Use weighted cHPI coils during position fitting

[larsoner]

Closes #11330

This turned out to way simpler than I realized:

1. Use a linear ramp from gof_limit to 1.
2. Combine this with the dist_limit coil goodness estimate
3. Pass these weights to our quat fitting function, which already supports weights

Implementation drafted with Opus 4.8 but I edited and vouch for all code.

Adapting the minimal example from the linked issue (data available there):

Minimial code

import mne
raw_file = 'te01a1.fif'
raw = mne.io.read_raw_fif(raw_file)
chpi_amps = mne.chpi.compute_chpi_amplitudes(raw, t_step_min=0.25, t_window=0.5)
chpi_locs = mne.chpi.compute_chpi_locs(raw.info, chpi_amps)
head_pos = mne.chpi.compute_head_pos(raw.info, chpi_locs, weighted=False)
mne.viz.plot_head_positions(head_pos)
head_pos = mne.chpi.compute_head_pos(raw.info, chpi_locs, weighted=True)
mne.viz.plot_head_positions(head_pos)

weighted=False	weighted=True

[larsoner]

cc @SeungCheolBaek did you want to try this?

[SeungCheolBaek]

cc @SeungCheolBaek did you want to try this?

Wow, great! Thanks for working on this problem.

I'd be nice if I can try this.

But this functionality has not implemented in the current dev. version (1.13), right?
Because I couldn't find the weighted argument in the mne.chpi.compute_head_pos.

Thanks for letting me know about this!

[larsoner]

Correct, it hasn't been merged into main or released yet. You should be able to do something like pip install "mne @ https://github.com/larsoner/mne-python/archive/refs/heads/chpiw.zip" and it should install this branch directly to test it out.

[SeungCheolBaek]

Correct, it hasn't been merged into main or released yet. You should be able to do something like pip install "mne @ https://github.com/larsoner/mne-python/archive/refs/heads/chpiw.zip" and it should install this branch directly to test it out.

I've just tried it out, and it seems like it works pretty well!
Thanks again for introducing this to me :)

I hope it will be implemented in stable MNE versions soon!

[larsoner]

Okay great, thanks for testing!