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

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.

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

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  1. xKalman program descriptionI.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

  2. Geometry of the ATLAS Inner Detector xKalman iPatRec PixlRec xKalman

  3. Display of simulated H events xKalman

  4. History of the xKalman development TRT-barrel uniform MF THTRec Atlas Technical Proposal. 1994 TRT uniform MF ATLAS Inner Detector TDR. 1997 TBTrec ATLAS Trigger Performance Status Report. 1998 Inner detector uniform MF xKalman ATLAS Detector and Physics Performance TDR. 1999 xKalman++ Inner detector non-uniform MF xKalman

  5. Main xKalman algorithms Histogramming method Kalman filter-smoother Cellular automaton F Barrel TRT End cap Smoother P Hit Noise P Noise Hit Fo + Fo + + - - C C P Hit Noise P Noise Hit r z + + + - - Fo P Hit Noise P Noise Hit Space point Segment + + + - - P Hit Noise + + E= STijWiWj Filter C Vertex xKalman

  6. 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 extension in TRT using Kalman filter-smoother formalism Tracks comparison Tracks combination with EM-calorimeter Tracks combination with Muon System xKalman

  7. xKalman++ classes and design Input information Tracker Surface Layer Counter Cluster ClusterP ClusterT SpacePo Algorithm Helix Noise Segment Histogram SpacePt Output information BTrack Track Event GEANT Tracker Alignment Algorithm 1 Algorithm 2 Analysis BTrack BTrack xKalman

  8. Class Tracker structure Tracker Surface pTr Layer pL Counter pCo Cluster ClusterP ClusterT pCl SpacePoint xKalman

  9. Transverse view of the Atlas Inner Detectorprecision layers only Layer Wafer(Counter) xKalman

  10. Kalman filter Hkk-1= f(HKK) where Hkk - filterd helix in layer k and Hkk-1 -projection of its parameters to layer k-1 Ckk-1=Fk-1(Ckk+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+Ckk-1UK-1)-1Ckk-1, Hk-1k-1=Hkk-1+Ck-1k-1Uk-1(MK-1-Hkk-1) where Mk-1 and Uk-1 represent the measured hit parameters and their weight matrix, and Hk-1k-1and Ck-1k-1 are the updated helix parameters and covariance matrix. dc2=(Hk-1k-1-Hkk-1)Ckk-1-1(Hk-1k-1-Hkk-1)T+(Hk-1k-1-Mk-1)Uk-1(Hk-1k-1-Mk-1)T k-2k-1 k Hk-1k-1 Hkk Hkk-1 Hk+1k xKalman

  11. Smoother Hk-1k= f(Hnk-1) where Hnk-1 - smoother helix in layer k-1 and Hk-1k -projection of its parameters to layer k Ck-1k=FkCnk-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-1kBT+Qk), Hnk=Hk-1k-BA(Hk-1k-Hkk) 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-2k-1 k Hk-2k-1 Hk-1k Hnk-1 Hnk xKalman

  12. Classe Helix Surface Propagation to Surface Helix 5 parameters 15 covariance x Fr Im y Z Z F F F T T T=ctan(q)=Pz/pT C C C=q/p Search closest cluster from the Counter Add or subtract cluster information Add or subtract noise contribution xKalman

  13. Classes Cluster and Space points. Cluster Pointer to Counter. Kine. Azimuthal angle. User parameter. 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) ClusterP First parameter. Second parameter. Error of first parameter. Error of second parameter. Angle. ClusterT Drift time information. High or low energy. xKalman

  14. Class Noise Noise Cov(F,F) Cov(T,T) Cov(C,C) Correction C Multiple scattering Energy loss due to ionization Muon track model Energy loss due to bremsstrahlung Electron track model xKalman

  15. Classes BTrack and Track BTrack Track Surface Helix p Infor p ClusA p InforTRTSeed ClusAP InforSILRec ClusAT InforTRTUpd xKalman

  16. 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: Bdo->J/YKso, Bso->Ds-p+. Vertex b-tagging. B-physics triggers. Muon identification. Higgs bosons reconstruction. xKalman

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