1. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D On Calibrating the Magnetometry Package Data Nils Olsen, DTU Space

2. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D What is a ”Calibration”? ”Calibration” includes two steps: 1.to determine the calibration parameters 2.to apply the estimated parameters to the data VFM calibration Parameter estimation

3. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D at mission level at single-satellite level but co-estimation The various calibration steps VFM calibration (offset, scale-values, non-orthogonalities) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) SW-A SW-C SW-B Euler angles from L2 processing (multi-satellite co-estimation with geomagnetic field model) VFM characterisation (sun-position dependent disturbance field) Parameter estimation Parameter estimation Parameter estimation

4. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D at mission level at single-satellite level but co-estimation Inter-satellite calibration of SW-C Differential calibration: F(A)  F(C) VFM calibration (offset, scale-values, non-orthogonalities) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) SW-A SW-C SW-B Euler angles from L2 processing (multi-satellite co-estimation with geomagnetic field model) VFM characterisation (sun-position dependent disturbance field)

5. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Inter-satellite calibration of SW-C How to calibrate VFM(C) without ASM(C) ? Mapping of F : SW-A  SW-C F ASM (A) subtract F model (A), add F model (C) … … to obtain an estimate of F’ (C) use this value to calibrate VFM(C) all data:  = 0.55 nT nightside non polar:  = 0.28 nT Comparison F ASM (A  C) – F ASM (C) dayside nightside

6. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Gradient data Magnetic field difference between SW-A and SW-C is a key element of Swarm Used e.g. for studying small-scale crustal field structures or determination of Field-Aligned Currents (curl-B technique) Requires ultra-precise knowledge of the relative calibration/alignment between SW-A and SW-C Relative values can be determined with higher accuracy than the difference of absolute values Idea: Differential Calibration Differential Characterization Differential Alignment

7. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D at mission level at single-satellite level but co-estimation Differential Alignment Differential alignment: Euler angles VFM(A)  VFM(C) VFM calibration (offset, scale-values, non-orthogonalities) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) SW-A SW-C SW-B Euler angles from L2 processing (multi-satellite co-estimation with geomagnetic field model) VFM characterisation (sun-position dependent disturbance field)

8. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Differential alignment SW-A vs. SW-C Mapping of B: SW-A  SW-C B VFM (A)  B NEC (A) using STR(A) data and Euler angles for SW-A Mapping A  C: subtract B model (A), add B model (C) … … to obtain an estimate of B’ NEC (C) B’ NEC (C)  B’ VFM (C) using STR(C) data and Euler angles for SW-C Estimate differential Euler angles A  C by comparing B’ VFM (C) and B VFM (C) absolute reference level Euler angle  SW-A SW-C Difference of (absolute, but less accurate) Euler angles Differential Euler angle (relative, but more accurate)  A determined by SW-A  C determined by SW-C  A -  A determined by SW-A – SW-C How to combine absolute and differential Euler angles ?

9. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Difference B VFM (A  C) – B VFM (C) Assumptions: VFM calibration VFM characterization VFM alignment STR data are perfectly known (error-free) Non-zero difference can be used to improve calibration characterization alignment Vector-vector calibration/ characterization allows better y-axis parameter estimation

10. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Differential Euler angles between SW-A and SW-C

11. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D at mission level at single-satellite level but co-estimation Differential Calibration / Alignment Differential calibration: F(A)  F(C) Differential alignment: Euler angles VFM(A)  VFM(C) VFM calibration (offset, scale-values, non-orthogonalities) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) SW-A SW-C SW-B Euler angles from L2 processing (multi-satellite co-estimation with geomagnetic field model) VFM characterisation (sun-position dependent disturbance field)

12. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D at mission level at single-satellite level but co-estimation Complete Calibration / Alignment Differential calibration: F(A)  F(C) Differential alignment: Euler angles VFM(A)  VFM(C) VFM calibration (offset, scale-values, non-orthogonalities) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) VFM calibration (offset, scale-values, non-orthogonalities) VFM characterisation (sun-position dependent disturbance field) VFM alignment (Euler angles, VFM  NEC) SW-A SW-C SW-B Euler angles from L2 processing (multi-satellite co-estimation with geomagnetic field model) VFM characterisation (sun-position dependent disturbance field)

13. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Ultimate Goal To co-estimate (absolute) calibration/alignment/alignment (CCA) parameters for each satellite, accounting for (better determined) differential CCA values Has to be done by co-estimation with geomagnetic field model Differential CCA parameters determined using more data (including dayside data, higher geomagnetic activity) Possibility for vector-vector differential calibration/characterization more sensitive to typically weakly determined y-axis calibration

14. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Combined absolute and differential CCA: Concept of parameter co-estimation

15. 4 th Swarm QWG Meeting 2 – 5 December 2014GFZ Potsdam/D Ultimate Goal To co-estimate (absolute) calibration/alignment/alignment (CCA) parameters for each satellite, accounting for (better determined) differential CCA values Has to be done by co-estimation with geomagnetic field model Differential CCA parameters determined using more data (including dayside data, higher geomagnetic activity) Possibility for vector-vector differential calibration/characterization more sensitive to typically weakly determined y-axis calibration Estimation of CCA parameters by scientific experts Application of CCA parameters within L1b processor by PDGS