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Enhanced Magnetic Field Inversion Analysis for SwarmPM1

Explore advanced techniques for improved orbit prediction and magnetic field inversion analysis for SwarmPM1 mission. Discussing novel approaches and validation against CHAMP data.

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Enhanced Magnetic Field Inversion Analysis for SwarmPM1

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  1. Study of an Improved Comprehensive Magnetic Field Inversion Analysis for SwarmPM1, 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 Progress Meeting 1, March 29 2006, at DNSC Copenhagen 09:00 Welcome 09:05 Presentation of activities done so far (NIO) Fast Orbit Prediction (theory plus practical demonstration) Results of re-analysis of E2E CI Task 3 data using higher sampling rate Gradient Approach: first ideas and their implementation Plans for the near future General discussion 12:30 lunch 13:30 AOB 14:45 Adjourn 29. March 2006 | PM1 E2Eplus | page 2

  3. Fast Orbit Prediction(FOP) 29. March 2006 | PM1 E2Eplus | page 3

  4. Fast Orbit Prediction • Approach used for E2E (Phase A): • Numerical integration of equations of motion, considering a lot of (tiny) effects • Some of the small effects are rather uncertain (e.g., air-drag), and therefore the position prediction error increases tremendously with time • Due to this uncertainty, a ”precise” orbit prediction (extrapolating several months/years in future) is not more precise than an approach that focuses on time-averaged effects (plus short-term effects due to change of air-drag) • New approach • considering what is needed for the simulation : • circular near-polar orbits • realistic drift in local time • realistic altitude decay (solar activity effects …) • realistic maintenance of constellation 29. March 2006 | PM1 E2Eplus | page 4

  5. Fast Orbit Prediction • Circular orbit of radius asma and inclination i in the orbit-fixed coordinate system • Rotation by around z-axis to get orbit in ICRF: • Rotation by -GAST around z-axis to get orbit in ITRF: 29. March 2006 | PM1 E2Eplus | page 5

  6. Orbit Decay due to Air-Drag • For a circular orbit, the decrease Dasma of the semi-major axis asmaper orbitis is the ballistic coefficient, and r is air density • Since 1/Tp with is the number of orbits per day, the decrease of the semi-major axis per dayis • Calculation of daily mean air density (MSIS) along orbit • Linear distribution of Dasma over the day in consideration 29. March 2006 | PM1 E2Eplus | page 6

  7. The Algorithm • Initial values (asma, n, W) for epoch t0 • Calculation of one day of positions rITRF • Calculation of mean air density along orbit • Calculation of mean orbit decay, Dasma • Linear distribution of Dasma over the day, • New initial values (asma, n, W) for next day, i.e. epoch t=t0+1 day • Repeat steps 1 – 6 until end of mission (altitude < 200 km) 29. March 2006 | PM1 E2Eplus | page 7

  8. Validation against CHAMP orbit observations • Simulation of 5.5 years of CHAMP orbits • Initial conditions, August 1, 2000, 00:00 UT • inclination i = 87.255° • semi-major axis asma = a + 457.1 km • mean anomaly n = 63.816° • RAAN W = 144.43° • Ballistic coefficient B = m/(A CD) • m is satellite mass • CD is drag coefficient • A is effective satellite cross section(Ax = 0.74 m2, Ay = 3.12 m2, Az = 4.2 m2) • 5° misalignment between x-direction and actual flight direction: A = 1.01 m2 • B = 230 kg/m2 is a reasonable value, according to Hermann Lühr(compatible with A = 0.9 m2, m = 500 kg, CD=2.4) 29. March 2006 | PM1 E2Eplus | page 8

  9. Geomagnetic and Solar activity 29. March 2006 | PM1 E2Eplus | page 9

  10. Observed vs. simulated altitude and LT 29. March 2006 | PM1 E2Eplus | page 10

  11. Difference CHAMP observed - simulated 29. March 2006 | PM1 E2Eplus | page 11

  12. Impact of higher sampling rate on lithospheric field recovery 29. March 2006 | PM1 E2Eplus | page 12

  13. Comparison of Filter Method and CI, E2E • Phase A: • CI superior at n<80, especially for terms m close to 0 • Gradient method is superior for n > 80 Gradient Method Sensitivity matrix CI 29. March 2006 | PM1 E2Eplus | page 13

  14. Conceptual Example • Orbit period: about 90 minutes, corresponding to 4°/min • 1-min sampling rate: along-track structures smaller than 4° are not resolved • Consider an orbit in the equatorial plane (inclination=0°) • 1-min sampling rate: only spherical harmonic coefficients of order m < 360°/4°=90 are resolved;coefficients of orders m > 90 are unresolved • Example:a) Equatorial orbit with spherical harmonic coefficientsb) transformation to system with orbit inclination 86.8° 29. March 2006 | PM1 E2Eplus | page 14

  15. Result: 29. March 2006 | PM1 E2Eplus | page 15

  16. Assessment criteria • Test quantities: Difference between recovered and original model • Power spectrum of the model SH coefficients and of the coefficients of the difference (original – recovered) • Degree correlation rn of coefficients • Sensitivity matrix • Global Maps (e.g., of Br) of the model difference 29. March 2006 | PM1 E2Eplus | page 16

  17. Assessment, lithospheric field, Phase A • Combined solution: • CI result for n < 83 • Gradient method result for n ≥ 83 29. March 2006 | PM1 E2Eplus | page 17

  18. Re-analysis of Constellation #2 data • Phase A: 1 min sampling rate • Now: 30 secs, respect. 15 secs sampling rate 29. March 2006 | PM1 E2Eplus | page 18

  19. Re-analysis of Constellation #2 data 29. March 2006 | PM1 E2Eplus | page 19

  20. The Gradient Method in the Comprehensive Inversion Approach 29. March 2006 | PM1 E2Eplus | page 20

  21. On the Comprehensive Approach • Comprehensive Approach:Modeling of all relevant contributions to Earth’s magnetic fieldSimultaneous (co-) estimation of all sources • Presently: all data are sensitive to all parts of the model • Example 1: crustal field is obtained from all (also dayside) datainsufficient description of day-side equatorial electrojet may lead to contamination of crustal field • Example 2:high- as well as low-order lithospheric field is determined from all datano explicit use of field gradient information 29. March 2006 | PM1 E2Eplus | page 21

  22. “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 data sum 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, d3) yh is high-order crustal field (sensed by dd) 29. March 2006 | PM1 E2Eplus | page 22

  23. Plans for the Near Future • Implementation of selective weighting scheme in CI code • Application to constellation # 3 data • Results expected to be presented at Swarm workshop in Nantes (May 2006) • Implementation of in-flight alignment (co-estimation of Euler angles) in CI code • Application to constellation # 3 data • Results expected to be presented at MTR(June 2006) 29. March 2006 | PM1 E2Eplus | page 23

  24. Action Items • AI-001 of KO meeting: ”Info on error characteristic of Optical Bench model in terms of Euler angles“This information is requested needed at the beginning of May (Swarm workshop in Nantes), rather than MTR. 29. March 2006 | PM1 E2Eplus | page 24

  25. 29. March 2006 | PM1 E2Eplus | page 25

  26. E2Eplus Study Logic 29. March 2006 | PM1 E2Eplus | page 26

  27. Work Breakdown Structure 29. March 2006 | PM1 E2Eplus | page 27

  28. Updated list of proposed Meetings and Deliverables 29. March 2006 | PM1 E2Eplus | page 28

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