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

4

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.

8

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.

9

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

10

ResultsThreshold x Matched Filter

Train

MF Threshold

Test

MF Threshold

11

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

14

Free-RunningFind optimal parameters

• Noise and signal concatenated in a known sequency.• If index output belongs to any signal sample – signal found.

15

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.