tracking at lhcb introduction: tracking performance at lhcb kalman filter technique speed...

Tracking at LHCb

• Introduction: Tracking Performance at LHCb

• Kalman Filter Technique

• Speed Optimization

• Status & Plans

June 4, 2004 NIKHEF B-physics meeting 2Jeroen van Hunen

Detector response: test-beam data (resolution, efficiency, noise, cross-talk) Spill-over effects included (25 ns bunch spacing)

PYTHIA and GEANT simulation

Trigger simulation: thresholds tuned to get maximal signal efficiencies at limited output rates of 1 MHz (L0) and 40 kHz (L1)

Offline reconstruction: Full pattern recognition (track finding, RICH reco.)


Track finding strategy

VELO seeds

Long track (forward)

Long track (matched)

T seeds

Upstream track

Downstream track

T track

VELO track

T tracks useful for RICH2 pattern recognition

Long tracks highest quality for physics (good IP & p resolution)Downstream tracks needed for efficient KS finding (good p resolution)Upstream tracks lower p, worse p resolution, but useful for RICH1 pattern recognition

VELO tracks useful for primary vertex reconstruction (good IP resolution)


Tracking performance

Red: Geant hits

Blue: reconstructed tracks

- 2050 hits assigned to a long track - 98.7% correctly assigned- Efficiency: 94%

On average:26 long tracks11 upstream tracks4 downstream tracks5 T tracks26 VELO tracks



Eff = 94% (p > 10 GeV)

Ghost rate = 3%(for pT > 0.5 GeV)



IP resolutionp/p

0.37 %p

p

IP 20μm Typical:


Kalman Filter Technique


Prediction and filter step

Kalman technique : Efficient iterative solution for a least-squares fit

Detector planes Measurement and error

State vector (x,y,tx,ty,q/p) is updated at each measurement by performing a prediction and filter step.

• prediction Estimate of state at a given z-position based on previous planes

• filter (update) Weighted mean of the prediction and measurement at given z-pos.

Direction of Kalman filter


Detector Material

Detector material is taken into account by adjusting the state vector and it’s covariance matrix:

• Multiple scattering For small deflection angles Gaussian, increases the covariance matrix elements of tx, ty. Additional factor tuned to give track parameters with pull=1.

• Energy loss:

Charged hadrons + muons ( ) Affects the momentum, but not the covariance matrix. The factor cion is tuned to give a momentum pull that is centered around zero.

Electrons (bremsstrahlung) Affects the momentum and the covariance matrix. (Increase of covariance allows to correct a sudden momentum change LHCb classic only)

0X

c

dx

dE ion

ion

Note : Covariance matrix V:

22 2/

2

1)(

xexG

uxVux

n

T

eV

xG

1

21

||2

1)( 2/ ))(( jjiiij uxuxEV


Magnetic field

Prediction and with Fk = Propagation matrix.

Fk : determined using Runge-Kutta (The LHCb B-field is not homogeneous and has Bx,By and Bz components). A 5th order adaptive Runge-Kutta is used (the step size is automatically adjusted to obtain a given precision, by comparing with a fourth order Runge-Kutta).

11 ~~

kkkk xFx

Filter (update) Weighted mean of the prediction and measurement.

Smoother Information of last state is propagated backwards to earlier states.

kTkkk

kk QFCFC

11


Kalman Filter needs a state to start with ( ) taken from pattern recognition

Seeding (example):

Seed for Kalman filter

1~

kx

magnet

1kCCovariance matrix

should be ‘infinite’ in order to use the measurements only one time and create artificially small errors


Speed Issues


Long Tracks Filter and Smooth : 17ms per track on (1GHz Pentium III)

• Filtering (prediction and update)

• Smoothing

• Outlier removal

Reference : HLT processing time 60 ms (1GHz Pentium III). HLT should do pattern recognition, track fitting and a selection for specific final states.

States Including the determination of the states at 5 specified z-positions (beam line, RICH1, RICH2) it is 24ms.

From this 24 ms, 21ms is used for the Transport Service (88%).

How long takes the Kalman filtering

( FilterandSmooth = 240s, for 14000 tracks from which 13000 have 3 hits in the Velo and 3 hits in the OT )

Tool to obtain the radiation length of detector material that is encountered by the particleVELO (50%), OT/IT (19%), RICH2

(13%), TT (9%), RICH1 (4%)


Gaining time

Look for possible improvements in:

-TransportSvc / XML

-Extrapolation (Runge-Kutta)

TransportSvc / XML

• TransportSvc implementation ( C++ and Gaudi)

• XML

• Check if we can simplify

• Volume distribution

• Used logical volumes with solid

• Use assemblies (but reimplemented)


Gaining time

• Use Transport service differently:

Request the transport service less often, but for longer distances, thus:

• Call transportSvc for long distance

• Store information from transportSvc

• Take small steps in extrapolation using stored information until the deviation of the track with respect to the original estimate is too large.

Needs testing

Extrapolation (Runge-Kutta)

• C++ and Gaudi (only use msgSvc in case of error, etc.)

• Runge-kutta (4th , 5th, other ?)

• Use of extrapolator : Runge-kutta parabolic extrapolator (small steps)

In Velo region: It is 3.8 times faster to call the TransportSvc one time for 80 cm than 10 times for 8 cm


Other applications of Kalman Technique

Kalman technique is generally implemented because it is fast

Higher level trigger applications

At LHCb:

- HLT processing time 60 ms

-Current track fit 17 ms/track , thus about 0.5 sec/event.

Would like to do the track fit in a few ms/event, thus need to speed up by a factor 100

Seems possible :

- Ignore detector material (gives factor 10)

- Replace/Improve Runge-Kutta (G. Raven : Pt-kick to get through magnet)

- Only prediction and update (no smoother step)


Status & Plans

• Implement fast Kalman Fit (for HLT, etc.) without material, Runge-kutta, smoother, etc.

(a first version exist, but still has some strange features)

• Try improve use of transport svc, by calling it less often (at the moment 700.000 times for 500 events) and store information.

tracking at lhcb introduction: tracking performance at lhcb kalman filter technique speed...

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