xKalman

xKalman program description I.Gavrilenko P.N.Lebedev/CERN

• Geometry of the ATLAS Inner Detector.

• Overview of pattern recognition programs.

• History of the xKalman development.

• Main xKalman algorithms.

• xKalman strategy of the reconstruction.

• Main xKalman++ classes and design.

• xKalman applications.

xKalman

Geometry of the ATLAS Inner Detector

xKalman

iPatRec

PixlRec

xKalman

Display of simulated H events

xKalman

History of the xKalman development

THTRecTHTRec

TBTrecTBTrec

xKalmanxKalman

xKalman++xKalman++

ATLAS Inner Detector TDR. 1997ATLAS Inner Detector TDR. 1997

Atlas Technical Proposal. 1994Atlas Technical Proposal. 1994

ATLAS Trigger Performance Status Report. 1998

ATLAS Trigger Performance Status Report. 1998

ATLAS Detector and Physics Performance TDR. 1999

ATLAS Detector and Physics Performance TDR. 1999

TRT-barrel

uniform MF

TRT-barrel

uniform MF

TRT

uniform MF

TRT

uniform MF

Inner detector

uniform MF

Inner detector

uniform MF

Inner detector

non-uniform MF

Inner detector

non-uniform MF

xKalman

Main xKalman algorithms

Kalman filter-smoother

Kalman filter-smoother

Histogramming method Histogramming method Cellular automaton Cellular automaton

zr

C

C C

Barrel TRT End cap

Space point

Segment

E= TijWiWj

Smoother

Filter

+ +

+ +

+ +

+ +

Vertex

-

-

-

Noise

Noise

Noise

Noise

Noise

Noise

Hit

Hit

Hit

Hit

Hit

Hit

P

P

P

P

P

P

P Hit Noise

+

+

+

-

-

-

xKalman

xKalman strategy of the reconstruction

Track candidates finding

in TRT

using histograming

Track candidates finding

in TRT

using histograming

Track candidates finding

in SILICONS

using cellular automation

Track candidates finding

in SILICONS

using cellular automation

Track candidates finding

in PIXELS

using cellular automaton

Track candidates finding

in PIXELS

using cellular automaton

Local pattern recognition in PIXELS and SILICONS using Kalman filter-smoother formalism

Local pattern recognition in PIXELS and SILICONS using Kalman filter-smoother formalism

Tracks comparison Tracks comparison

Tracks extension in TRT using Kalman filter-smoother formalism

Tracks extension in TRT using Kalman filter-smoother formalism

Tracks combination with

EM-calorimeter

Tracks combination with

EM-calorimeter

Tracks combination with

Muon System

Tracks combination with

Muon System

xKalman

xKalman++ classes and design

Input information

Tracker

Surface

Layer

Counter

Cluster

ClusterP

ClusterT

SpacePo

Input information

Tracker

Surface

Layer

Counter

Cluster

ClusterP

ClusterT

SpacePo

Algorithm

Helix

Noise

Segment

Histogram

SpacePt

Algorithm

Helix

Noise

Segment

Histogram

SpacePt

Output information

BTrack

Track

Output information

BTrack

Track

Tracker Tracker

Algorithm

1

Algorithm

1Algorithm

2

Algorithm

2BTrack BTrack Analysis

Analysis

GEANT Alignment

Event

xKalman

Class Tracker structure

Tracker Tracker

Layer Layer

Counter Counter

Cluster Cluster

SpacePoint SpacePoint

SurfaceSurface

ClusterP ClusterP ClusterT ClusterTpCl

pCo

pL

pTr

xKalman

Transverse view of the Atlas Inner Detectorprecision layers only

LayerLayer

Wafer(Counter)Wafer(Counter)

xKalman

Kalman filter

Hkk-1= f(HK

K)

where Hkk - filterd helix in layer k and Hk

k-1 -projection of its parameters to layer k-1

Ckk-1=Fk-1(Ck

k+QK)FTK-1

where Ckk - covariance matrix of the filtered helix parameters in layer k,

Qk - additional covariance to be added due to intercation with the material of layer k

and Fk - Jacobian matrix of the helix transformation

Ck-1k-1=(1+Ck

k-1UK-1)-1Ckk-1,

Hk-1k-1=Hk

k-1+Ck-1k-1Uk-1(MK-1-Hk

k-1)

where Mk-1 and Uk-1 represent the measured hit parameters and their weight matrix,

and Hk-1k-1and Ck-1

k-1 are the updated helix parameters and covariance matrix.

k-1k-1-Hk

k-1)Ckk-1

-1(Hk-1k-1-Hk

k-1)T+(Hk-1k-1-Mk-1)Uk-1(Hk-1

k-1-Mk-1)T

k-2kk

Hk-1

k-1kk

Hk

k-1 Hk+1k

Hkk-1= f(HK

K)

where Hkk - filterd helix in layer k and Hk

k-1 -projection of its parameters to layer k-1

Ckk-1=Fk-1(Ck

k+QK)FTK-1

where Ckk - covariance matrix of the filtered helix parameters in layer k,

Qk - additional covariance to be added due to intercation with the material of layer k

and Fk - Jacobian matrix of the helix transformation

Ck-1k-1=(1+Ck

k-1UK-1)-1Ckk-1,

Hk-1k-1=Hk

k-1+Ck-1k-1Uk-1(MK-1-Hk

k-1)

where Mk-1 and Uk-1 represent the measured hit parameters and their weight matrix,

and Hk-1k-1and Ck-1

k-1 are the updated helix parameters and covariance matrix.

