Slide 1

MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA DFHRS (Digital FEM Height Reference Surface) A Rigorous Approach for the Integrated Adjustment of Fitted Height Reference Surfaces (HRS) - Reiner Jger Hochschule Karlsruhe Technik und Wirtschaft - University of Applied Sciences Faculty of Geomatics Studiengang Vermessung und Geomatik & International Programme Geomatics (MSc) Institut fr Angewandte Forschung (IAF) Moltkestrasse 30, D-76133 Karlsruhe www.dfhbf.de ; www.geozilla.de; www.galileo-bw.de; www.moldpos.eu Slide 2 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Height Systems - Definitions and Terrestrial Realisiation H Geoid = Ideal Height Reference Surface (HRS) h N A Gepotential Numbers C Levelling and Gravity Observations Terrestrial Height Determination H=const. Small Area ~ constant Waterlevel Slide 3 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA NewEuropeanNormal-HeightNetwork EUREF/UELN 95/98 AdjustmentbyGeopotential Numbers (Differences Datumspoint W 0 bzw. C 0 AmsterdamNAPDHHN92 ( Diff.: 1 cm) AccuracySituation Slide 4 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA H = h - N GNSS-Heightung H H from h-GNSS HRS-Model N h h N H HRS Geoid Quasigeoid Slide 5 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Gravity Potential W of the Earth at Point P(r,, ) Gravitational Potential of the Earth Masses HRS = Geoid / Quasigeoid Physical Definition & Realisation Centrifgal - Potential due to Earth-Rotation Q-Geoid Geoid (W=W o =const) Spherical Harmonics Coefficients as Parameters HBF Slide 6 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Original Observation: Laserranges Derived of it: Orbit Disturbances Derived of it: Spherical Harmonics (Mller/Kaula, 1960,1962) Satellite Geodetic Methods of Gravity Field Determination Satellite Laser Ranging (SLR) LEOS (Low Earth Orbit Satellites) LAGEOS 1, 2 STELLA, etc. Slide 7 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Observation Quantities 1.) Abs. Positionierung via GPS (Black-Jack Receiver/NASA, JPL): x(t) 2.) Relative Orbitmovements by Inter-Satellite Observations: 3.) Precise Accelerometers a i STAR (Onera/Frankreich): 4.) Gradiometers (e.g. GOCE) Derived of these: 1.) Orbit Determinations 2.) Gravitational Accelerations g i (x,t) and Gradiometer-Tensor Present Missions Hybride Sensors Aktice Measurements Spherical Harmonics Coefficients Derived from that: Spherical Harmonics Coefficients CHAMP Satellite Geodetic Methods of Gravity Field Determination Slide 8 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA EIGEN ( = EIG EN EIGEN ( = European Improved Gravity Model of the Earth by New Techniques) [cm] HHJHHJ M6 Earth Geopotential Model 96 (NASA) HHJHHJ Satellite Geodetic Methods of Gravity Field Determination Slide 9 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA EIGEN ( = EIG EN EIGEN ( = European Improved Gravity Model of the Earth by New Techniques) [cm] HHJHHJ M6 Earth Geopotential Model 96 (NASA) HHJHHJ N(p) Latitude(degree) Longitude(dgree) DFHRS_DB Namibia and Tanzania: 1.) Identical Points (N=h-H) & 2.) EGM96 bzw. EIGEN-GL04C Satellite Geodetic Methods of Gravity Field Determination Slide 10 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Bilance for Satellite Geodetic GPM(EGM2008; EIGEN) N n,m N Not sufficient for GNSS-Heighting N H = h N !!! Further Information for further HRS N Improvement of the HRS and N necessary! Hybrid and redundant Models! Terrestrial Gravity Measurements Identical Points (H, h) N=h-H GeoidFitting Slide 11 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Short-Waved: ~ (1 3) cm Medium-/Long Waved 0.1-1.5 m ! 1.) EGG97 - European Gravimetric QGeoid 1997 (IfE, Hannover) (h, H) Hybride Modeling in HRS-Computation Weg 1: Stokes-based RepresentationGRID Slide 12 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA (h, H) + + Dgl.-based GPM 98 2.) Prof. Dr.-Ing. H.