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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

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

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- 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

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- 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:

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- 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

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- 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)

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- 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)

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- 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

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- 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°

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- 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

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

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

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- 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

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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)

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- 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)

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- 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.

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