k-1k-1-Hk

k-1)Ckk-1

-1(Hk-1k-1-Hk

k-1)T+(Hk-1k-1-Mk-1)Uk-1(Hk-1

k-1-Mk-1)T

k-2kk

Hk-1

k-1kk

Hk

k-1 Hk+1k

xKalman

Smoother

Hk-1k= f(Hn

k-1)

where Hnk-1 - smoother helix in layer k-1 and Hk-1

k -projection of its parameters to layer k

Ck-1k=FkCn

k-1FTk

where Cnk-1 - covariance matrix of the smoother helix parameters in layer k-1,

and Fk - Jacobian matrix of the helix transformation

Cnk=B(Ck-1

kBT+Qk),

Hnk=Hk-1

k-BA(Hk-1k-Hk

k)

with A=QKWkk and B=(1+A)-1

where Hkk,Ck,Wk are respectively the filtered helix and its covariance and weight matrices

and Qk is the ‘noise’ matrix for for filtering. In the absence of ‘noise’ process, where Qk=0

the smoothing procedure is equivalent to a pure outward-going extrapolaton.

k-2kk

Hk-2

k-1k-1k

Hn

k-1 Hnk

Hk-1k= f(Hn

k-1)

where Hnk-1 - smoother helix in layer k-1 and Hk-1

k -projection of its parameters to layer k

Ck-1k=FkCn

k-1FTk

where Cnk-1 - covariance matrix of the smoother helix parameters in layer k-1,

and Fk - Jacobian matrix of the helix transformation

Cnk=B(Ck-1

kBT+Qk),

Hnk=Hk-1

k-BA(Hk-1k-Hk

k)

with A=QKWkk and B=(1+A)-1

where Hkk,Ck,Wk are respectively the filtered helix and its covariance and weight matrices

and Qk is the ‘noise’ matrix for for filtering. In the absence of ‘noise’ process, where Qk=0

the smoothing procedure is equivalent to a pure outward-going extrapolaton.

k-2kk

Hk-2

k-1k-1k

Hn

k-1 Hnk

xKalman

Classe Helix

Helix

5 parameters

15 covariance

x r Im

y Z Z

T T T=ctan()=Pz/pT

C C C=q/p

Helix

5 parameters

15 covariance

x r Im

y Z Z

T T T=ctan()=Pz/pT

C C C=q/p

Surface Surface

Propagation to SurfacePropagation to Surface

Search closest cluster from the CounterSearch closest cluster from the Counter

Add or subtract cluster informationAdd or subtract cluster information

Add or subtract noise contributionAdd or subtract noise contribution

xKalman

Classes Cluster and Space points.

Cluster

Pointer to Counter.

Kine.

Azimuthal angle.

User parameter.

Cluster

Pointer to Counter.

Kine.

Azimuthal angle.

User parameter.

ClusterP

First parameter.

Second parameter.

Error of first parameter.

Error of second parameter.

Angle.

ClusterP

First parameter.

Second parameter.

Error of first parameter.

Error of second parameter.

Angle.

ClusterT

Drift time information.

High or low energy.

ClusterT

Drift time information.

High or low energy.

SpacePo

Pointer to first Cluster

Pointer to second Cluster

Radius (R).

Azimuthal angle ().

Z-coordinate.

Cov(R,R)

Cov()

Cov(Z,Z)

SpacePo

Pointer to first Cluster

Pointer to second Cluster

Radius (R).

Azimuthal angle ().

Z-coordinate.

Cov(R,R)

Cov()

Cov(Z,Z)

xKalman

Class Noise

Noise

Cov(F,F)

Cov(T,T)

Cov(C,C)

Correction C

Noise

Cov(F,F)

Cov(T,T)

Cov(C,C)

Correction C

Multiple scatteringMultiple scattering

Energy loss due

to ionization

Energy loss due

to ionization

Energy loss due

to bremsstrahlung

Energy loss due

to bremsstrahlung

Muon

track model

Muon

track model

Electron

track model

Electron

track model

xKalman

Classes BTrack and Track

BTrack BTrack

Track Track

Helix Helix Infor Infor ClusA ClusA

Surface Surface

InforTRTSeed InforTRTSeed

InforSILRec InforSILRec

ClusAP ClusAP

ClusAT ClusAT

InforTRTUpd InforTRTUpd

p p p

xKalman

xKalman applications

Single track performance: Momentum , Angular and Impact parameter resolution.

Pattern recognition : Efficiencies, Tails, Fake rate, Effect of Noise and Detector inefficiency

High-pT electrons and QCD-Jet rejection.

Low -pT electrons: J/ e+e-, Lepton b-tagging, photon identification.

Primary vertex reconstruction.

Reconstruction of exclusive B-decays: Bdo->J/Ks

o, Bso->Ds

-+.

Vertex b-tagging.

B-physics triggers.

Muon identification.

Higgs bosons reconstruction.

Single track performance: Momentum , Angular and Impact parameter resolution.

Pattern recognition : Efficiencies, Tails, Fake rate, Effect of Noise and Detector inefficiency

High-pT electrons and QCD-Jet rejection.

Low -pT electrons: J/ e+e-, Lepton b-tagging, photon identification.

Primary vertex reconstruction.

Reconstruction of exclusive B-decays: Bdo->J/Ks

o, Bso->Ds

-+.

Vertex b-tagging.

B-physics triggers.

Muon identification.

Higgs bosons reconstruction.