1 / 48

DFHRS (Digital FEM Height Reference Surface)

DFHRS (Digital FEM Height Reference Surface) – A Rigorous Approach for the Integrated Adjustment of Fitted Height Reference Surfaces (HRS) -. Reiner Jäger Hochschule Karlsruhe Technik und Wirtschaft - University of Applied Sciences Faculty of Geomatics

cindy
Download Presentation

DFHRS (Digital FEM Height Reference Surface)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DFHRS (Digital FEM Height Reference Surface) – A Rigorous Approach for the Integrated Adjustment of Fitted Height Reference Surfaces (HRS) - Reiner Jäger Hochschule Karlsruhe Technik und Wirtschaft - University of Applied Sciences Faculty of Geomatics Studiengang Vermessung und Geomatik & International Programme Geomatics (MSc) Institut für Angewandte Forschung (IAF) Moltkestrasse 30, D-76133 Karlsruhe www.dfhbf.de ; www.geozilla.de; www.galileo-bw.de; www.moldpos.eu

  2. Height Systems - Definitions and Terrestrial Realisiation H=const. Small Area ~ „constant Waterlevel“ H h Geoid = Ideal Height Reference Surface (HRS) N Levelling and Gravity Observations Gepotential Numbers C Terrestrial Height Determination A

  3. New European Normal-Height Network EUREF/UELN ‚95/98 Adjustment by Geopotential Numbers (Differences Datumspoint W0 bzw. C0 Amsterdam „NAP“ DHHN‘92 ( Diff.: 1 cm) Accuracy Situation

  4. GNSS-Heightung „Hfrom h-GNSS“ HRS-Model N H Geoid h „HRS“ Quasigeoid h N H = h - N

  5. HRS = Geoid / Quasigeoid – Physical Definition & Realisation Gravity Potential W of the Earth at Point P(r,λ, ) Centrifgal - Potential due to Earth-Rotation Gravitational Potential of the Earth Masses Spherical Harmonics Coefficients as Parameters Q-Geoid Geoid (W=Wo=const) HBF

  6. Satellite Geodetic Methods of Gravity Field Determination • Satellite Laser Ranging (SLR) „LEOS“ (Low Earth OrbitSatellites) LAGEOS 1, 2 STELLA, etc. Original Observation:Laserranges Derived of it:Orbit Disturbances Derived of it: Spherical Harmonics (Müller/Kaula, 1960,1962)

  7. Satellite Geodetic Methods of Gravity Field Determination • Present Missions • Hybride Sensors • Aktice Measurements CHAMP Observation Quantities 1.) Abs. Positionierung via GPS (Black-Jack Receiver/NASA, JPL): x(t) 2.) Relative Orbitmovements by Inter-Satellite Observations: 3.) Precise Accelerometers aiSTAR (Onera/Frankreich): 4.) Gradiometers (e.g. GOCE) Derived of these:1.) Orbit Determinations 2.) Gravitational Accelerations gi(x,t) and Gradiometer-Tensor Derived from that:Spherical Harmonics Coefficients

  8. Satellite Geodetic Methods of Gravity Field Determination H H J H H J [cm] Earth Geopotential Model 96 (NASA) EIGEN ( = European Improved Gravity Model of the Earth by New Techniques)

  9. N(p) Latitude(degree) Longitude(dgree) Satellite Geodetic Methods of Gravity Field Determination DFHRS_DB Namibia and Tanzania: 1.) Identical Points (N=h-H) & 2.) EGM96 bzw. EIGEN-GL04C H H J H H J [cm] Earth Geopotential Model 96 (NASA) EIGEN ( = European Improved Gravity Model of the Earth by New Techniques)

  10. Bilance for Satellite Geodetic GPM(EGM2008; EIGEN) Not sufficient for GNSS-Heighting H = h – N !!! n,m < 500 => N < 0.3 m ! => Further Informationfor further Improvement of the HRS and N necessary! Hybrid and redundant Models! Terrestrial Gravity Measurements Identical Points (H, h) N=h-H “Geoid Fitting“

  11. Hybride Modeling in HRS-Computation 1.) EGG97 - European Gravimetric QGeoid 1997 (IfE, Hannover) Representation GRID Short-Waved: ~ (1 – 3) cm Medium-/Long Waved 0.1-1.5 m ! Weg 1: Stokes-based (h, H)

  12. Hybride Modeling in HRS-Computation 2.) Prof. Dr.-Ing. H.-G. Wenzel – Fitted Geopotenzialmodell (GPM 98) Dgl.-based + + (h, H) n = m = 1800 Accuracy of N ~ (10 - 30) cm Parametrice Represenation (or Grid)

  13. Hybride Modeling in HRS-Computation 3.) „BKG-Model – Parametrisation of the Potentials by additional Mass Points Massen-Points as essential additional Parameters (h, H) Representation of BKG HRS: Grid

  14. DFHRS-Concept Direct - No Identical Points - - Online - Postpro- cessed DFHRS-DB H = hGPS(B,L) - DFHRS(B,L,h)korr H = hGPS(B,L) - (NFEM(p|B,L,h) +∆m·h)

  15. FEM representation of height reference surfaces 3D difference at any point P(x,y) along the border SA_SE of the meshes m and n has to vanish

