1. Updates on the P0D reconstruction
LE PHUOC TRUNG
BROOK
Track fitting using Kalman filter
Extrapolation tracks from the TPC
T2K US-ND280 meeting, June 24, 2008

2. Track fitting overview
Warning: not P0D actual scintillator plane layout!
Particle trajectory
Scintillator plane
Recon. position + direction
Before fitting: only a set of hits, no track parameters
Calculate the best estimates of position and direction of the particle trajectory at each scintillator plane.
After fitting: track parameters: position and direction

3. The Kalman filter System matrix Process noise State to be estimated
A linear discrete-time system:
System matrix
Process noise
State to be estimated
Measurements
Measurement noise
Measurement matrix
State notation:
State estimate BEFORE using measurement k
The key element in the Kalman filter is the Kalman filter gain.
State estimate AFTER using measurement k
Iterative formula:
Prediction step:
Kalman filter gain
Update step:
Contain new information

4. Kalman filter for track fitting
State:
Dynamic system:
zero-mean Gaussian
Mention deltaz,
Random, small direction change
Measurement:

5. Forward-backward smoothing
Measurement:
charge-weighted position
Forward filtering
Backward filtering
Forward/backward direction is not important, just pick a direction. Kalman filter update step uses measurements up to and including measurement k, we want to use as much information as possible in the estimation => smooth
Smoothing
Calculated from forward, backward cov. matrices

6. Fitting results Evaluate performance:
Use muon MC with small step length, 1mm  Save more trajectory points
At each plane, calculate the x,y deviations of the recon. position from the true position
The true position is the true GEANT4 track point that is z closest to the recon. point. mm mm

7. TPC track extrapolation
Motivation: improve 0 purity
P0D
TPC
Muon track obscured by showers
P0D
TPC
0 sample after all 0 selection cuts
Muon track obscured by showers
A CC event passing all 0 selection cuts

8. Extrapolation procedure and result
Extrapolate using Kalman filter:
4cm gate
TPC k
k-1
scintillator planes
Need to mention that fact that extrapolation is fully 3D
Hits within the gate are used as new position measurement. Measurement update the filter.
If the gate is empty, stop extrapolating.
Note: 3D extrapolation, alternate x,y scintillator planes
A TPC track successfully extrapolated into the P0D

9. Summary and to-do list Summary: To do:
Track fitting using Kalman filter
Extrapolation TPC tracks
To do:
Full-spill reconstruction
 Through-and-through muon tracking
 Muon decay tagging
 Improve 0 reconstruction

10. Forward-backward smoothing
Forward filtering
Backward filtering
Smoothing
Forward/backward direction is not important, just pick a direction

11. Fitting results
Angle (degrees)
Delta z(mm)

12. Charge-weighted position
Original hits
Charge weighted position
MC hits and weighted positions