(d)
+/- 3.5 cm „Tilt“
15km
15mm
Net
Residuals
GIPS-2 - DFHBF 4.0 „Patching“ ∂∂∂∂N(d) using Identical Points
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Tallinn Tallinn ExampleExample
EGG97-QGeoid
WithDatum∂∂∂∂N(d)
+/- 4 mm 15kmNet
20mmResiduals
HBF:= NG + ∂NG(d)
GIPS-2 DFHBF 4.0 „Patching“ ∂∂∂∂N(d) using Identical Points
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
hGNSS+ v = H + NFEM(p) - hGPS·∆∆∆∆ m
H + v = H
NG‘ j + v j = NFEM(p) + ∂NG(d j)
ξj + v = - FB / M(B) ⋅ p + ∂ ξ (dξξξξ,ηηηη) j
ηηηη j + v = - FL/(N(B)⋅cos(B)) ⋅ p + ∂ η(dξξξξ,ηηηη) j
Complete New Computation of continuous HRS ( p and ∆∆∆∆ m)!
DFHRS – Adjustment ApproachState of the Art < 2005< 2005
)(4 ∫∫σγ⋅π⋅ B
a ∆∆∆∆g·S(ψ)dσ + v = NFEM(p)
NFEM(p)
N(p j)
(Global, regional, local)
<= Sets of Deflections from Vertical
(Zenith Cameras or Geoidmodels)
<= GPS/Levelling Fitting Points
<= Any number Geoidmodels
<= „Gravity“ by correlated GeoidmodelsIn the sense of an 2 step adjustment
GIPS- 2 DFHBF 4.0 - Approach FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Software 4.2Software 4.2SreenshotSreenshot
•• IdenticalIdentical„Fitting“„Fitting“PointsPoints
((B,L,h;HB,L,h;H))
•• MeshesMeshes
www.dfhbf.dewww.dfhbf.de
GISP- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
-- DataBasesDataBases
Quasi-Geoid N QG Quasi-Geoid N G
Hg
NN QGG ⋅γ
γ−+=
Hg
NN QGG ⋅γ
γ−+=
GISP- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
11 -- 3 cm D
FH
BF
3 cm
DF
HB
F D
atabasesD
atabases
DFHBF--DLL/-Tools
DFHBF-Software
11--3 cm DFHBF_DB 3 cm DFHBF_DB … … GrmanyGrmany
< 1 cm (Bayern, < 1 cm (Bayern, BaBa--WüWü, RLP, Saarland, Hessen), RLP, Saarland, Hessen)
…… Estonia,Estonia, Latvia,Latvia, Lithuania (2012/13)Lithuania (2012/13)
…… HungaryHungary
NFEM(p)
GIPS- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
11-- 5 cm5 cmDFHBF_DBDFHBF_DB
FloridaFlorida
NFEM(p)
GIPS- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
www.dfhbf.dewww.dfhbf.de
Geoid-Computationfor Brazil: Patches
and Meshes
Brazil 2012
GIPS- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
www.moldpos.eu 1-3 cm Quasigeoid for Moldova (2011)„Patching“ of
EGG97 or EGM2008 GPMnearly same results
GIPS- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Punktnummer Höhe/Zielsys. Verb. [m]---------------------------------------------
11137 99.982 0.00330 11138 11.353 0.00539 11230 155.743 0.00623 11255 140.332 0.00792 11292 44.045 0.00634 11298 240.484 0.00805 11329 421.242 -0.00335 11463 940.048 0.00337 12339 15.261 -0.01416 12446 531.371 -0.01271 12475 381.966 0.00075 12486 374.872 0.01078 12492 621.275 0.02941 12583 1344.926 -0.03352 12608 952.015 0.00000 12643 926.835 -0.01037 12656 1224.130 0.01931 12687 1037.405 0.01431 13647 1448.707 -0.03311 13674 332.859 0.02693 13678 103.174 -0.00026 13758 310.588 -0.00993 13779 383.962 0.00097 13840 1053.998 0.03660 13844 848.199 -0.04238 65100 376.512 0.01078
