Kalman Filter backward pass is using measurements twice without weights

[andiwand]

After a discussion in acts-project/traccc#788 I believe that our backward pass smoothing implementation in the Kalman Filter is not correct. We simply start from the last state and run the same filter back in the other direction. This will result in using measurements twice without applying any weights and potentially biased covariances and parameters.

This might also affect the GSF implementation.

References

• Backward filter for Two-filter Smoothing traccc#788
• https://link.springer.com/book/10.1007/978-3-030-65771-0

[paulgessinger]

Which one is this? The jacobian unrolling or backwards propagation?

[andiwand]

This only affects the backward propagation smoother for both KF and GSF. #3996 improves the situation by inflating the covariance in the backward pass. This will result in the best possible resolution at the reference surface and innermost measurement. However all the other track states will not have the best possible resolution. The question is if this is even necessary usually even though we definitely want to be able to produce them.

If forward, backward and smoothing steps would be decoupled the user could choose what they really want. This might also need some EDM changes.