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Physics Laboratory

Physics Laboratory. School of Science and Technology. Hellenic Open University. Application of Kalman filter methods to event filtering and reconstruction for Neutrino Telescopy. A. G. Tsirigotis. VLVnT08 - Toulon, Var, France, 22-24 April 2008. In the framework of the KM3NeT Design Study.

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Physics Laboratory

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  1. Physics Laboratory School of Science and Technology Hellenic Open University Application of Kalman filter methods to event filtering and reconstruction for Neutrino Telescopy A. G. Tsirigotis VLVnT08 - Toulon, Var, France, 22-24 April 2008 In the framework of the KM3NeT Design Study

  2. IceCube Geometry: 9600 OMs looking up & down in a hexagonal grid. 80 Strings, 60 storeys each. 17m between storeys 125 meters

  3. MultiPMT Optical Module (NIKHEF Design) 20 x 3” PMTs (Photonis XP53X2) in each 17” Optical Module Optical Noise Outside view Inside View Single PMT Rate (dark current + K40) ~ 4kHz 120 Hz Double coincidence rate per OM (20 ns window) 6 Noise Hits per 6μsec window (9600 MultiPMT OMs in a KM3 Grid)

  4. Muon Event Generation (1 TeV Muons, isotropic flux, IceCube Geometry, 9600 OMs) KM3NeT

  5. Prefit, filtering and muon reconstruction algorithms d L-dm (x,y,z) θc dγ Track Parameters θ : zenith angle φ: azimuth angle (Vx,Vy,Vz): pseudo-vertex coordinates dm (Vx,Vy,Vz) pseudo-vertex • Local (storey) Coincidence (Applicable only when there are more than one PMT looking towards the same hemisphere) • Global clustering (causality) filter • Local clustering (causality) filter • Prefit and Filtering based on clustering of candidate track segments • Χ2fit without taking into account the charge (number of photons) • Kalman Filter (novel application in this area)

  6. Kalman Filter – Basics (Linear system) Definitions Vector of parameters describing the state of the system (State vector) a priori estimation of the state vector based on the previous (k-1) measurements Estimated state vector after inclusion of the kth measurement (hit) (a posteriori estimation) Measurement k Equation describing the evolution of the state vector (System Equation): Track propagator Process noise (e.g. multiple scattering) Measurement equation: Projection (in measurement space) matrix Measurement noise

  7. Kalman Filter – Basics (Linear system) Prediction (Estimation based on previous knowledge) Extrapolation of the state vector Extrapolation of the covariance matrix Residual of predictions (criterion to decide the quality of the measurement) Covariance matrix of predicted residuals

  8. Kalman Filter – Basics (Linear system) Filtering (Update equations) where, is the Kalman Gain Matrix Filtered residuals: Contribution of the filtered point: (criterion to decide the quality of the measurement)

  9. Kalman Filter – (Non-Linear system) Extended Kalman Filter (EKF) Unscented Kalman Filter (UKF) A new extension of the Kalman Filter to nonlinear systems, S. J. Julier and J. K. Uhlmann (1997)

  10. Kalman Filter Extensions – Gaussian Sum Filter (GSF) • Approximation of proccess or measurement noise by a sum of Gaussians • Run several Kalman filters in parallel one for each Gaussian component t-texpected

  11. Kalman Filter – Muon Track Reconstruction Pseudo-vertex Zenith angle State vector Azimuth angle Hit Arrival time Measurement vector Hit charge System Equation: Track Propagator=1 (parameter estimation) No Process noise (multiple scattering negligible for Eμ>1TeV) Measurement equation:

  12. Kalman Filter – Muon Track Reconstruction - Algorithm Filtering Prediction Update the state vector Extrapolate the state vector Update the covariance matrix Extrapolate the covariance matrix Calculate the residual of predictions Decide to include or not the measurement (rough criterion) Calculate the contribution of the filtered point Decide to include or not the measurement (precise criterion) Initial estimates for the state vector and covariance matrix

  13. Chi-square vs Kalman Filter – Comparison (1TeV muons isotropic flux) With initial background filtering Space angle resolution Zenith angle resolution σ=0.081±0.004 σ=0.074±0.004 KF KF degrees degrees degrees degrees efficiency = 56% KF efficiency = 54%

  14. Filtering Efficiency (1 TeV Muons, isotropic flux, IceCube Geometry, 9600 OMs) Events passing after background filtering Noise Events with number of hits (noise+signal) >4 Signal Number of Active OMs Noise Percentage of noise hits after filtering Signal Number of Active OMs percentage

  15. Chi-square vs Kalman Filter – Comparison (1TeV muons isotropic flux) Without initial background filtering Space angle resolution Zenith angle resolution KF KF degrees degrees degrees degrees efficiency = 11% KF efficiency = 48%

  16. Conclusions Kalman Filter is a promising new way for filtering and reconstruction for KM3NeT Presented by Apostolos G. Tsirigotis Email: tsirigotis@eap.gr

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