Extension of the DFHRS-Approach. Gravity Observations and Computation Design for a 1cm fitted DFHRS of Europe

Transcription

1 Extension of the DFHRS Approach for Gravity Observations and Computation Design for a 1cm fitted DFHRS of Europe Reiner Jä ger and Sascha Schneid Hochschule Karlsruhe für Technik und Wirtschaft - University of Applied Sciences Faculty of Geoinformatics Studiengang Vermessung und Geomatik & International Programme Geomatics (MSc) Institut fü r Angewandte Forschung (IAF) Moltkestrasse 30, D Karlsruhe

2 DFHRS-Concept Idea: All observations / data types to set in relation to the parameters p of a continuous one layer representation NFEM(p) of the HRS - Adjustment. NFEM(p) N(p k) NFEM( p B, L) N(p k ) = [1 x y x xy y x x y xy...] [p00 p10 p01 p20 p11 p02 p30...] k = : T = f pk + ContunuityConditionsalongthe Borders N(p k )= Local Taylor- Series Expansion of the HRS

3 Digital FEM Height Reference Surface (DFHRS)- Concept Complete New Computation of con- tinuous HRS (p and D m)! DFHRS Adjustment Approach State of the Art < 2005 h GNSS + v = H + NFEM(p) - h GPS D m H + v = H N G j + v j = NFEM(p) + N G (d j ) ξ j + v = - F B / M(B) p + ξ (d x,h ) j h j + v = - F L /(N(B) cos(b)) p + η(d x,h ) j NFEM(p) N(p j ) <= GPS/Levelling Fitting Points <= Any number Geoidmodels (Global, regional, local) <= Sets of Deflections from Vertical (Zenith Cameras or Geoidmodels) a 4 π γ ( B) σ Dg S(ψ)dσ + v = NFEM(p) <= Gravity by correlated Geoidmodels In the sense of an 2 step adjustment

4 DFHRS Software Identical Fitting Points (B,L,h;H) Meshes Patches

5 DFHRS Software Every geoidand/or vertical deflection model N can be patched Hochschule fü r Technik und Wirtschaft - University of Applied Sciences LVA Baden-Wü rttemberg LVA Hessen LVA Rheinland-Pfalz LVA Riga, Latvia University of Federal Forces Munich University Darmstadt N G (d j )

6 DFHRS Approach - Patching NG j + v j = NFEM(p) + NG(d j ) Residuals of a Geoid Model NG One Datum 7 Patches

7 Accuracy Surface based on DFHRS_DB - Quality Proof Kovariance Matrix of the DFHRS-Parameters (p,δ m) <_3_cm DFHBf_DB Windhuk, Namibia EGM96 + Statistical Tests + Variance-Component-Estimation

8 DFHRS_DB Design Parameters <_3_cm DFHRS_DB Windhuk, Namibia EGM96 Meshsize (p=3) km : HRS approximation error < (5-10) cm 10 km: HRS approximation error <1 cm 5 km: HRS approximation error < 0.5 cm Fitting Point Density (< 10 mm (< 10 mm points,, EGG97) 50 points per (100 km x 100 km): <_1_cm DFHRS_DB 10 points per (100 km x 100 km): < 3_cm DFHRS_DB 3-4 points per (100 km x100 km): < 5-10_cm 5 DFHRS_DB

9 DFHRS_DB Design Parameters Design Studies < 5-10_cm DFHRS Germany Patch-Size (EGG97) km for a < 1_cm DFHRS_DB km for a < 3_cm DFHRS_DB 300 km for a < 10_cm DFHRS_DB (3-5) points per patch

10 <_10_cm DFHBF_DB Europa Isolines 30 km FEM Meshes

11 < 10cm DFHRS Europe Fittingpoint-Design ETRS89/EVRS GPS-/Levelling- Points of EVN Fitting Points NFEM(p) =: h - H Used for the 1st Version < 10_cm DFHBFS Europe

12 <_10_cm DFHRS_DB - Indepent Quality Control <1_dm EVRF2004 (Present Version, 35 km meshes, 34 Patches) Austria Germany Estonia Latvia Lithuania Switzerland Number of unused control points RMS [cm]

13 European HRS. including Baltics (Latvia, Estonia, Lithuania) <(1-3)cm_DFHRS Baltics 10 km FEM Meshes Master Thesis of Mrs. Lauma Lace, Latvia at Karlsruhe University of Applied Sciences

14 European HRS including < 3cm DFHRS_DB Germany 10 km FEM Meshes

15 European DFHRS_DB including New km FEM Meshes < 1 cm DFHRS_DB Hungary Test - Area (50 x 90 ) km 1-2_cm DFHRS_DB Budapest

