Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm PM1, E2Eplus Study Work performed by Nils Olsen, Terence J. Sabaka, Luis.

Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm

PM1, E2Eplus Study

Work performed by Nils Olsen, Terence J. Sabaka, Luis R. Gaya-Pique, Lars Tøffner-Clausen, and Alexei Kuvshinov,

Presented by: Nils Olsen

29. March 2006 | PM1 E2Eplus | page 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


Fast Orbit Prediction(FOP)


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


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:


Orbit Decay due to Air-Drag

• For a circular orbit, the decrease asma of the semi-major axis asma per orbit is

is the ballistic coefficient, and is air density

• Since 1/Tp with is the number of orbits per day,

the decrease of the semi-major axis per day is

• Calculation of daily mean air density (MSIS) along orbit

• Linear distribution of asma over the day in consideration


The Algorithm

1. Initial values (asma, , ) for epoch t02. Calculation of one day of positions rITRF

3. Calculation of mean air density along orbit

4. Calculation of mean orbit decay, asma

5. Linear distribution of asma over the day,

6. New initial values (asma, , ) for next day, i.e. epoch t=t0+1 day

7. Repeat steps 1 – 6 until end of mission (altitude < 200 km)


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 = 63.816°

– RAAN = 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)


Geomagnetic and Solar activity


Observed vs. simulated altitude and LT


Difference CHAMP observed - simulated


Impact of higher sampling rate on lithospheric field recovery


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


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 coefficients

b) transformation to system with orbit inclination 86.8°

0 , 88

1 , 88

for

for mn

n ma

n m


Result:


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 n of coefficients– Sensitivity matrix– Global Maps (e.g., of Br) of the model difference


Assessment, lithospheric field, Phase A

• Combined solution:– CI result for n < 83

– Gradient method result for n ≥ 83


Re-analysis of Constellation #2 data

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


Re-analysis of Constellation #2 data


The Gradient Method in the Comprehensive Inversion Approach


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


“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

1

2

3 3

3 3 3 3 3

1 10

2 21 1

02 2

0 0 1

0 0

0 0

0 0

s

d

l hs s s s s

h lhd d d d d

ll

h

l

h

x

A yB B

A B B

A B B n

y

n

d d

d d

d d

d

d

d

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)


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)


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.



E2Eplus Study Logic


Work Breakdown Structure


Updated list of proposed Meetings and Deliverables

MeetingPlace Participants Planned Date Deliverables

Kick-Off Meeting (KO) DNSC All January 27, 2006 -

Progress Meeting 1 DNSC 3 March 29, 2006 -

Midterm Review (MTR) ESTEC 4 June 19, 2006 Draft report

Progress Meeting 2 DNSC 3 September 25, 2006

-

Final Presentation (FP) ESTEC 4 December 4, 2006

Final report

Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm PM1, E2Eplus Study Work performed by Nils Olsen, Terence J. Sabaka, Luis.

Documents

precise orbit prediction

pm1 e2eplus page

fast orbit prediction

orbit linear distribution

swarm pm1

consideration slide

nils olsen slide

e2eplus study work