  16. Continuous Finite Element Representation of HRS

  17. FEM representation of height reference surfaces Result: Continuous Height Reference Surface: NFEM(p)

  18. Digital FEM Height Reference Surface (DFHRS)- Concept Complete New Computation of continuous HRS (p and  m)! DFHRS – Adjustment Approach State of the Art < 2005 NFEM(p) N(pj) hGNSS+ v = H + NFEM(p)- hGPS· m H + v = H NG‘j + v j = NFEM(p) + NG(d j) <=GPS/Levelling Fitting Points <= Any number Geoidmodels (Global, regional, local) • j + v = - FB / M(B) p +  (d,) j  j + v = - FL/(N(B)cos(B)) p + (d,) j <= Sets of Deflections from Vertical (Zenith Cameras or Geoidmodels) g·S()dσ + v =NFEM(p) <= „Gravity“ by correlated Geoidmodels In the sense of an 2 step adjustment

  19. Weak-Shapes of Classical Gravimetric „Geoid“models EGG97 European Gravimetric Geoid 1997 Mean- up to lang-waved Errors 0.1 – 1.5 m ! => New Concepts, more „precise“ or better: (H,h)-fitted solutions

  20. Standard GNSS/GPS-heighting Approaches using identical Points Tallinn Example Pure Geoid-Approach EGG97-Geoid without Datum N(d) +/- 3.5 cm „Tilt“

  21. Standard GNSS/GPS-heighting Approaches using identical Points HBF:= NG + NG(d) Tallinn Example Pure Geoidapproach EGG97-Geoid With Datum N(d) +/- 4 mm

  22. DFHRS Software • Identical • „Fitting“ • Points • (B,L,h;H) • Meshes • Patches

  23. Hochschule für Technik und Wirtschaft • - University of Applied Sciences • LVA Baden-Württemberg • LVA Hessen • LVA Rheinland-Pfalz • LVA Riga, Latvia • University of Federal Forces Munich • University Darmstadt DFHRS Software Every geoid- and/or vertical deflection model N can be „patched“ NG(d j)

  24. DFHRS_DB Design Parameters <_3_cm DFHRS_DB Windhuk, Namibia EGM96 • Meshsize (p=3) • 20-30 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 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 DFHRS_DB

  25. DFHRS_DB Design Parameters Design Studies < 5 - 10_cm DFHRS Germany • Patch-Size (EGG97) • 30 - 40 km for a < 1_cm DFHRS_DB • 50 – 60 km for a < 3_cm DFHRS_DB • 300 km for a < 10_cm DFHRS_DB (3-5) points per patch

  26. < 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

  27. Austria Germany Estonia Latvia Lithuania Switzerland Number of unused control points 9 95 21 25 46 13 RMS [cm] 7.5 4.2 8.8 9.2 6.8 7.0 <_10_cm DFHRS_DB - Indepent Quality Control <1_dm EVRF2004 (Present Version, 35 km meshes, 34 Patches)

  28. Overview about European DFHRS_DB 2003 5 km < 1 cm 10 km < 3 cm 2005 30 km Mesh Size New 2006 < 10 cm

  29. DFHRS_DB - Product as CD-Installation of State Land Services in Germany CopyProtection inclusive

  30. < 5 cm DFHRS_DB Florida (… Masterthesis )

  31. European DFHRS_DB… including < 1 cm DFHRS_DB Ungary Test - Area (50 x 90 ) km 1-2_cm DFHRS_DB Budapest 5 km FEM Meshes DFHRS 4.0 Software

  32. DFHRS in Practice

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

  34. DFHRS - Extension to Gravity Observations Sensor-Observation

  35. Extension of the DFHRS-Concept to Gravity Observations „<1cm-Resolution („2mm“) of HRS“ Instead of classical global spherical harmonics (n=m=7200) Spherical Cap Harmonics (SCHA) Cap P

  36. Sperical- Harmonics l = 2, l = 6, l = 4 Global Spherical Cap Harmonics (SCHA) q0=90° q0 =90° q0 arbitrary q0 =arbitrary l(2) = 109.2714 l(4) =200.4828 l(6) = 290.9488

  37. DFHRS - Extension to Gravity Observations SCHA „Handling“ SCHA „Resolution“ („2mm Geoid“, n=7200 u =50.000.000) α= 1° (=110 km area) => k-SCHA = 80 and u = 6.400 α= 3° (=330 km area) => k-SCHA = 250 and u= 62.500 α= 25° (Europe) => k-SCHA = 2000 and u =4.000.000

  38. DFHRS - Extension to Gravity Observations Treatment of Gravity Observations Sensor-Observation at Position P(x,y,z)

  39. Treatment of GPM - EGM96 / EGM99, EIGEN, etc

  40. Extension of the DFHRS-Concept to gravity observations hGNSS+ v = H + fT  p- hGPS· m H + v = H NG‘j + v j = fTp + NG(d j) NFEM(p) N(pk) • j + v = - fBT/ M(B) p +  (d,) j  j + v = - fLT/(N(B)cos(B)) p + (d,) j g·S()dσ + v =NFEM(p)= fT p

  41. Example Saarland: 825 Gravity Observations

  42. Example Saarland (Jan. 06) DFHRS-Software with Computation Design Version 1 ( 1cm Reference) EGG97 („Gravity indirect“) + Identical Points Version 2 („Gravity indirect“) Gravity Disturbances dg GPM98 Identical Points 1 CAP Result: 1_cm Coincidence of the HRS between Version 1 and Version 2

  43. „1_cm DFHRS of Baden-Württemberg“ (EIGEN-GPM, Gravity Values, Fitting Points)

  44. „1_cm DFHRS of Baden-Württemberg“ (EIGEN-GPM, Gravity Values, Fitting Points)

  45. „1_cm DFHRS of Baden-Württemberg“ (EIGEN-GPM, gravity values)

  46. Solution Concept for • HRS-Computation and • GNSS-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 all over the world • Industrial Standard in GNSS-Equipment and GIS • DFHRS_DB => RTCM 3.q Message used in GNSS-Services, NTRIP etc. • - High Capacities for International Cooperations and for EVRS

More Related