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Transcript of Physics Laboratory
Progress report of the HOU contribution to TDR (WP2)
A. G. Tsirigotis
In the framework of the KM3NeT Design Study
WP2 - Demokritos, 31 March 2009
The HOU software chain
Underwater Detector
•Generation of atmospheric muons and neutrino events (F77)
•Detailed detector simulation (GEANT4-GDML) (C++)
•Optical noise and PMT response simulation (F77)
•Filtering Algorithms (F77 –C++)
•Muon reconstruction (C++)
•Effective areas, resolution and more (scripts)
Calibration (Sea top) Detector
•Atmospheric Shower Simulation (CORSIKA) – Unthinning Algorithm (F77)
•Detailed Scintillation Counter Simulation (GEANT4) (C++) – Fast Scintillation Counter Simulation (F77)
•Reconstruction of the shower direction (F77)
•Muon Transportation to the Underwater Detector (C++)
•Estimation of: resolution, offset (F77)
Event Generation – Flux Parameterization
•Neutrino Interaction Events
•Atmospheric Muon Generation(CORSIKA Files, Parametrized fluxes )
μ
•Atmospheric Neutrinos(Bartol Flux)
ν
ν•Cosmic Neutrinos(AGN – GRB – GZK and more) Earth
Survival probability
Shadowing of neutrinos by Earth
GEANT4 Simulation – Detector Description
• Any detector geometry can be described in a very effective way
Use of Geomery Description Markup Language (GDML-XML) software package
•All the relevant physics processes are included in the simulation• (NO SCATTERING)
Fast Simulation EM Shower Parameterization
•Number of Cherenkov Photons Emitted (~shower energy)
•Angular and Longitudal profile of emitted photons
Visualization
Detector componentsParticle Tracks and Hits
Prefit, filtering and muon reconstruction algorithms
•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 (Direct Walk)
•Compination of Χ2 fit and Kalman Filter (novel application in this area) using the arrival time information of the hits•Charge – Direction Likelihood using the charge (number of photons) of the hits
dm
L-dm
(Vx,Vy,Vz) pseudo-vertex
dγ
d
Track Parameters
θ : zenith angle φ: azimuth angle (Vx,Vy,Vz): pseudo-vertex coordinates
θc
(x,y,z)
State vector
1
exp
k
k
x x
tH
x
0 0,x CInitial estimation
Update Equations
Kalman Gain Matrix
Updated residual and chi-square contribution (rejection criterion for hit)
Kalman Filter application to track reconstruction
timing uncertainty
Many (40-200) candidate tracks are estimated starting from different initial conditions The best candidate is chosen using the chi-square value and the number of hits each track has accumulated.
0 0( , ).x C
Charge Likelihood
hit nohit
hit nohit
N N
i data ii 1 i 1
;E,D, ;E,D,
(N N )
ln P (V ) P (0 )
L
i data PMTresolutiondatan 1
P (V ;E,D, ) F(n;E,D, )G n(V ;n, )
dataV Hit charge in PEs
Probability depends on muon energy, distance from track and PMT orientation
F(n;E,D, ) Not a poisson distribution, due to discrete radiation processes
Ln(F
(n))
Ln(n)
E=1TeVD=37mθ=0deg
Log(E/GeV)
hit nohitL (N N )
8m
20 floors per tower30m seperationBetween floors
30m
Tower Geometry Floor Geometry
45o 45o
Detector Geometry: 10920 OMs in a hexagonal grid.91 Towers seperated by 130m, 20 floors each. 30m between floors
Working Example 60 meters maximum abs. length no scattering
Optical Module
•10 inch PMT housed in a 17inch benthos sphere•35%Maximum Quantum Efficiency•Genova ANTARES Parametrization for angular acceptance
50KHz of K40 optical noise
Working Example
Results
Atmospheric Muons (Corsika files - 1 hour of generated showers)
Cos(theta)
dN
dTd(Time in days)
Without any cuts (21000/day misrec. as upgoing)
With optimal cuts(0 misrec. as upgoing)#hit>=12#solutions>=20#compatible>=10#compatible / #sol >0.5
Mild likelihood cut depended on reconstructed energy
Neutrino effective area (E-2 spectrum)Results
Eff
ecti
ve a
rea
(m2 )
Neutrino Energy (log(E/GeV))
Without any cuts
With optimal cuts
Neutrino Angular resolution (median in degrees)Results
Neutrino Energy (log(E/GeV))
An
gu
lar
reso
luti
on
(m
edia
n d
egre
es)
Without any cuts
With optimal cuts
Results Atmospheric neutrinos (Bartol Flux)
Cos(theta)
dN
dTd
(Time in days)
With optimal cuts (130/day rec.)
