Cassini FGM Calibration

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Cassini FGM Calibration

• Krishan Khurana
• With a lot of help from
• Professor Chris Russell and
• Steve Kellock

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Why is calibration needed?

• There are clear artifacts in the data which
  correlate with the motions of the spacecraft. The
  figure below shows oscillations in the spacecraft
  data (black) when the nine elements of the
  rotation matrix (S/C to KRTP) show rotations.
  Also plotted is model field in red, (Khurana, et
  al. 2004)

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Why is calibration needed? 2

• These artifacts can distort real signatures. For
  example, the inbound and outbound portions of
  Enceladus 4 data do not match because there were
  spacecraft rotations during the encounter shown
  in plot on next page.

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Why is calibration needed? 3
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How do we calibrate?

• There are two different techniques one could
  devise.
• If there is a good magnetic field model
  available, one could rotate that model field into
  the spacecraft coordinates and ask that the
  difference between the model and the observations
  be minimized.
• One essentially solves for a calibration matrix
  (nine elements 3 offsets)
• The above problem can be written as a least
  squares problem and one solves for 12 unknowns.

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Method 1 Continued

• Unfortunately, because the models are accurate
  only to within a few nT, this technique is also
  good only to that level.
• Another problem with the data is that there are
  discontinuous jumps during range changes. So, I
  decided to use data only from range 1. So, the
  new calibration matrix would be useful only for
  this range.
• I used data only from a very small interval (see
  next page).
• I was able to reduce the spin tone some what.

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Method 1 Input data used
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DATA, CORRECTED, MODEL
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But the rest of the data look terrible
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And the matrix and offsets are not believable

• .9781178 .0037285 .0060719
• -.0001612 .9821783 -.0391826
• -.0028709 .0035563 .9874757
• -.4980705 2.3017098 .9237360

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Method 2

• Try to reduce the spacecraft artifacts in the
  KRTP data by using a gradient search technique. I
  fit second order polynomials to segments of KRTP
  field data that are from range 1 and where the
  spacecraft is executing rotations. I subtract out
  the background to get what I call the spin tone
  in the data. Next, I ask what changes to the U
  matrix would reduce it.
• Where the A matrix rotates the sc data to KRTP
  coordinates.
• This technique works spectacularly well.

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The spin tone is gone.
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And here is the matrix that fixed the problem

• U11 U12 U13 U21 U22 U23 U31 U32 U33
• 1.0000000 .0019527 .0003716
• .0022913 1.0043066 -.0069244
• -.0029060 .0042452 1.0042616
• -.0000173 -.0000313 .0000008
• O1 O2 O3
• -.0000173 -.0000313 .0000008
• I had fixed the element U11 to a value of 1.0.
• The small values of offsets indicates that the
  solutions may be non-unique.

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And the rest of the data look good DATA,
CORRECTED, MODEL
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The improvement to Enceladus data is substantial
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The sharp rotation near 1030 is gone
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Future imrprovements

• To be discussed.