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Navigation docs #1856

Merged
merged 5 commits into from
Oct 30, 2024
Merged

Navigation docs #1856

merged 5 commits into from
Oct 30, 2024

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dellaert
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  • Generated explainer for attitude factor with o1-preview
  • Edited above heavily
  • Added README
  • Updated IMU Factor reference

* This factor enforces that when a known reference direction in the body frame
* (e.g., accelerometer axis) is rotated into the navigation frame using the
* rotation variable, it should align with a measured direction in the
* navigation frame (e.g., gravity vector).
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What is confusing here is the choice of ref / measured:

  • one would expect the direction read from the accelerometer (in body) to be measured, and the known gravity direction in nav to be ref

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OK. This was a big change, but I switched all the mentions of reference and measured. I agree it is much more clear and even the tests had "measurement" in quotes.


### Jacobians

For optimization, the $2 \times 3$ Jacobian of the error function with respect to the rotation parameters is required. The Jacobian is computed using chain rule differentiation, involving the derivative of the rotated vector with respect to the rotation parameters and the derivative of the error with respect to the rotated vector.
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Maybe a mention here of the singularity we found w.r.t. the Jacobian, which also vanishes 180 degrees away from the true direction (because it is calculated in the tangent space?)

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Done

@dellaert dellaert merged commit ecc7366 into develop Oct 30, 2024
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@dellaert dellaert deleted the feature/attitude branch October 30, 2024 20:52
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2 participants