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4th ILIAS-GW Annual General Meeting Universit ät Tübingen, October 8-9 2007

LIGO-G 07XXXX -00- Z. The Waves Group. 4th ILIAS-GW Annual General Meeting Universit ät Tübingen, October 8-9 2007. Glitch Rejection Capabilities of a Coherent Burst Detection Algorithm . Maria Principe , Innocenzo M. Pinto TWG, University of Sannio @ Benevento, INFN and LSC.

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4th ILIAS-GW Annual General Meeting Universit ät Tübingen, October 8-9 2007

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  1. LIGO-G07XXXX-00-Z The Waves Group 4th ILIAS-GW Annual General Meeting Universität Tübingen, October 8-9 2007 Glitch Rejection Capabilities of a Coherent Burst Detection Algorithm Maria Principe, Innocenzo M. Pinto TWG, University of Sannio @ Benevento, INFN and LSC

  2. Outlook • Sought signals vs local disturbances: GW bursts, glitches and atoms • Simplest coherent network algorithm • Rationale and model • Conclusions and future work 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  3. Sought Signals: GWB (Stolen from Katsavounidis, LIGO-G-070033-00-Z) 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  4. Sought Signals: GWBs • Poorly modeled or unmodeled transient signals: • Sine-Gaussians and Gaussians also probed • Gross Features: • Time duration: 1-100 ms typical • Center frequency: 50 Hz up to few kHz • Expected strenght ~ 3.6 10-22 Hz-1/2 ( SNR~ 10 ) 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  5. Triggered or UntriggeredGWB Searches • TRIGGERED SEARCH Targets events which produce EM or neutrino signatures (e.g. supernovae, gamma-ray bursts). These signatures provide independent estimates of time of occurrence and source position.A small subset of the data stream must be sieved. • UNTRIGGERED (“BLIND”) SEARCH No information available as to time of occurrence, and direction of arrival (DOA), both to be estimated from data. All available data must be sieved. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  6. Glitches • Non-GWB transients (glitches) show up in several IFO channels • Glitches in each channel tend to clusterin TF plane[Mukherjee, LIGO P070051-00-Z ] • Strategies to identify/reject some of them make use of knowledge about the couplingof instrumental channels with the main det-ector output. [Ajith, ArXiv:0705.1111] • Glitches observed in data (DARM_ERR) seem to fall into a few simple categories (e.g., SG, RD)[Saulson, LIGO G-070548-00-Z] • Glitches occur in each detector as Poisson processes with a characteristic rate λ 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  7. Atoms (1/2) • Both GW and noisy bursts can be modeled as atoms (Gabor, Rihaczek) in the TF plane. • Atoms are transient signals with “almost” compact time-frequency support. Can be characterized by fewest moments, e.g., time-frequency barycenter (t0, f0) and spreads (σt ,σf) [P. Flandrin, Time-Frequency/ Time-Scale Methods, Academic Press,1999] • The atom’s shape, as well as the ranges of its moments and the related probability distributions, can be inferred from theoretical and/or experimental evidences. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  8. Atoms (2/2) • A simplest choice for the atoms, for both GW and spurious noise bursts is perhaps the Sine-Gaussian (SG) • Spurious glitches can be statistic-ally characterized in terms of thedistributions (priors) of their rele-vant parameters Q, f0 , t0 , h0 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  9. Network Operation • A single detector cannot discriminate a GW burst from a transient (instrumental) glitch • Need to operate an ensemble of GW detector • How many ? How oriented ? • Two network data analysis strategies developed • incoherent (e.g. coincidence; experience from bar-detectors) • coherent (e.g. Gursel-Tinto technique) • Key benefits: • Reject spurious glitches; • Identify direction of arrival (blind search). 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  10. Coherent Network Analysis • Exploits the redundancy of the network: • only 2 unknown quantities, h+(t) and h×(t), while D ≥2 detector outputs (over-determined problem, redundant network) • Network redundancy is crucial to estimate the DOA, and to reject spurious transient signals • Expected to achieve better performance compared to incoherent analysis [Arnaud et al, PRD 68 (2003) 102005]; • Improved performance paid in terms of heavier com-putational load. