Regularized coherent network analysis pipeline for triggered - - PowerPoint PPT Presentation

Regularized coherent network analysis pipeline for triggered searches

Kazuhiro Hayama Center for Gravitational Wave Astronomy University of Texas at Brownsville Malik Rakhmanov, Shantanu Desai(Penn State) Soumya Mohanty(UTB)

LIGO-G060653-00-0

Burst Triggered Search

• Gamma ray burst, Neutrino burst, X-ray burst from transient

astronomical events

• The time and sky location of these events can be estimated by
• ther astronomical observations such as HETE,

SuperKamiokande, Chandra etc. Triggered search already going

• GRB - Cross Correlation method ----- S. Mohanty’s talk
• SGR - Excess Power method ----- L. Matone’s talk

Our approach ----- regularized coherent network method Outline

• Data Conditioning
• Event Selection based on

regularized coherent network analysis

• Analysis
• Detection Efficiency
• Accuracy of waveform estimation

CGWA LIGO-G060653-00-0

Data Conditioning likelihood sky map sky map post-processing

0"02 0"04 0"06 0"08 0"1 0"12 0"14 !2 !1 1 2 ()10

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Band-pass filtered(64-2000Hz) signals

4 data at H1-H2-L1-GEO with same simulated detector noise(right figure). A burst signal is injected.

Data for Demonstration

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Simulated line features: sinusoids

strain noise spectrum(Hz )

frequency(Hz) time strain

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CGWA LIGO-G060653-00-0

Time domain method Wavelet-based method Data Conditioning likelihood sky map sky map post-processing

0.02 0.04 0.06 0.08 0.1 0.12 !5 5 x 10

!20

0.02 0.04 0.06 0.08 0.1 0.12 !0.5 0.5

Regularized coherent network analysis pipeline Time domain method

• Time domain noise floor

whitening

• S. Mukherjee CQG 21 (2004)

S1783

• Remove lines by Median Based

Line Tracker

• S. Mohanty CQG 19 (2002) 1513

strain time(sec) band pass filtered at 64Hz-2000Hz after conditioning CGWA LIGO-G060653-00-0

Time domain method Wavelet-based method Data Conditioning likelihood sky map sky map post-processing

0"02 0"04 0"06 0"08 0"1 0"12 !( ( )*10

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+,-.*/,00*123456.*,4*6478!200078 0"02 0"04 0"06 0"08 0"1 0"12 !0"( 0"( ,1456*9:-.242:-2-;

• Select frequency region to

analyze by nulling around lines

• In frequency region, spectrum is

estimated by wavelet de-noising.

• Whiten data using estimated

spectrum

Regularized coherent network analysis pipeline

time(sec) strain

Wavelet-based method

band pass filtered at 64Hz-2000Hz CGWA LIGO-G060653-00-0

Data Conditioning likelihood sky map sky map post-processing

• 1. Data is divided into chunks
• 2. generate skymap at each chunk

signal included Detector output Ill-posed problem One Solution-- Tikhonov regularization

• M. Rakhmanov CQG 23 (2006) S673

R@source location rank defficiency

CGWA LIGO-G060653-00-0

Regularized coherent network analysis pipeline

(h)

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0.2 0.4 0.6 0.8 1 false alar/ rate 1123o5r6 7etection ;ro<a<ility

5000 trials in which a burst is in the simulated noise (sampling rate = 4096Hz) The burst: black hole merger 5000 trials in noise data Receiver Operating Characteristic Curve

SNR(H1,H2,L1,G1)=

(11.3,11.3, 13.9, 9.3) (8.5, 8.5, 10.4, 7.0) (7.3, 7.3, 9.0, 6.0)

Simulation

Data Conditioning likelihood sky map sky map post-processing

(hour )

• 1

for 1 year observation, 1 in 876 triggers with confidence 95%

CGWA

Detection Efficiency

LIGO-G060653-00-0

!150 !100 !50 50 100 150 !80 !60 !40 !20 20 40 60 80 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 x 10

