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1
A Matched Filter for Cosmic Ray Detection from Eletromagnetic Wave Reflection
Luciano Andrade
Thiago Ciodaro
José Seixas
Federal University of Rio de Janeiro/COPPE
2
Outline
Cosmic shower detection by radio-wave reflection. The detector setup. Signal detection in low signal-to-noise ratio
environments → The Matched-Filter (MF).– Whitening– Detection efficiency
Free-running. Conclusions.
3
Cosmic shower detection by radio-wave reflection
1. Particule shower generation.2. Radio wave reflection.3. Transmitter antenna.4. Receiver antenna.5. Receptor station.6. Scintilators.
Well known approach for metheor detection.
Very High Frequency (VHF) waves – 30 to 300 MHz.
Commercial DTV - channel 2 (55.25 MHz) and 4 (67.25 MHz).
Scintilators - high efficiency, but small area. Only for test.
transmitterreceptor
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The Detector Setup
antenna
GPS – to synchronize several stations
soundboard
(80 kHz)
radioreceivers
NIM crate for the scintilators
hard disc(high capacity)
50 0.5 1 1.5 2 2.5
x 105
-4
-2
0
2
4
6
8
10
12
14
16x 10
-3
Raw data and typical signal shape
3 seconds recorded data (only noise)
Typical cosmic signal
Vol
ts
# sample
# sample
Vol
ts
• MARIACHI in Brookhaven.
• DRACON in Rio.
• Only one antenna.
• No coincidence with scintilator.
• Data selected by hand.
• To test the matched filter method.
• Automatic detection – event filter.
6
Signal detection in low signal-to-noise ratio environment
Hypothese test: H0 - only noise, H1 - noise + signal.
If the noise is gaussian, with zero mean and decorrelated
The detected cosmic signal is a stochastic process.
S will be aproximates by the mean of the several pre-selected signals.
The decision is given by the likelihood ratio
s
l
MF
decision
This is the matched filter equation.
7
Data Set
Tipical signal length – 36 samples.
480 signals selected.
3600 noise segments (36 samples).
50 % train set, 50% test set.
S = mean signal.
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Noise characterization
• Gaussian fit
• Chi-square = 1.475
• Mean = 0.032 mVolts
Noise distribution
Noise covariance matrix
• Samples are correlated.
• It will be considered white for the first tests.
• Whitening pre-processing should be done.
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Whitening
W MFl
Sw
WS Sw
Covariance of the whitened noise - Train Covariance of the whitened noise - Test
• Remove the noise mean.• Projection in a decorrelated base.• Normalize each component (σ2 = 1)
decision
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ResultsThreshold x Matched Filter
Train
MF Threshold
Test
MF Threshold
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ResultsThreshold x Matched Filter
Receiver Operating Characteristic - Train Receiver Operating Characteristic - Test
12
Whitening
13
Free-Running algorithm
MF
> threshold step
output
memory = 0
step
memory = output
MF
> memory
output
memory = output
back
Find indexwith max
correlation
memory = 0
index
yes
no yes
no
• Input – raw data.• Output – index of signal candidates.• Need two parameters: step and threshold.
raw data
• scan in step samples.• until output > threshold.
Looking for the best index for the signal
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Free-RunningFind optimal parameters
• Noise and signal concatenated in a known sequency.• If index output belongs to any signal sample – signal found.
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Free Running results(step = 6, threshold = 0.5)
Receiver Operating Characteristic - Train Receiver Operating Characteristic - Test
16
Conclusion and To-Do list
New approach in cosmic shower detection. Low cust environment. Free-running matched filter → stored data
reduction. Next steps
– Whitening pre-processing + free-running.– Implement stochastic signal detection.– Coincidence with scintilator.
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