xkalman program description i.gavrilenko p.n.lebedev/cern
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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.