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Without DC With DC

Effect of Data Conditioning

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10 0.2 0.4 0.6 0.8 1 false alarm probability detection probability

Up

longitude (deg) Latitude (deg) CGWA LIGO-G060653-00-0

Data Conditioning likelihood sky map sky map post-processing

sky map whitening

LIGO-G060653-00-0

Preliminary

> CGWA standard deviation:noise map mean noise map standard deviation:after standardized standard deviation:raw sky map location of minimum after standardized location of minimum before standarized KL basis component number

0.02 0.04 0.06 0.08 0.1 0.12 !2 2 x 10

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0.02 0.04 0.06 0.08 0.1 0.12 !5 5 x 10

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h+ hx

time(sec) strain

Accuracy of Waveform Estimation

Data Conditioning likelihood sky map sky map post-processing CGWA LIGO-G060653-00-0

signal gain=1 : corresponds to SNR(H1,H2,L1,L2)= (11.3,11.3, 13.9, 9.3)

blue:original green:reconstructed

Data Conditioning likelihood sky map sky map post-processing 0.02 0.04 0.06 0.08 0.1 0.12 !2 2 x 10

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0.02 0.04 0.06 0.08 0.1 0.12 !* * x 10

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To de-noise, wavelet-based waveform estimation method is used (red)

Hayama, Fujimoto CQG 23 (2006) S9

Accuracy of Waveform Estimation

h+ hx

time(sec) strain

CGWA LIGO-G060653-00-0 blue:original red:estimated

0"0#6 0"0#8 0"06 0"062 0"064 0"066 0"068 0"0( !# # )*10

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Accuracy of Waveform Estimation

Using H1-L1-VIRGO..... these detectors have comparable sensitivity Supernova signal at (112, -30) at 2kpc distant from Earth SNR(H1,L1,V)=(11.1, 14.0, 3.5) h waveform(duration=14msec) of the burst from 2kpc at (112,-30) can be estimated within MSE of 0.3 Dimmelmeier et al. A1B1G1_R strain time(sec)

CGWA LIGO-G060653-00-0

blue:original red:estimated

SNR (with rough spectrum estimation) Hp:7.8 Hc:3.2

Reconstruction of Inspiral signal

Idea: Join continuous reconstructed h+,hx segments

• ----->> we can get arbitrary signal’s h+, hx time series.

Example : Inspiral signal(1M-1M),1Mpc Matched filter on h+, hx Theoretical SNR H1:16.6 H2:16.6 L1:17.8 GEO:4.5

CGWA

0.2 0.4 0.6 0.8 !6 !4 !2 2 4 x 10!20

reconstructed hx

LIGO-G060653-00-0

Noise spectrum of reconstructed hx, h+

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CGWA frequency (Hz) frequency (Hz)

strain noise spectrum(Hz )

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strain noise spectrum(Hz )

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Regularized coherent network analysis pipeline for triggered search has been developed From the pipeline, we get not only a detection statistic but also the reconstructed polarization waveforms. Using wavelet-based waveform estimation, we showed accuracy of estimated waveform We can get h+, hx time series for any given direction

• n the sky and can search for signals other than

bursts.(e.g. template based search) In progress: application to real data

Summary and future work

CGWA LIGO-G060653-00-0

Data Conditioning likelihood sky map sky map post-processing

sky map whitening

CGWA

Location of minimum R Standard deviation of skymap

LIGO-G060653-00-0

Reconstruction of Inspiral signal

0.02 0.04 0.06 0.08 0.1 0.12 !5 5 x 10

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0.02 0.04 0.06 0.08 0.1 !1 !0.( 0.( 1 x 10!21

SNR H1:4.34 H2:8.65 L1:8.6 GEO:1.83 SNR:8.65 Waveform

strain strain time(sec) time(sec) CGWA

0.5 1 1.5 2 0.5 1 1.5 signal gain mean square error h+ 0.5 1 1.5 2 5 10 signal gain mean square error hx

Averaged mean square error normalized signal energy as a function of signal gain. # of trials at each SNR is 1000.

