soma mukherjee gwdaw8, milwaukee, dec. 17-20'03 interferometric data modeling: issues in...
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Interferometric Data Modeling: Issues in realistic data generation.
Soma Mukherjee CGWA
University of Texas Brownsville
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Why ?
Astrophysical searches estimate efficiency from playground data.
Extrig search – how representative is the’off-source’ segment of the ‘on-source’ one ?
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Data Modeling: Basis
Interferometric data has three components : lines, transients and noise floor.As a first approximation, the three components are independent and appear additively. Physically different sources for each
Basic idea is to split a channel into these components with mutual exclusion Classify Transients, fit ARMA models to line
amplitude and phase modulation, ARMA models for noise floor rms
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Issue I :Slowly drifting noise floor
Data from present generation of interferometers is non-stationary.Results obtained by running
MNFT1 on a stretch of LIGO
S2 data.[1Mukherjee, CQG, 2003]
Low pass and
resample
Estimate spectral
Noise floor with
Running Median
Whiten data using
FIR whitening
Filter.
Clean lines and
Highpass
Compute RunningMedian of the
Squared timeseriesSet threshold
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Issue II : Modeling ALL lines
MBLT1 : Non-parametricLine estimation. [1 Mohanty
CQG, 2001 ]
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
KSCDKolmogorv-Smirnov test based Change point Detector Mohanty, PRD (2000); Mohanty, GWDAW (2002)
Issue III : Transient Clasification
12 top wavelet coefficients of data surrounding each KSCD trigger. Visualized using GGobi. (Preliminary).
Mukherjee, 2003, Amaldi, Pisa
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
MNFT outline:MNFT outline:
Algorithm:1. Lowpass and resample given timeseries x(k).2. Construct FIR filter that whitens the noise
floor. Resulting timeseries : w(k)3. Remove lines using notch filter. Cleaned
timeseries : c(k)4. Track variation in second moment of c(k)
using Running Median and apply smoothing (SRM).
5. Obtain significance levels of the sampling distribution via Monte Carlo simulations.
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Model Noise Generation
Model Noise Floor (low order ARMA).Estimate lines, model amplitude and phase, add reconstructed lines to synthetic data .Add transients .
Use MNFT toCompute smoothed
Running Median
Fit ARMA to theSRM
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
ARMA (p,q)
A(q) y(t) = C(q) e(t)Y(t) : Outpute(t) : White noiseC(q)/A(q) : Transfer functionq: Time shift operatorA and C : Polynomials
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
How faithful is the model ?
Apply statistical tests of hypothesis
Kolmogorov-Smirnov
Akaike Information criterionIakaike (p,q) = ln 2
p,q + 2 (p+q)/N
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Result I : Noise floor model – ARMA (12,7)
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Result II : Line Amplitude - ARMA (27,11)
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Line model : Amplitude & Phase
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Soma Mukherjee GWDAW8, Milwaukee, Dec. 17-20'03
Comments
Applicable to band limited data.Use as an ‘infinite’ playground for astrophysical searches.Gives a better handle on non-stationarity and hence testing the robustness of the search algorithm.Allows us to do ‘controlled tests’.Signal injection and efficiency estimation