Coherent Analysis of Signals from Misaligned Interferometers

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• Coherent Analysis of Signals from Misaligned
  Interferometers
• M. Rakhmanov, S. Klimenko
• Department of Physics, University of Florida,
• Gainesville, FL 32611, USA
• The 9th GWDAW Workshop,
• Annecy, France, 15-18 Dec. 2004

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table of content

• Introduction
• motivation, existing methods
• Correlation of mixed signals
• Numerical simulation
• fixed source
• all sky search
• Further developments
• Summary

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GW burst searches with detector network
Search algorithms for bursts with network of
interferometers utilize incoherent and coherent
analysis techniques. Incoherent (excess
power) analysis relies mostly on timing.
(TFCLUSTER, POWER,) Coherent (x-correlation)
analysis include the waveform consistency tests.
(like r-statistics) Combined approaches Maximum
likelihood Methods like WaveBurst Goal
detection source parameter reconstruction

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Related papers
Y.Gursel and M.Tinto, Near optimal solution to
the inverse problem for GW bursts, Phys.Rev.
D40 (1989) 3884 A.Vicere, Optimal detection of
burs events in GW interferometric
observatories, LIGO P010019-02 N.Arnaud,
M.Barsuglia, M.-A.Bizouard, V.Brisson,
F.Cavalier, M.Davier, P.Hello,
S.Kreckelbergh, E.Porter, Coincidence and
coherent data analysis methods for GW
bursts in a network of interferometric detectors,
Phys.Rev.D68 (2003) 102001 W.Anderson, P.Brady,
J.Creighton, E.Flanagan, An excess power
statistic for detection of burst sources of
gravitational radiation, Phys.Rev.D63 (2001)
042003 S.Bose, A robust and coherent network
statistic for detecting GW from inspiraling
compact binaries in non-Gaussian noise.
Class.Quant.Grav. 19 (2002) 1437 J.Sylvestre,
Power filters for GW bursts network operation
for source position estimation,
Class.Quant.Grav.20 (2003)S753 L.Cadonati,
Coherent waveform consistency test for LIGO burst
candidates, Class.Quant.Grav.21 (2004)
S1695 R. Johnston and S.Mohanty, Detection
strategies for multi-interferometer triggered
seach, 2004 UTB Report

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methods for coherent detection

• Pearson x-correlation (r-statistic)
• assume identical waveforms
• 2 polarizations
• GW signals
• antenna patterns
  and delays are
• defined by the location of the source
• Gursel-Tinto technique
• Constraint (gt2 ifos)

L.Cadonati, Class.Quant.Grav.21 (2004) S1695
Y.Gursel and M.Tinto, Phys.Rev.D40 (1989) 3884
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correlation of mixed signals
given multiple signals (minimum 3)
Gursel-Tinto recipe for
mixing signals correlation of mixed
signals Cauchy-Schwarz guarantees max C at
source location similar to cosine-test
redundancy algorithm form mixed signals and
combine correlation functions

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numerical simulations
single source analysis GW burst signals with
two independent polarizations a given source
(fixed location, fixed polarization) detector
locations and orientations H1, H2, L, GEO
time-lag search is replaced by sky search with
1-degree resolution noise model normal
distribution (sigma1) SNR varies within
approx 1,20 all-sky simulation sources
randomly distributed on the sky random
polarization angles 2000 trials for each SNR
(signal present) 20000 trials for noise
simulation

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simulated waveforms

BH-BH 10SM (Lazarus waveforms) dt 1/16384
s V1,V2,V3 Hanford, Livingston, GEO filter
bandpass(100Hz, 2kHz), window 696 dt delays
are defined by the position of the GW source
J.Baker, M.Companelli, C.Lousto, Phys.Rev.D 65
044001
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simulated waveforms
Hrss 0.07, 0.06, 0.13 SNR 9.0,
8.4, 16.9
Hrss 0.23, 0.22, 0.44 SNR 29.8,
28.0, 56.3

variance of noise rate (number of points in
1s)
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fixed source detection (aligned detectors)

source location polarization perfectly
aligned detectors (HLG) gt maximum
correlation R-statistic
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fixed source detection (misaligned detectors)

source location polarization misaligned
detectors H,L,G orientations M-statistics
calculate C1, C2, C3, and select maximum value
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all sky simulation (r-stat)

Gaussian noise random source location random
polarization perfectly aligned pair
H1,H2 (assume equal sensitivity) misaligned
detectors H,L,G
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all sky simulation (m-stat)

Gaussian noise random source location random
polarization misaligned detectors H,L,G max(3)
maximum value of C1,C2,C3
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comparison of two methods

three misaligned detectors are about the same
as two aligned detectors
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source localization
H1x(L1xG1)
L1x(H1xG1)

C1 C2
G1x(H1xL1)
SNR20
C3 Cp
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waveform reconstruction
localization of the source polarization angle is
set to Once the angles are found, the
waveforms can be reconstructed from the detector
signals. Gursel and Tinto equations and
cyclic permutations.

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summary
Correlation of GW burst signals detected with
misaligned detectors can be performed by mixing
the signals from several detectors. This
approach can be viewed as an extension of the
r-statistics, a method used for burst searches in
LIGO S2 and S3 data. The performance of the
method was studied with numerical
simulations. The method can also be used for
source location and waveform reconstruction. We
are currently studying other detection and source
reconstruction algorithm including the methods
based on network maximum likelihood.