Accuracy of Waveform Estimation

signal gain=1 corresponds to SNR (H1,H2,L1,G1)= (11.3,11.3, 13.9, 9.3)

CGWA

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0.2 0.4 0.6 0.8 1 false alar/ rate 1123o5r6 7etection ;ro<a<ility

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

To obtain ROC, the numerical simulation consists of 5000 trials in which the burst is in simulated LIGO noise, and 5000 trials in only noise.

Detection Efficiency

Detection probability vs False alarm probability ?? Receiver Operating Characteristic Curve

SNR(H1,H2,L1,G1)=

(11.3,11.3, 13.9, 9.3) (8.5, 8.5, 10.4, 7.0) (7.3, 7.3, 9.0, 6.0)

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Comparison of trigg and untrigg

CGWA

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Data Conditioning Event Selection Detection Efficiency Event Reconstruction

To obtain ROC, the numerical simulation consists of 5000 trials in which the burst is in simulated LIGO noise, and 5000 trials in only noise.

Detection Efficiency

Detection probability vs False alarm probability ?? Receiver Operating Characteristic Curve

SNR(H1,H2,L1,G1)=

(11.3,11.3, 13.9, 9.3) (8.5, 8.5, 10.4, 7.0) (7.3, 7.3, 9.0, 6.0)

Untriggered Search

CGWA

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

!30 !20 !10 10 100 200 300 400 500 '00 n)r+a-i/ed 3 4re5uen78 nu+9er :tatisti7a- pr)pert8 )4 3

Noise Only Noise plus Signal SNRs of signal at each detectors are (H1,H2,L1,G1)= (11.3,11.3, 13.9, 9.3)

Statistical Property of R

Histograms are normalized by mean and variance of R of noise only data For event selection, Threshold of detection is decided to satisfy adequate false alarm rate and detection probability

Regularized coherent network analysis pipeline

CGWA

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

Reconstructed sky maps around the true segment (Center)

Regularized coherent network analysis pipeline

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

Efficiency of Source Location

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• Fraction of signals detected

within 8 of their true position ??

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

4 6 8 10 12 14 0.1 0.2 0.3 0.4 0.5 0.6 0.7 signal!to!noise ratio efficiency

# of trials at each SNR is 1000 Location of supernova from Galactic center can be estimated within error of pm 8 at efficiency 0.6 !

Efficiency of Source Location

0.02 0.04 0.06 0.08 0.1 0.12 !2 2 x 10

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0.02 0.04 0.06 0.08 0.1 0.12 !5 5 x 10

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Data Conditioning Event Selection Detection Efficiency Event Reconstruction

Accuracy of Waveform Estimation

h+ hx In case of gain = 2

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

Regularized coherent network analysis pipeline Time domain method

• Time domain noise floor

whitening

• S. Mukherjee CQG 21 (2004)

S1783

• Remove lines by Median Based

Line Tracker

• S. Mohanty CQG 19 (2002) 1513

Time Frequency 0.5 1 1.5 2 2.5 3 3.5 1000 2000 !40 !20 20 40 Time Frequency 0.5 1 1.5 2 2.5 3 3.5 1000 2000 !40 !20 20 40

500 1000 1500 2000 2500 !500 !400 !300 !200 !100 100 First stage whitening Input data Whitened data

Data Conditioning Event Selection Detection Efficiency Event Reconstruction

Regularized coherent network analysis pipeline Time domain method

• Time domain noise floor

whitening

• S. Mukherjee CQG 21 (2004)

S1783

• Remove lines by Median Based

Line Tracker

• S. Mohanty CQG 19 (2002) 1513