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  11. Rationale of this Work • Abundant Literature exists about coherent algorithms performance for DOA retrieval and signal detection. • Only a few papers discuss in quantitative terms the capabilities of coherent algorithm in rejecting spurious glitches [Chatterjee et al., LIGO-P060009-01-E]; • We propose a simple approach to quantify such capa-bilities, for the special case of the LH-LL-V network, and the possibly simplest coherent algorithm, proposed by Rakhmanov and Klimenko [CQG 22 (2005) S1311]; 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  12. GW Polarization waveforms at Earth’s center Antenna Patterns • The matrix is also rank-2 • , (no noise) , Wican be used as a noisy template (M)-RK Statistic(s) • Output of i-th detector , In matrix form rank-2 antenna response matrix 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  13. The Ai (Ωs) 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  14. Detection Statistics • Define the noisy-template based correlations: • A suitable function of the Ci, must be formed to be used as a detection statistic. Several choices possible. • R&K proposed This is not the best one (does not exploit all the information collected) • A better choice is a linear combination of the Ci maximizing the deflection for which the statistical properties can still be obtained in analytic form , i =1,2,…,D , (s known, fixed) , 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  15. Statistical Distribution of Ci • Explicit expression of Ci • In view of the large (>> 103) number of samples in the integration window, the (extended) CLT applies, the Ci being sums of many independent random variables: Noise term in the template AWGN power equal in any detector Q i(Ωs) 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  16. ∞ Ai→ 0 • Choosing AiWi(t) as a template Statistical Distribution of Ci :H1 hypothesis independent on Ai 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  17. Statistical Distribution of Ci H0 hypothesis (AWGN only) H0 (AWGN) H1 (GWburst) This is all we need to compute ROCs. ROC may be written in such a way so as to highlight difference with “perfect” matched filter. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  18. Would be one for the perfect MF acting on the GW waveform K-R ROCs (AWGN only) Deflection of perfect MF acting on GW waveform 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  19. The 2 function (+), 10 (+), 20 H+, dmf=20 (), 10 (), 20 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  20. Glitches: a Recipe • Assume a “network glitch set”, i.e., specify the presence, firing-time, amplitude, center-frequency and t-f spread parameters of the glitches (represented by a suitable atom) in each detector. • Compute the related distribution (first two moments) of the detection statistic: this is a conditional distribution, corresponding to the assumed “networkglitch-pattern”; • Average out using the fiducial prior distributions of the glitch para-meters. The resulting distribution will be different from the AWGN-only case (nonzero average and broader spread). • Use the resulting distribution for setting the detection threshold as a function of the prescribed AWGN+glitch-mix false alarm rate. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  21. H0 (AWGN+glitches) hyp. Working Assumptions • The rate λ of Poisson process which models the occurrence of glitches is assigned (e.g., in [0.1 , 0.5]) • We choose the analysis window T three times the maximum duration of a bursts, i.e. T ~ 70 ms. Accordingly we make the sim-plifying working assumptions that in each detector P(at least a glitch) P(one glitch occurs) P(glitch and GWB) 0 • Glitches  SG-atoms, f0 [Hz] ~ U( {700, 849, 1053, 1304, 1615, 2000}) t0~ Poisson(), h0 ~U( [0, max]), Q = 8.9 • “Loud” glitches (max :local SNR SNRmax) vetoed out. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  22. H0 (AWGN+glitches) hyp. Marginal Distribution of Ci • These quantities must be averaged out over random (exponential) inter-arrival times between events and over (uniform) SG parameters. • Denote as the averaged quantities. 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  23. Would be one for the perfect MF acting on the GW waveform K-R ROCs (AWGN+glitches) Deflection of perfect MF acting on GW waveform 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  24. 5.88 4.70 3.53 2.35 1.17 ROC (AWGN+glitches): Cmax PRELIMINARY RESULTS 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  25. Conclusions • All ingredients for assessing quantitatively the glitch rejection capabilities of the LH-LL-V network have been derived for the R-K coherent statistic. Extensive numerical simulations for the triggered search case (known DOA, and time of occurrence) in progress. • The more general case where the time and direction of arrival are unknown and should be estimated can be also formalized, and is under scrutiny. • Plans to use better atomic objects (chirplets [Sutton, GWDAW 10, UTB, 2005]) 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  26. Detector performance depends on ratio  x > , H1 accepted x <  , H1 rejected Detection/Decision 1.0 0.8 0.6 0.4 For low , should be  > E(x|H0) + stdev(x|H0) For low , should be E(x|H1) >  + stdev(x|H1) 0.2 x 0.0 - - 2 1 0 1 2 3 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  27. NP-Strategy NP strategy : assign false alarm probability; deduce  from 1stMequation . 4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

  28. Each point on the curve corresponds to a different  i.e. a different decision-rule. One can prove that =slope ROCs 1- For given signal and noise, plot the curve {1-(), ()},known asthe Receiver Operating Characteristic  4th ILIAS-GW Annual General Meeting Universität Tubingen, October 8,9 2007

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