Without any cuts (200/day rec.) 65% cut efficiency
Neutrino Energy (log(E/GeV))
dN
dTdE
(Time in days)
Results Muon energy reconstruction (at the closest approach to the detector)Simulation data from E-2 neutrino flux
Log(Etrue/GeV)
Lo
g(E
rec/
GeV
)
Results Muon energy reconstruction resolution
Log(Etrue/GeV)
RM
S(L
og
(E/G
eV))
Δ(Log(E/GeV))
Work to be done
•Calculation of point source sensitivities for varius depths (~ 2 weeks)
•Simulation of more Geometries (Benchmark – MultiPMT string detector and more) (~ 2 weeks)
•Optical photon scattering in GEANT4 simulation (~ 1 month)
Conclusions
Kalman Filter is a promising new way for filtering and reconstruction for KM3NeT
However for the rejection of badly misreconstructed tracks additional cuts must be applied
Presented by Apostolos G. TsirigotisEmail: [email protected]
Kalman Filter – Basics (Linear system)
1kk k kx F x w
Equation describing the evolution of the state vector (System Equation):
k k k km H x Measurement equation:
Definitions
kx Estimated state vector after inclusion of the kth measurement (hit) (a
posteriori estimation)
km Measurement k
x Vector of parameters describing the state of the system (State vector)
kF Track propagator
kw Process noise (e.g. multiple scattering)
k Measurement noise
kH Projection (in measurement space) matrix
kx a priori estimation of the state vector based on the previous (k-1)
measurements
cov( )k kw Q
cov( )k kV
Kalman Filter – Basics (Linear system)
Prediction (Estimation based on previous knowledge)
1kk kx F x
Extrapolation of the state vector
Extrapolation of the covariance matrix
1cov( )
k
Tk k k k kC x F C F Q
Residual of predictions
k k k kr m H x
Covariance matrix of predicted residuals
Tk k k k kR V H C H
(criterion to decide the quality of the measurement)
Kalman Filter – Basics (Linear system)
Filtering (Update equations)
( )k k k k k kx x K m H x
(1 )k k k kC K H C
where,
1( )T Tk k k k k kK C H V H C H
is the Kalman Gain Matrix
Filtered residuals:
(1 )k kk k k k kr m H x H K r cov( ) (1 )k k k k kR r K H V 2 Contribution of the filtered point:
2 1,
Tk F k k kr R r (criterion to decide the quality of the measurement)
Kalman Filter – (Non-Linear system)
( )k k k kF x f x ( )k k k kH x h x
Extended Kalman Filter (EKF)
kk
k
fF
x
k
kk
hH
x
Unscented Kalman Filter (UKF)
A new extension of the Kalman Filter to nonlinear systems, S. J. Julier and J. K. Uhlmann (1997)
Kalman Filter Extensions – Gaussian Sum Filter (GSF)
t-texpected
•Approximation of proccess or measurement noise by a sum of Gaussians
•Run several Kalman filters in parallel one for each Gaussian component
V
x
Kalman Filter – Muon Track Reconstruction
Pseudo-vertex
Zenith angle
Azimuth angle
State vector
Measurement vector t
mq
Hit Arrival time
Hit charge
1kkx x
System Equation:
Track Propagator=1 (parameter estimation)
No Process noise (multiple scattering negligible for Eμ>1TeV)
( )k k k km h x
Measurement equation:
exp
exp
( )( )
( )
t xh x
q x
2
2
0cov( )
0t
kq
Simulation of the PMT response to optical photons
Single Photoelectron Spectrum
mV
Quantum Efficiency
Πρότυπος παλμός
Standard electrical pulse for a response to a single p.e.
Arrival Pulse Time resolution
Simulation of the PMT response to optical photons
Quantum Efficiency
Arrival Pulse Time resolution
Standard electrical pulse for a response to a single p.e.
Single Photoelectron Spectrum
Kalman Filter – Muon Track Reconstruction - Algorithm
Extrapolate the state vector
Extrapolate the covariance matrix
Calculate the residual of predictionsDecide to include or not the measurement (rough criterion)
Update the state vector
Update the covariance matrix
2Calculate the contribution of the filtered pointDecide to include or not the measurement (precise criterion)
Prediction Filtering
Initial estimates for the state vector and
covariance matrix