New data analysis for AURIGA Lucio Baggio Italy, INFN and University of Trento AURIGA AURIGA
The (new) AURIGA data analysis Since 2001 the AURIGA data analysis for burst search have been rewritten from scratch (G. Vedovato), in parallel with major upgrades taking place on the detector The main goals and specifications to achieve were: • Be flexible and modular, with easy adaptation to new algorithms • Adopt the VIRGO/LIGO frame format for data storage and exchange � new data acquisition system • Recycle software (and be recyclable) open source project, C++ widespread use of supported and well known libraries: ROOT ( http://root.cern.ch ) VEGA ( http://wwwlapp.in2p3.fr/virgo/vega ) FrameLibs ( http://wwwlapp.in2p3.fr/virgo/FrameL ) FFTW ( http://www.fftw.org ) LAL ( http://www.lsc-group.phys.uwm.edu/lal ) MKFilter (http://www-users.cs.york.ac.uk/~fisher/mkfilter) • And, develop new algorithms, indeed! (highlight: Karhunen-Loeve decomposition)
Overview (see poster) The data analysis of raw or simulated data for burst search divides in a series of tasks 1. Estimate parameters of the analytic part of the noise model (Full Model Estimate, FME) 2. Remove noise correlation (Full Whitening, FW) 3. Perform a matched template filtering and event search (EVT) 4. Define epoch vetoes based on Gaussianity monitors (Data Quality, DQ) 5. Compute distribution of errors in event parameters estimators (Monte Carlo, MTC) DAQ FME DQ EVT FW MTC DAQS
Event search (1) see poster Within this task the whitened data are optimally filtered in the frequency domain for a specified template signal . Then, the time series is passed to the event search algorithm EVT event search optimal filter & coarse interpolation max-hold raw data noise model template bank fine interpolation
Event search (2) •The time series is downsampled to a convenient sampling rate •The absolute value of the downsampled time series is searched for the local maxima (max- hold algorithm with a given dead time ), and when it is above a proper threshold a candidate event trigger is issued •For each event trigger, the exact time of arrival and amplitude are computed after fine interpolation of the samples, along with sum of squared residuals (for χ 2 -test), Karhunen- Loeve components, etc time
Event statistics from Monte Carlo (MTC) see poster The goal of this task is to estimate numerically the distributions of time of arrival and amplitude errors , for a bank of filter templates, possibly not exactly matched with the input signal. Software signal injection takes place in the time domain, by adding a chosen template (properly rescaled in amplitude and time-shifted) to the actually measured white noise of the system. Template injection and search is automatically cycled for specified time and amplitude increments, and can be repeated for indipendently specified signal and filter templates. MTC Phase 2 template injection whitened data Phase 1 event coarse search interpolation template bank
http://www.ligo.caltech.edu/docs/P/P010019-01.pdf Karhunen-Loeve Decomposition (1) signal h optimally filtered with template Wiener filter +noise ( S h ) amplitude templateless suboptimal KLD δ -filtered energy estimate δ -filter: F( ω ) = S h ( ω ) -1 ↔ R -1 (inverse autocorrelation matrix) -2 = 1) ( σ f Karhunen-Loeve eigenfunctions { ψ k } k=1,…,N R ψ k = σ k 2 ψ k ( Σ k σ k -2 = 1) signal noise input: Σ k h k ψ k + Σ k n k ψ k n k ~Gauss(0, σ k ) -2 h k ψ k + Σ k σ k f δ = R -1 h = Σ k σ k -2 n k ψ k 2 = f δ ·Rf δ = Σ k σ k -2 h k 2 + Σ k σ k 2 + 2 Σ k σ k -2 h k n k ≠ f δ ·f δ = Σ k σ k -4 h k 2 + … Define: A KL -2 n k average power without signal: A KL ~ Chi(N) 2 ) 1/2 + Σ k σ k with signal: A KL = ( Σ k σ k -2 h k n k ( Σ i σ j -2 h k -2 h j 2 ) -1/2 + O 2 (n/A KL ) ω ω 2 | H | ( ) d ∫ SNR h = Gauss(0,1) ω π S ( ) 2
Karhunen-Loeve Decomposition (2) linear filter with mismatched template Karhunen-Loeve decomposition probability density amplitude SNR δ SNR h • Pros : The signal-to-noise ratio through KLD equals the maximum one achievable with template knowledge • Cons : increased tail of fake events definition of event baricenter?
Summary see also poster • Brand new code, rewritten from scratch in C++, running on standalone PCs • Integrated ARMA noise simulator, generating stationary or time varying correlated gaussian noise, possibly polluted with power line harmonics, periodic signals and bursts. • Adaptive parametric noise model estimate • Support for non-parametric frequency-dependent calibration function • Support for template bank search. • Embedded Monte Carlo and tools for measuring efficency. To do: • Re-implementation of data conditioning, study for optimization of the (still) empirical vetoing rules. Tuning on forthcoming sensitivity and stability of the detector. • Make the analysis more robust with respect to heavy data corruption by spectral lines and transient disturbances. • Training on templateless search, tuning of time interval size for K-L decomposition comparison with time-frequency methods • Intensify collaboration with other research groups, in order to share algorithms
Pararametric noise model estimator Phase 1 Iterative fit and data conditioning Periodograms quality check FME Phase 1 avr : 64x26.8 Wed Apr 2 19:18:48 2003 FFT1 FME Volt^2/Hz -8 10 Phase 1 Phase 2 FFT2 Periodograms quality Iterative fit and data Time series smoothing -9 check conditioning 10 FFT3 raw data FFT1 FME Phase 1 avr : 64x26.8 Wed Apr 2 19:18:48 2003 -10 SDFT FFT2 Volt^2/Hz 10 -8 10 FFT3 -9 10 -10 10 -11 10 -11 10 -12 10 -12 -13 10 10 Outlier removal 800 900 1000 1100 1200 1300 1400 1500 1600 1700 FFTn Hz FFTn -13 10 800 900 1000 1100 1200 1300 1400 1500 1600 1700 Hz
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