16 European HRS including < (1-3) cm DFHRS_DB Ungary - Masterthesis in DFHRS- Project & Cooperationproject with A.Kenyeres,Fö mi, Hungary New km FEM Meshes

17 including < 1cm DFHRS_DB Germany < 1cm DFHRS_DB Luxembourg Official State Standard over years 5 km FEM Meshes

18 Overview about European DFHRS_DB 5 km < 1 cm 10 km < 3 cm New km Mesh Size < 10 cm New 2005

19 DFHRS_DB USA New 2005

20 < 5 cm DFHRS_DB Florida ( Masterthesis ) New 2005

21 DFHRS in Practice Trimble MAP500 Trimble Survey Manager

22 DFHRS in Practice

23 DFHRS in Practice TOPSurv many other independent GNSS- Controller Software and GIS Packages GART-2000! New 2005! See

24 DFHRS - Extension to Gravity Observations Gravity Potential of the Earth at position P : W = V + Z n G M n a 2 V = (1 + (C nm cos mλ + Snm sin mλ) Pnm (cos ϑ) and ω 2 Z = r sin r n= 1m= 0 r 2 Gravitational Potential. Coordinate System for Spherical Harmonices = Geocentre Center of Masses n=2 G M n V = (1 + r Observables at point P W g r = W W x y z mit n= 2m= 0 2 x 2 y a r n g = W + W + W 2 z (C nm cos mλ + S nm Wx λ = arctan( ) Wz Wz ϕ = arctan( 2 W + x W sin mλ) P 2 y und nm (cos ϑ) cos ϕ cos λ g cos ϕ sin λ sin ϕ 2 ϑ As observables in an adjustment? Integrated 3D network adjustment (Krarup 1980, Hein 1980) now again in the DFHRS concept

25 DFHRS - Extension to Gravity Observations = DFHRS Concept

26 DFHRS - Extension of Gravity Observations

27 DFHRS - Extension to Gravity Observations = DFHRS Concept

28 DFHRS Extended Observation Equations h GNSS + v = H + f T p H + v = H - h GPS D m NFEM(p) N G j + v j = f T p + N G (d j ) ξ j + v = - f B T / M(B) p + ξ (d x,h ) j N(p k ) h j + v = - f L T /(N(B) cos(b)) p + η(d x,h ) j a 4 π γ ( B) σ g Dg S(ψ)dσ + v = NFEM(p)= f T p n G M a n P + v = (n 1) ( δcnm cosmλ + δsnm sin mλ) Pnm(cosϑ) 2 r n= 2 r m= v = f T p - G M a γ (Q) a n 2 r n+ 1 n = m= 0 ( δc nm cos mλ + δs nm sin mλ) P nm (cos ϑ)

29 DFHRS Extension to Gravity Observations Spherical Cap Cap P Harmonics g P (r, η, ϑ) = = G M r 2 Q0 n k = 2m= 0 a r Q0 n k (m) (n k (m) 1) (C n k (m),m cos mλ + S n k (m),m sin mλ) P n k (m),m (cos( ϑ))

30 DFRHS Extension to Gravity Observations Integration of Gravity Observations into the DFHRS-Concept and the DFHRS-Software and Application to the Gravity Data of Baden-Würrtemberg

31 DFRHS Extension to Gravity Observations Protocol Extract DFRHS Software - Identical Points Normal Heights H Punktnummer Höhe/Zielsys. Verb. Std.abw. [m] [m] [m] : : : :

32 DFRHS Extension to Gravity Observations Protocol Extract DFRHS Software - Gravity Anomaly Observations Nr B L H Dg v r(%) NV :: :: :: :: :: :: :: ::

33 DFRHS Extension to Gravity Observations Geodetic Network Optimization - 1st/2nd/3rd Order Design: A,P =>C p

34 GNSS-Age GNSS-Positioning Summary and Conlusions Fundamental Transformation / Transition Problems Solution Concept for Heighting - Strict mathematical base for continuous FEM_HRS & *DFHRS-Software* - New concept for an overdetermined BVP =>parametric HRS determination - Mesh and patch-design => Any accuracy and any! area size (<= FEM) - Open for all geometrical & physical (e.g. gravity) observations! - DFHRS = (Leading) Geoidfitting Concept - Ready for 1 cm EVRS using existing data +EPN densification fitting-points! - High practical relevance for GNSS services and GIS - Industrial Standard in GNSS-Equipment and GIS - DFHRS_DB => RTCM 3.0 Message used in GNSS-Services, NTRIP etc. - High Capacities for International Co-operations