Kalman Filter Areal Density Uncertainty

[jdkio]

The areal density (often called track length in the code) is a measure of the density of the material traveled through times the distance traveled. It's directly related to the track energy for muons, and so is used to calculate the muon energy.

Right now, we use the 2d U and V track length and average it. This is because the y position jumps, so using the 3d track would give an incorrect answer (we should try with a constant y, and then maybe correct with average track angle).

Kalman Filter

The kalman filter measures the y position much better. So we can replace our current track length with this new calculation (it'd be nice to retain the old one in a different branch to compare). This should give us the most accurate measurement.

On top of that, we can add a measure of uncertainty in the energy using the covariance matrix states from the kalman filter. I'm not entirely sure how to do this. To first order, it may be enough to offset the positions in Y by +/-1 sigma and recalculate the track length

We also have some uncertainty in z assuming we got the ending plane correct. So we can also add an uncertainty based on this uncertainty.

And finally there's the known unknown style errors. Basically we know sometimes we fail to reco to the true endpoint of the track. Like reco may get confused or we miss some hits. Can we say something about this, or is that beyond the scope of this uncertainty? We may want to run a sample, measure the average error based on the style of track (good y resolution vs bad resolution) and make that our uncertainty.