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Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm MTR, E2Eplus Study

Explore a study on enhanced magnetic field inversion analysis for Swarm satellites, including orbit calculations, alignment tests, and gradient approaches. Results and future plans are discussed in detail.

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Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm MTR, E2Eplus Study

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  1. Study of an Improved Comprehensive Magnetic Field Inversion Analysis for SwarmMTR, E2Eplus Study Work performed by Nils Olsen, Terence J. Sabaka, Luis R. Gaya-Pique, Lars Tøffner-Clausen, and Alexei Kuvshinov, Presented by: Nils Olsen

  2. Draft Agenda Swarm E2Eplus Mid Term Review, June 26 2006, at ESTEC, Noordwijk 11:00 Welcome 11:05 Presentation of activities done so far (NIO) Summary of activities already presented at PM1 Forward calculation, Constellations #3 and #4 Results of Gradient Approach First results of multi-satellite in-flight alignment List of failure and imperfection cases Plans for the near future 13:00 lunch 14:00 General discussion Telecon with Terence J. Sabaka and L. R. Gaya-Pique, GSFC 17:00 Adjourn 26. June 2006 | MTR E2Eplus | page 2

  3. E2Eplus Study Logic • Status of June 2006: • New, fast orbit generation scheme • Gradient approach • Multi-satellite alignment (tests partly concluded) 26. June 2006 | MTR E2Eplus | page 3

  4. Forward calculationConstellation #3 and #4 26. June 2006 | MTR E2Eplus | page 4

  5. Fast Orbit Prediction • circular near-polar orbits • realistic drift in local time • realistic altitude decay (solar activity effects …) • realistic maintenance of constellation Validation of method with CHAMP orbits 26. June 2006 | MTR E2Eplus | page 5

  6. Constellation #3 and #4 • Constellation #3 • Essentially similar to constellation #2, but using new orbit propagation method • Data only used for test purposes. This constellation will not be considered further • Constellation #4 • Launch on July 1, 1998 (1.5 years later than in Phase A, to account for launch delay) • Inclination Swarm A+B: 87.4ºSwarm C: 88.0º • Initial altitude: 450 km (A+B) and 530 km (C) • Longitudinal difference between Swarm A and B: 1.4º 26. June 2006 | MTR E2Eplus | page 6

  7. Solar and geomagnetic activity 26. June 2006 | MTR E2Eplus | page 7

  8. Orbit decay for Swarm A, for various launch times 26. June 2006 | MTR E2Eplus | page 8

  9. Local Time and altitude evolution, constellation #4 26. June 2006 | MTR E2Eplus | page 9

  10. Impact of higher sampling rate on lithospheric field recovery 26. June 2006 | MTR E2Eplus | page 10

  11. Re-analysis of Constellation #2 data 26. June 2006 | MTR E2Eplus | page 11

  12. The Gradient Method in the Comprehensive Inversion Approach 26. June 2006 | MTR E2Eplus | page 12

  13. “Selective Infinite Variance Weighting” Development of an approach that produces/identifies data subsets that are particularly sensitive to certain parameter subsetsand applying appropriate weighting such that these data strongly influence the determination of such parameters • Example: high-order crustal field is resolved by gradient information (data difference) low-order field is resolved by all data d1, d2, d3 are data of Swarm 1,2,3 ds, dd, are sum and difference of Swarm 1,2 x is all model parameters but crustal field (sensed by all satellites) yl is low-order crustal field (sensed by ds, dd, d3) yh is high-order crustal field (sensed by dd) 26. June 2006 | MTR E2Eplus | page 13

  14. Results: Gradient approach Difference data contribute only to lithospheric field coefficients of order m > 20 All data (sums and differences) contribute to all other coefficients 26. June 2006 | MTR E2Eplus | page 14

  15. Results: Gradient approach 26. June 2006 | MTR E2Eplus | page 15

  16. Multi-Satellite In-flight Alignment 26. June 2006 | MTR E2Eplus | page 16

  17. The principle of in-flight alignment Model parameters:SHA expansion coefficients gnm, hnm Euler angles a,b,g • New: • CI approach BNEC includes all relevant contributions to Earth’s magnetic field: internal and external potential fields plus toroidal fields • Simultaneous estimation of the Euler angles for all Swarm satellites 26. June 2006 | MTR E2Eplus | page 17

  18. Tests • Data from all 3 satellites (constellation #4) • Solved for 3 x 3 Euler angles plus magnetic field model • Only solved for the contributions that are included in the synthetic data • Test 1: core field only (up to n=13, temporal variation described by splines) • Test 2: lithospheric field (up to n=150) added • Test 3: magnetospheric (primary and induced field) added • Test 4: ionospheric (primary and induced field) added • Test 5: toroidal field added Tests 1 – 3 successfully completed (near perfect recovery of core and lithospheric field and Euler angles) Test 4 partly completed(good recovery of core and lithospheric field, but retrieved Euler angles are different from the true ones) 26. June 2006 | MTR E2Eplus | page 18

  19. Result of Test 3 Input data contain core, lithospheric and magnetospheric (primary and induced) field Difference between true and retrieved Euler angles < 1 arcsec 26. June 2006 | MTR E2Eplus | page 19

  20. Result of Test 4 Input data contain static internal field (n = 1-150, no SV!) and ionospheric plus magnetospheric (primary and induced) field Difference between true and retrieved Euler angles: 26. June 2006 | MTR E2Eplus | page 20

  21. Result of Test 4 • Spectra of model differences 26. June 2006 | MTR E2Eplus | page 21

  22. Plans for the near Future • Further tests of the multi-satellite alignment • Inclusion of ionospheric field: what went wrong, if anything? • Inclusion of toroidal fields (first tests completed) • The Great Unified Code: Combination of gradient and multi-satellite approach • Tests • Application to various imperfection and failure scenarii 26. June 2006 | MTR E2Eplus | page 22

  23. Failure and Imperfection Cases • Failure of VFM and/or STR on a single satellite • Only scalar (no vector) data available for Swarm A • Only scalar (no vector) data available for Swarm C • Impact of a S/C magnetic field on a single satellite (Swarm A) • Constant S/C dipole moment (hard magnetization), corresponding to 2 nT at the location of the ASM • Induced S/C dipole moment (soft magnetization), corresponding to 3 nT at the location of the ASM over the poles (i.e. the area of maximum Earth’s magnetic field strength) • Noise in the CRF attitude of a single satellite (Swarm A) • Time dependent attitude noise (all components) 2 sin(wt) arcsecs + 10 sin(2pT/24) arcsecswhere t is UT, w is orbital frequency, and T is Local Time in hours. • Failure of one or more satellite (extension of Phase A analysis) • Magnetic data from all 3 satellites (Swarm A, B and C) • Magnetic data from (Swarm A and C) only • Magnetic data from (Swarm A and B) only • Magnetic data from (Swarm A) only 26. June 2006 | MTR E2Eplus | page 23

  24. 26. June 2006 | MTR E2Eplus | page 24

  25. Work Breakdown Structure 26. June 2006 | MTR E2Eplus | page 25

  26. Updated list of proposed Meetings and Deliverables 26. June 2006 | MTR E2Eplus | page 26

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