swarm End-To-End Mission Performance Study Working meeting on Task 2 Eigil Friis-Christensen and Nils Olsen Danish Space Research Institute Copenhagen

Why in-flight alignment Why in-flight alignment? (Determination of the VFM – ASC transformation) VFM – ASC transformation (Euler angles) depend on ASC software parameter settings. In-orbit parameter change (e.g. to optimize performance) will require a new alignment but one-by-one parameter change may allow to determine the change by intercalibration of the individual camera heads Large discrepancy between pre-flight and in-flight estimated values for all previous missions means that preflight calibrations are not adequate for scientific use.

Principles of in-flight alignment Compare the observed vector field with a model vector field in the instrument frame Adjust a,b,g such that the difference is minimized in the LS sense Model field consists of main-field + Dst correction Discrepancy between observed and model field is due to error in the MF model (potential field) This error is absent if MF is co-estimated LT dependency of ionsopheric and magnetospheric sources (non-potential field due to data sampling near LT=0, although curl B = 0) existence of toroidal field contributions (curl B ¹ 0) Since the method aims to minimize |Bobs-Bmod|, it is important that this difference is not biased, i.e. its mean in the instrument frame should be zero This is a problem if the instrument (satellite) has a preferred flight direction (for instance, if the instruments z-axis is mostly in radial direction)

Coordinate system a b g

Some experiments 5 years of data from swarm1 Usual data selection criteria (quiet time, night-side, non-polar latitudes) Observed field consists of core, crust, ionospheric+magnetospheric (+induced), toroidal (all sources) core, crust, ionospheric+magnetospheric (+induced), (no toroidal field) core, toroidal (only toroidal field) Model field consists of core field + Dst-correction ”True” Euler angles with time-dependency a=20” (t/1000 days) b=10” g=30” (t/1000 days)2 Such a time-dependency is not relevant for swarm, for which a stability of the angles within 5” is required according to the SRD Such a stability has, however, not yet been proven in space This time dependency is used here to study the robustness of the solution.

Stable satellite, all source contributions rms misfit is the discrepancy between model field and true (observed) field (aligned using the estimated values of a,b,c) rms alignment error is the discrepancy between the true field and the aligned true field

Stable satellite, no toroidal field

Stable satellite, only toroidal field

All contributions, satellite spinning around x-axis

Satellite spinning around z-axis

Satellite spinning (tumbling) around x and z-axes

Application to swarm Rotation of the satellite around a specific axis does not help to find the Euler angle around that axis (explanation has been given by Terry Sabaka) Is it possible to recover the Euler angles if it is assumed that they are are constant? What is the minimum of attitude maneuvers needed for the estimation of the Euler angles?

Accumulated accuracy, stable satellite Value for time t is obtained using all data up to t (data accumulation) biased estimate of g (by 15-20”), even when data of 5 years are used

Satellite rotated by 180 deg around z-axis once per month

Satellite rotated by 180 deg around x-axis once per month

Satellite rotated by +/- 45 deg around x-axis once per month

Preliminary Conclusion and Recommendation With existing single satellite calibration methods: Only a fully spinning (tumbling) satellite allows to estimate time-varying Euler angles (values are off by 10”-100”) Reliable estimate of a,b possible if mechanical stability is assumed and data from several years are used. But g is biased (by 15-20”) Attitude maneuvers (rotation of the satellite around z axis) do not help to solve this problem But such maneuvers might be needed for the VFM-ASM calibration New calibration methods taking advantage of a multi satellite configuration may be developed and used in case of non-ideal distribution of sensor directions.

Preliminary Conclusion and Recommendation Single satellite calibration method requires: Rotation around x (flight direction) Rotations of ±180 deg ( ±90 deg is not sufficient) Sufficient amount of data sampled in the rotated configuration is important (the number of rotations is less important)) Possible solution: rotation / swapping of the whole boom (or of the VFM/ASC package) around x ”Mechanism need not be very reliable” (if mechanism of one satellite fails, intercalibration with the other satellites may help)