124102 361.056 0.02017 440_1 177.386 0.00076
631 847.169 -0.00950 1103 810.053 0.01804 6399 9.201 0.01604
1176_1 228.362 -0.02767 1384_1 867.251 0.03291
641_1 1069.442 -0.02536
GIPS- 2 DFHBF 4.0 – Based on FEM Representation of HRS
Pktr Höhe/Zielsys. Verb. [m] ------------------------------------
502 282.914 0.00832 547 466.421 -0.00113
1721 156.942 -0.00766 5121 1154.851 0.01081 5256 1773.778 0.03211 5332 348.495 -0.01315 6331 73.973 0.00021 6333 25.473 0.00546 6484 1143.221 0.00108 6583 974.753 0.00699 6585 944.169 -0.02735 7530 274.611 -0.01726 7532 23.566 -0.00566 7618 176.022 0.00680 7685 418.179 -0.02839 7693 732.667 -0.00159 7730 810.063 0.02328 7733 627.059 0.01427 7759 1102.272 0.00026 7783 934.590 -0.00485 7807 1385.507 -0.01562 8844 1150.900 0.00959 8851 111.850 -0.01132
10008 311.618 0.00216 10060 724.697 -0.00568 10066 105.636 -0.01091 10087 190.456 -0.01442 10093 312.034 0.01423 10119 1398.276 0.00175 10190 881.655 -0.00892 10195 1663.985 0.0043410229 1124.945 -0.01924 11125 11.827 -0.00454
Geoid Computation for Geoid Computation for ALBPOS (Albania) 2013ALBPOS (Albania) 2013
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPSGIPS--2 2
HeightHeight ReferenceReference SurfaceSurface
((QGeoidQGeoid//GeoidGeoid))
DFHBFDFHBF--Approach Version 5.0Approach Version 5.0
StageStage 22
„Integrated„Integrated Approach“Approach“
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
CapPP
DFHRS DFHRS -- StageStage 2 2 IntegratedIntegrated „Approach“„Approach“
SpericalSperical CapCapHarmonicsHarmonics
(SCHA)(SCHA)
asas
CarrierCarrier FunctionsFunctionsof of thethe
GravityGravity Potential VPotential V
))'(cosP)'msin'S 'mcos'C(r
a
a
MG)',',r(V m)),k(nm),k(nm),k(n
maxk
0k
k
0m
1)k(n
θ⋅λ⋅+λ⋅∑ ∑
⋅=θλ= =
+
GIPS- 2 DFHBF 5.0 – Based Spherical Cap Harmonics SCHA
)λλcos(φsinφcosφcosφsin)λλsin(.φcos
'λtan000
0−−
−=
)λλcos(φcosφcosφsinφsin'θcos 000 −−=
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
θ0=90°
α0 =90° α 0 = arbitrary
GlobalSpherical-Harmonics(SH)
Spherical Cap Harmonics (SCHA)
5.0)5.0,k(90
)k(nn SCHASHA −+⋅α
°≈=
SCHA „Resolution“ for „2mm QGeoid“n=7200 and u =50.000.000 Coefficients
α = 1° (=110 km area) => k-SCHA = 80 and u = 6.400
3° (=330 km area) => k-SCHA = 250 and u= 62.500α =
α = 25° (Europe) => k-SCHA = 2000 and u =4.000.000
GIPS- 2 DFHBF 5.0 – Based Spherical Cap Harmonics SCHA
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
1. Treatment of Global Gravity Models – Example Baden-W ürttemberg
