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Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm PM1, E2Eplus StudyPowerPoint Presentation

Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm PM1, E2Eplus Study

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### 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

Draft Agenda Analysis for Swarm

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

Fast Orbit Prediction Analysis for Swarm(FOP)

29. March 2006 | PM1 E2Eplus | page 3

Fast Orbit Prediction Analysis for Swarm

- 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

Fast Orbit Prediction Analysis for Swarm

- 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

Orbit Decay due to Air-Drag Analysis for Swarm

- 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

The Algorithm Analysis for Swarm

- 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

Validation against CHAMP orbit observations Analysis for Swarm

- 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

Geomagnetic and Solar activity Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 9

Observed vs. simulated altitude and LT Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 10

Difference CHAMP observed - simulated Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 11

Impact of higher sampling rate Analysis for Swarmon lithospheric field recovery

29. March 2006 | PM1 E2Eplus | page 12

Comparison of Filter Method and CI, E2E Analysis for Swarm

- 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

Conceptual Example Analysis for Swarm

- 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

Result: Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 15

Assessment criteria Analysis for Swarm

- 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

Assessment, lithospheric field, Phase A Analysis for Swarm

- Combined solution:
- CI result for n < 83
- Gradient method result for n ≥ 83

29. March 2006 | PM1 E2Eplus | page 17

Re-analysis of Constellation #2 data Analysis for Swarm

- Phase A: 1 min sampling rate
- Now: 30 secs, respect. 15 secs sampling rate

29. March 2006 | PM1 E2Eplus | page 18

Re-analysis of Constellation #2 data Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 19

The Gradient Method in the Analysis for SwarmComprehensive Inversion Approach

29. March 2006 | PM1 E2Eplus | page 20

On the Comprehensive Approach Analysis for Swarm

- 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

“Selective Infinite Variance Weighting” Analysis for Swarm

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

Plans for the Near Future Analysis for Swarm

- 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

Action Items Analysis for Swarm

- 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

29. March 2006 Analysis for Swarm | PM1 E2Eplus | page 25

E2Eplus Study Logic Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 26

Work Breakdown Structure Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 27

Updated list of proposed Meetings and Deliverables Analysis for Swarm

29. March 2006 | PM1 E2Eplus | page 28

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