Comparison of filters for burst detection

1. Comparison of filters for burst detection M.-A. Bizouard on behalf of the LAL-Orsay group GWDAW 7th IIAS-Kyoto 2002/12/19

2. Goals • Several filters developed so far. • What are their performance? How do they compare? Which criteria should we use to enlarge our benchmark? • Efficiency/robustness to badly modeled source waveforms Receiver Operating Characteristics (ROC) determination for different signal families • Timing proprietiessignal arrival time estimation (coincidence with other GW detectors, ν and optical detectors • Sensitivity to residual lines (after data whitening)

3. List of filters considered in the benchmark • Time domain filters, rather signal independent: one hypothesis about signal duration: several sliding windows (size N) in parallel for practical implementation • Norm Filter (NF): • Mean Filter (MF): (new studied filter) • ALF (linear fit of data (x=at+b) and slope and offset filter combination): slope: offset:

4. ROC for optimized filters • Optimized filters = the window size is matched to the signal size • Signal = Gaussian peak (ω=1ms) (N=40 for MF and NF, N=140 for ALF) MF and ALF performs identically in this ideal working case One always gain to combine slope (SF) and offset (OF) filters NF performance are low (4 order of magnitude more f.a. @ same efficiency)

5. Filters are running with 10 sliding windows: signal duration: 0.5, 0.75, 2, 1.25, 1.5, 2, 2.5 3.5 7.5 and 10 ms SNR = 5 (exhibit at most the filters’ difference) Gaussian peak (ω=1ms) ALF performance is about the same! MF efficiency decreases dramatically compared to the use of 1 single signal matched window ! The non matched windows increase the number of false alarm for MF f.a.rate @ efficiency = 50% ROC in a practical filter implementation

6. ROC in a practical implementation: signal robustness • ROC for damped sine signal (f = 1 kHz, τ = 1 ms) and ZM (a2b2g1) the filters performance may depend strongly on signal waveform. (ALF: f.a. = 2.10-7(Gaussian) 3.10-4 (Damped Sine) @ 50% efficiency) MF : same behavior as for Gaussian because one of the window size matches one of the peaks of the damped sine signal. ALF: best performance to detect ZM like waveforms Damped sine ZM (a2b2g1)

7. Timing accuracy • Estimation of signal arrival time is important for: • working in a network of interferometers (coincidence analysis) • reconstructing the source location (maximal time delay between Hanford and Virgo is 27 ms) • coincidence with ν detectors and optical telescopes ν masses determination require a timing precision <1 ms • Estimators construction: • Non trivial because it may depend both on the filters and the waveforms • Need to construct unbiased estimators or at least determine on simulation their systematic bias and statistical errors Study first the ideal case (Gaussian peak signal) one can obtain upper limit on the timing resolution More realistic signals (ZM) results

8. Timing accuracy: Gaussian signal (ideal case) • Definition: signal arrival time = time corresponding to the Gaussian peak maximum • Time estimator for NF and MF: • Time estimator for ALF: double peak structure • Systematic bias removed in the definition of the estimator

9. Timing accuracy: Gaussian signal – results • The systematic bias and statistical precision on the signal arrival time have been evaluated using simulations (Gaussian white noise + signals calibrated according to the optimal SNR ρ) • The statistical accuracy on the signal arrival time estimation depends on the optimal SNR ρ and the width ωof the signal • Optimal filter results: • NF filter: • MF filter: • ALF filter: Linear dependency on ω for all filters except NF! All filters estimators have a statistical accuracy well below 1 ms for a standard peak Gaussian signal ALF shows good timing proprieties (not a priori obvious)

10. Timing accuracy: realistic case • The good numbers obtained with Gaussian peaks must be moderated • Realistic SN waveforms exhibit more complicated structure (several peaks). That implies: • The systematic bias may depend on the signal waveform! • One has to define a “robust” arrival time estimator • An extended study has been performed with ALF filter (most efficient filter for ZM signal): • Estimators: time of maximal SNR, time of the first bin above threshold, average time between 2 SNR peaks, … No unbiased time estimator has been found The minimal systematic bias is about 0.5 ms for a SNR=5 (average over the 78 ZM waveforms) The time estimation precision may be much larger than 1 ms (especially for the type III ZM signals)

11. Sensitivity to residual lines • All the sub-optimal filters here require a data pre-whitening • But how much are they sensitive to imperfect whitening? Sensitivity to a single frequency component: Measure with simulations the relative excess of false when varying the amplitude Aand for f = 0.6 Hz (pendulum frequency) f= 100, 200 and 400 Hz (power line harmonics) Window size: MF, NF: N=50 ALF: N=170 Matched signal size: 2.5 ms for all the filters

12. Sensitivity to residual lines • Frequency dependence for MF: MF averages frequencies higher than a cut off frequency: Similar effect with ALF • Specification defined using the spectrum flatness: • Example: Amplitude line < 1%

13. Conclusions • New filter (Mean Filter) which performs the best for damped sine signals. • Battery of filters which are more complementary than concurrent. ALF is the most efficient for ZM signals, but less robust than MF filter. NF is quite robust but less efficient. • Timing proprieties known in the case of Gaussian peak signals. systematic bias can be suppressed in the time estimator definition. statistical error well below1 ms. less favorable situation for ZM signals … • Constraints on the whitening algorithms output have been determined in the case of imperfect lines removal. • One should extend this benchmark comparison to all the burst algorithms developed so far? reference paper: gr-qc/0210098