GIPS- 2 DFHBF 5.0 – Based Spherical Cap Harmonics SCHA
( ) )λ,θ,r(V)'θ(cosP'αmsinS'αmcosCrR
rGM
)'λ,θ,r(V Globalm,nmaxk
0k
k
0m
'nm
'nm
1)k(n
SCHA =+
= ∑ ∑= =
+'
„Mapping“ of Global SCH-Coefficients (e.g.EGM 2008) (Cnm, Snm) to localSCHA-Coefficients (Cnm ‘, Snm ‘)
1.1 3D-Grid Generation
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS- 2 DFHBF 5.0 – Based Spherical Cap Harmonics SCHA
lCAACAx 1l
T11l
T )(ˆ −−−=
1.2 Computation of (C nm,Snm)‘ from (C nm,Snm) as Adjustment
=
nnm
n
mm
10333
11333
10333
10222
11222
10222
10111
11111
10111
PαmsinrR
rGM
PαsinrR
rGM
PαcosrR
rGM
PrR
rGM
rGM
PαsinrR
rGM
PαcosrR
rGM
PrR
rGM
rGM
PαsinrR
rGM
PαcosrR
rGM
PrR
rGM
rGM
M
M
OM
LL
A
[ ]Tnn2011111000 SCSCCCˆ ′′′′′′= LLx
[ ]Tm4321 VVVVV LL=l
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
DFHBFDFHBF -- Extension to SCHAExtension to SCHA
LAVg=
− g
0
0
Sensor-Observation at Position P(x,y,z)
2. Treatmentof Gravity
Observations
LAV
ECFLAV
ECF
z
y
x
g
0
0
),,L,B(R
g
g
g
−⋅ξη=
TLGVgrav ]
r
V,
V
'sinr
1,
'
V
r
1[
∂∂
λ∂∂⋅
θ⋅θ∂∂⋅=g
[ ]ECFlcentrifuga
ECF
z
y
xECF
gravz
y
x
g
g
g
g
'g
'g
'g
−
=
ECFgrav
LGVECF
LGV
gravr
E
N
'g),(R
g
g
g
⋅λϕ=
∑ ∑ θ⋅λ⋅+λ⋅+
=+∞
= =
+
0k
k
0mm),k(nm),k(nm)),k(n
1)k(n
rLGVgrav )'(cosP)'msin'S'mcos'C(
r
)1)k(n(
r
avg
GIPS- 2 DFHBF 5.0 – Based Spherical Cap Harmonics SCHA
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Q
P
Q
PrefQGNormal
T)VV(NNh
γ=
γ−
==−
PQ
pQ
QG
N
QG )B
T(
)hM(
1T
B
1
)hM(
1
B
N
s
B
s
B
B
N
∂∂⋅
+⋅γ−=
∂∂⋅
γ⋅
+−=
∂∂
⋅∂∂−=
∂∂⋅
∂∂
−=ξ,
PQ
PQ
QG )L
T(
Bcos)hN(
1T
L
1
Bcos)hN(
1
L
N
s
L
∂∂⋅
⋅+⋅γ−=
∂∂⋅
γ⋅
⋅+−=
∂∂
⋅∂∂−=η
3. Vertical Deflections from Zenith Cameras (T = (V+Z) – U)
m),k(nm),k(n 'Cv)t('C =+ m),k(nm),k(n 'Sv)t('S =+and
4. Fitting Points Vertical DeflectionsZenith-Cameras
∑ ∑ θ⋅λ⋅+λ⋅+
=+∞
= =
+
0k
k
0mm),k(nm),k(nm)),k(n
1)k(n
rLGVgrav )'(cosP)'msin'S'mcos'C(
r
)1)k(n(
r
avg
2. Gravity Observations rotated to SCHA
www.dfhbf.dewww.dfhbf.dewww.moldpos.euwww.moldpos.eu
1. SCHA-Coefficients computed from global SH as direct observations
Observation Equations - DFHBF Version 5 (Dr.-Arbeit G. Younis)
Gravity-Meter
SatelliteMissions
GIPS- 2 DFHBF 5.0 – Based Spherical Cap Harmonics SCHA
FittingPoints
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPSGIPS--2 2
HeightHeight ReferenceReference SurfaceSurface
((QGeoidQGeoid//GeoidGeoid))
QGeoid Computation QGeoid Computation
BadenBaden--Württemberg Württemberg
„Integrated„Integrated Approach DFHBF 5.0“Approach DFHBF 5.0“
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS- 2 DFHBF 5.0 Integrated Approach – QGeoid Computation Baden- Württemberg -
11--3 cm QGeoid3 cm QGeoidGermany Germany DFHBF 4.0DFHBF 4.0
Reference1cm QGeoid
DHHN92DFHBF 4.0
(2006)