-G. Wenzel Fitted Geopotenzialmodell (GPM 98 ) n = m = 1800 Accuracy of N ~ (10 - 30) cm Parametrice Represenation (or Grid) Hybride Modeling in HRS-Computation Slide 13 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA 3.) BKG-Model Parametrisation of the Potentials by additional Mass Points (h, H) Massen-Points as essential additional Parameters Representation of BKG HRS: Grid Hybride Modeling in HRS-Computation Slide 14 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA H = h GPS (B,L) - DFHRS(B,L,h) korr H H = h GPS (B,L) - (NFEM(p|B,L,h) + mh) DFHRS-DB Direct - No - NoIdentical Points - - Online - Online - Postpro- cessed DFHRS-Concept Slide 15 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA 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 Slide 16 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Continuous Finite Element Representation of HRS Slide 17 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA FEM representation of height reference surfaces Result: Continuous Height Reference Surface: NFEM(p) Slide 18 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Digital FEM Height Reference Surface (DFHRS)- Concept h GNSS + v = H + NFEM(p) - h GPS m H + v = H N G j + v j = NFEM(p) + N G (d j ) j + v = - F B / M(B) p + (d , ) j j + v = - F L /(N(B) cos(B)) p + (d , ) j Complete New Computation of continuous HRS (p and m)! DFHRS Adjustment Approach < 2005 State of the Art < 2005 gS( )d + v = NFEM(p) NFEM(p) N(pj)N(pj) (Global, regional, local)k-SCHA = 250 and u= 62.500== ==25 (Europe) => k-SCHA = 2000 and u =4.000.000 Slide 40 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA DFHRS - Extension to Gravity Observations Sensor-Observation at Position P(x,y,z) Treatment of Gravity Observations Slide 41 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Treatment of GPM - EGM96 / EGM99, EIGEN, etc Slide 42 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA h GNSS + v = H + f T p - h GPS m H + v = H N G j + v j = f T p + N G (d j ) j + v = - f B T / M(B) p + (d , ) j j + v = - f L T /(N(B) cos(B)) p + (d , ) j gS( )d + v = NFEM(p)= f T p NFEM(p) N(pk)N(pk) Extension of the DFHRS-Concept to gravity observations Slide 43 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Example Saarland: 825 Gravity Observations Slide 44 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA 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 Slide 45 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA 1_cm DFHRS of Baden-Wrttemberg (EIGEN-GPM, Gravity Values, Fitting Points) Slide 46 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA 1_cm DFHRS of Baden-Wrttemberg (EIGEN-GPM, Gravity Values, Fitting Points) Slide 47 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA 1_cm DFHRS of Baden-Wrttemberg (EIGEN-GPM, gravity values) Number B[] L[] dg[mgal] v[mgal] -------------------------------------------------------------------- 6221803000 49.744402 9.325176 17.27052630 0.016 6221803100 49.754800 9.320541 18.29553958 0.004 6221810000 49.731079 9.322965 48.72880615 -0.002 6221810100 49.767690 9.323488 16.90448271 -0.009 6221810200 49.739588 9.295846 16.90117365 -0.005 : : : : : 6222803100 49.787317 9.482121 25.19440159 -0.006 6222803800 49.730625 9.411164 35.48699735 0.012 6222803900 49.748882 9.486150 46.45989551 -0.019 6222804000 49.735388 9.450240 45.58427649 -0.022 6222804104 49.717601 9.439384 46.62347815 -0.018 6222804204 49.702843 9.456634 55.15177619 -0.029 6222810000 49.699664 9.417770 47.55625221 -0.003 : : : : : Fig. 8 DFHRS-software report for the gravity disturbances dg with the list of corrections v Slide 48 MOLDPOS Initial Meeting, Chisinau, 10-05-10 HRS-Computation and DFHRS-Concept Prof. Dr. Reiner Jger, HSKA Solution Concept for HRS-Computation and GNSS-Heighting *DFHRS-Software - 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 ( RTCM 3.q Message used in GNSS-Services, NTRIP etc. - High Capacities for International Cooperations and for EVRS