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Coherent Analysis by using multiple interferometric detectors. Norichika Sago (Osaka) with Hideyuki Tagoshi (Osaka) Hirotaka Takahashi (Osaka City) Nobuyuki Kanda (Osaka City) S. Dhurandhar (IUCAA). 6th Edoardo Amaldi Conference, June 20-24, 2005

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coherent analysis by using multiple interferometric detectors

Coherent Analysis by usingmultiple interferometric detectors

Norichika Sago (Osaka)


Hideyuki Tagoshi (Osaka)

Hirotaka Takahashi (Osaka City)

Nobuyuki Kanda (Osaka City)

S. Dhurandhar (IUCAA)

6th Edoardo Amaldi Conference, June 20-24, 2005

at Bankoku Shinryoukan, Okinawa, Japan



  • Many plan of GW detectors are on going in the world.
  • Japanese future plan : LCGT

(Large-scale Cryogenic Gravitational Telescope)

Better sensitivity


Two interferometers

An analysis method of multiple data is needed !

Analysis method

  • Coincident analysis

Make event list of each detector

Compare these lists

Fake reduction

  • Coherent analysis

Analyze a data set from a network

of detectors simultaneously

Improve sensitivity

purpose of this work
Purpose of this work

Estimate the improvement of detection efficiency

by using multiple detectors

  • Comparison with coincidence and coherence
  • Take account of correlation between detectors
  • Semi-analytic estimate

: output of each detector


injection signal : chirp signal

2-detectors :

  • same location, same orientation
  • same noise spectrum
  • stationary Gaussian noise

Output from a network of detectors

From the assumption (same location, same orientation),

coherent analysis with two detectors no correlation between detectors

: modifided Bessel function

Coherent analysis with two detectors(no correlation between detectors)

Finn, PRD 63, 102001 (2001)

Pai, Dhurandhar and Bose, PRD 64, 042004 (2001)

  • SNR of 2-detector network

From the assumption,

  • Probability distribution of SNR

For data with signal :

For no signal data :


false alarm rate

(alert a detection for data without signal)

number of independent


false alarm probability for

a single template

We can calculate the threshold for a given false alarm rate:

  • false dismissal probability

(alert no detection for data with signal)

The detection efficiency is given by:

coincident analysis case
Coincident analysis case
  • false alarm rate

no window case

Taking account of parameter window

increasing the number of template

(Here, we assume Nwin=10.)

  • detection efficiency

: False dismissal rate for single detector

number of template
Number of template
  • considered parameter

mass of binary :

coalescence time :

  • estimate of the number of template

number of data point

number of template in mass space

Owen (’95)

for LCGT case

MM : minimal match (=0.97)

f0 : frequency at minimal noise spectrum

mmin : minimal mass for search

maximum mass for search :

lower limit of detection efficiency
Lower limit of detection efficiency

2 detector (LCGT)

1-yr observation

stationary Gaussian noise

no correlation between detectors

All templates are independent.

We assume Nwin = 10.

detection probability



false alarm rate

more accurate false alarm rate
More accurate false alarm rate

Actually, templates correlate each other.

: parameter set

Overestimate of false alarm rate

If events A and B are dependent,

We can estimate the more accurate false alarm rate

by considering the independent portion of all templates.

number of independent templates
Number of independent templates
  • correlation in time

We regard that two templates are independent if the difference

of the coalescence time between them is larger than 8 msec.

( Match of them is sufficiently small. )

  • correlation in mass space

Here we consider the cases that 1%, 10% and 50% of all templates

are independent, respectively.

(A estimate by simulations is needed for a more realistic evaluation.)

more accurate detection efficiency
More accurate detection efficiency

2detectors, coherent

If we take account of the cor-

relation between templates,

the number of independent

templates decreases.

The detection efficiency increases.

detection probability

false alarm rate

two detectors with correlation
Two detectors with correlation
  • correlation in same frequency (2detectors)
  • diagonalization of noise matrix

We define a new set of data with a linear combination of bare data.


The psuedo-detector 1 contains no signal.

We can regard the case that a signal with amplitude,

is injected into a detector with

detection efficiency correlated detectors
Detection efficiency (correlated detectors)

correlation factor between

two detectors, e

Here we assume the phase of

signal is known in advance.

detection efficiency

solid line : coherence

dashed line : coincidence

(Nwin = 10)

The blue, green and red lines

show the cases of

black solid : single detector

false alarm rate

summary and future works
Summary and Future works
  • Detection efficiency of coherent analysis is better than the
  • one of coincident analysis in stationary Gaussian noise case.
  • Correlation between detectors makes the efficiency get worse.
  • However, if the detectors’ correlation is less than 10%, they
  • can observe better efficiently than by a single one.

Future works

  • Simulation to estimate the more accurate detection efficiency
  • Analysis with more realistic noise
  • (non-Gaussian, non-stationary, …)