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS- 2 DFHBF 5.0 Integrated Geodesy Approach – QGeoid Computation Baden- Württemberg -
Used Data - Input DFHBF 5.0
- 129 Fitting Points (B,L,h|H)
- 13671 Gravity Values (final)
- EGM2008 Global GPM mapped to SCH
Fitting Points (h-H)
- Mean residual: 8 mm
- 1 blunder detected byData-Snooping Test
1. Output DFHBF 5.0)
•• SCH Degree (m,n(k)) = 300SCH Degree (m,n(k)) = 300
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
Used Data - Input DFHBF 5.0
- 129 Fitting Points (B,L,h|H)
- 13671 Gravity Values (final)
- EGM2008 Global GPM mapped to SCH
Terrestrial Gravity Points g(B,L,h)
- Mean Residual: 0.0032 mGal
- 1031 gravity values eliminated in advance due to wrong georeferencing
- 269 blunders detected in DFHBF V. 5.0 adjustment by datasnooping
2. Output DFHBF 5.0)
•• SCH Degree (m,n(k)) = 300SCH Degree (m,n(k)) = 300
GIPS- 2 DFHBF 5.0 Integrated Geodesy Approach – QGeoid Computation Baden- Württemberg -
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS- 2 DFHBF 5.0 Integrated Geodesy Approach – QGeoid Computation Baden- Württemberg -
Used Data - Input DFHBF 5.0
- 129 Fitting Points (B,L,h|H)
- 13671 Gravity Values
- EGM2008 Global GPM mapped to SCH
=> Mean Residual: 1.3 cm
3. Independent Validation Country-wide Comparison with 1 cm DFHBF 4.0 QGeoid of B.W.
•• SCH Degree (m,n(k)) = 300SCH Degree (m,n(k)) = 300
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
GIPS- 2 DFHBF 5.0 Integrated Geodesy Approach – QGeoid Computation for SRPOS Novosibirsk Region -
DFHBFDFHBF--Database QGeoid for SRPOS: DFHBF Version 4.0 or DFH BF Version 5.Database QGeoid for SRPOS: DFHBF Version 4.0 or DFH BF Version 5. 00To be computed in 2013 at SSGATo be computed in 2013 at SSGA
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger
ConclusionsConclusions
Integrated DFHBF-Approach “DFHBF 5.0” based on Regional Spherical Cap Harmonics Coefficients (Cnm’,Snm’) integrate all relevant original observations - Geometrical data - Physcical data and - Global GPM
DFHBF V 5.0 is worldwide unique and can be used - QGeoid or Geoid Computation (GIPS-2) - Gravity Field Modelling - Integrated Geodetic Networks of all Types
Present results in PhD (12/2012) of MSc Ghadi YounisDAAD funded PhD candidate in the DFHBF RaD project (www.dfhbf.de)
DFHBF 5.0 formulated as Gauss-Markov-Model (GMM)- Stat.Testing of all origina observations, e.g. gravity!
( ... impossible in e.g. Stokes-based approaches)- Open for Optimization- Scalable to any Size of Area
Further Research- Vertical Deflections from Zenith Cameras- Optimum Design for the Use of Gravity and Zenith Camera Data
Interexpo-GeoSiberia 2013 Master-Class „DFHBF 5.0 – Integrated Approach“ R. Jäger