xKalman program description

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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

THTRec

TBTrec

xKalman

xKalman++

ATLAS Inner Detector TDR. 1997

Atlas Technical Proposal. 1994

ATLAS Trigger Performance Status
Report. 1998

ATLAS Detector and Physics
Performance TDR. 1999

TRT
-
barrel

uniform MF


TRT

uniform MF

Inner detector

uniform MF

Inner detector

non
-
uniform MF

xKalman

Main xKalman algorithms

Kalman filter
-
smoother













Histogramming method













Cellular automaton












z

r

Fo

F
=
C
=
C

C

Barrel TRT End cap

Fo

Fo
=
Space point


Segment

E=
S
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 SILICONS

using cellular automation

Track candidates finding


in PIXELS


using cellular automaton

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


Tracks comparison

Tracks extension in TRT using
Kalman filter
-
smoother formalism


Tracks combination with


EM
-
calorimeter


Tracks combination with


Muon System

xKalman

xKalman++ classes and design


Input information


Tracker


Surface


Layer


Counter


Cluster


ClusterP


ClusterT


SpacePo


Algorithm


Helix


Noise


Segment


Histogram


SpacePt




Output information


BTrack


Track








Tracker

Algorithm


1

Algorithm


2

BTrack

BTrack

Analysis



GEANT

Alignment

Event

xKalman

Class Tracker structure


Tracker


Layer


Counter


Cluster


SpacePoint

Surface



ClusterP


ClusterT

pCl

pCo

pL

pTr

xKalman

Transverse view of the Atlas Inner Detector

precision layers only

Layer

Wafer(Counter)

xKalman

Kalman filter




H
k
k
-
1
= f(H
K
K
)

where H
k
k

-

filterd helix in layer k and H
k
k
-
1

-
projection of its parameters to layer k
-
1


C
k
k
-
1
=F
k
-
1
(C
k
k
+Q
K
)F
T
K
-
1

where C
k
k

-

covariance matrix of the filtered helix parameters in layer k,


Q
k

-

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

and F
k

-

Jacobian matrix of the helix transformation


C
k
-
1
k
-
1
=(1+C
k
k
-
1
U
K
-
1
)
-
1
C
k
k
-
1
,


H
k
-
1
k
-
1
=H
k
k
-
1
+C
k
-
1
k
-
1
U
k
-
1
(M
K
-
1
-
H
k
k
-
1
)

where M
k
-
1

and U
k
-
1
represent the measured hit parameters and their weight matrix,

and H
k
-
1
k
-
1
and C
k
-
1
k
-
1

are the updated helix parameters and covariance matrix.


dc
2
=(H
k
-
1
k
-
1
-
H
k
k
-
1
)C
k
k
-
1
-
1
(H
k
-
1
k
-
1
-
H
k
k
-
1
)
T
+(H
k
-
1
k
-
1
-
M
k
-
1
)U
k
-
1
(H
k
-
1
k
-
1
-
M
k
-
1
)
T



k
-
2

k
-
1
k


H
k
-
1
k
-
1

H
k
k


H
k
k
-
1
H
k+1
k

xKalman

Smoother




H
k
-
1
k
= f(H
n
k
-
1
)

where H
n
k
-
1

-

smoother helix in layer k
-
1 and H
k
-
1
k

-
projection of its parameters to layer k


C
k
-
1
k
=F
k
C
n
k
-
1
F
T
k

where C
n
k
-
1

-

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

and F
k

-

Jacobian matrix of the helix transformation


C
n
k
=B(C
k
-
1
k
B
T
+Q
k
),


H
n
k
=H
k
-
1
k
-
BA(H
k
-
1
k
-
H
k
k
)

with A=Q
K
W
k
k

and B=(1+A)
-
1

where H
k
k
,C
k
,W
k

are respectively the filtered helix and its covariance and weight matrices

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

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



k
-
2

k
-
1
k


H
k
-
2
k
-
1

H
k
-
1
k


H
n
k
-
1
H
n
k

xKalman

Classe Helix


Helix


5 parameters


15 covariance


x
F
r Im


y Z Z


F

F F


T T T=ctan(
q
)=Pz/pT


C C C=q/p


Surface

Propagation to Surface

Search closest cluster from the Counter

Add or subtract cluster information

Add or subtract noise contribution

xKalman

Classes Cluster and Space points.


Cluster

Pointer to Counter.

Kine.

Azimuthal angle.

User parameter.


ClusterP

First parameter.

Second parameter.

Error of first parameter.

Error of second parameter.

Angle.


ClusterT

Drift time information.

High or low energy.





SpacePo

Pointer to first Cluster

Pointer to second Cluster

Radius (R).

Azimuthal angle (
F
).

Z
-
coordinate.

Cov(R,R)

Cov(
F,F
)

Cov(Z,Z)

xKalman

Class Noise


Noise


Cov(F,F)


Cov(T,T)


Cov(C,C)


Correction C

Multiple scattering



Energy loss due


to ionizatio
n


Energy loss due


to bremsstrahlung


Muon


track model


Electron


track model

xKalman

Classes BTrack and Track


BTrack


Track


Helix


Infor


ClusA


Surface


InforTRTSeed


InforSILRec


ClusAP


ClusAT


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/
Y
-
>

e
+
e
-
, Lepton b
-
tagging, photon identification.

Primary vertex reconstruction.

Reconstruction of exclusive B
-
decays: B
d
o
-
>J/
Y
K
s
o
, B
s
o
-
>D
s
-
p
+
.

Vertex b
-
tagging.

B
-
physics triggers.

Muon identification.

Higgs bosons reconstruction.