Coincidence algorithm and an optimal unification of GW – detectors A.V.Gusev, V.N.Rudenko SAI MSU, Moscow, Russia Moscow University Physics Bulletin, 2009, Vol.64,№1, pp73-76 Original Russian:“Vestnik MU”, Fisika, N1, 2009

Sine-gaussian waveform

Wavelet transform S.Klimenko,G.Mitselmakher.C&QG,21(2004)

Non modeled Bursts Search outputs of two GW detectors: vectors a, b total energy : E = normalized and integrated at the (0<t<T) it is reduced to variables: Burst’s Excess Power: Burst’s Cross Power: L.Cadonati,S.Marka.C&QG,22(2005),S1159 S.Klimenko,G.Mitselmakher.C&QG,21(2004) W.Anderson,P.Brady,J.Creighton,E.Flanagan Int.J.Mod.Phys.D v.9,p.303,(2000)

Optimal Filtration theory for multi-receiver network Does not leads to a “coincidence strategy” (CS) How one has to formulate a “detection problem” for to get CS –recommendation ? What is an optimal unification of independent detectors?

LH estimate of Optimal receiver conclusion LH t) ?t) ? one detector

Two detectors + LH estimates Optimal receiver for Conclusion

Two approach in Optimal Filtering Problem of signal detection: Gaussian noise Stochastic pulses Problem of signal distinction:

Maximum LH algorithm For N independent detectors: In the case of Gaussian background:

Results of the distinction problem: Optimal statistics: threshold

The case of two equivalent detectors 0<t<T > ln C - accumulated output

Standard filtering theory requires unification of net detectors at the level of their inputs, then optimal algorithms becomes more complex then the simple CS Coincidence Strategy is resulted from the unification net detectors at the level their outputs: one has in disposal only individual optimal filtering outputs y i but no the common optimal output Σy i

How to unify problems: “detection” and “distinction”? - detection - substitution - distinction Stochastic pulses Gaussian noise It takes into account an interference of signal and noise pulses

Result correlation of the n(t) - remains unchanged

After substitution LH estimates Direct calculation depends on relation between and relaxation times of additive noises n(t) in each channels

Conclusions Coincidences algorithm (“bursts power” and “cross power”) results from the “unification of net detector’s outputs” Optimal procedure requires “unification of net detector’s inputs”. it deals with an accumulated “common net output” in respect of individual detector outputs. Correspondent optimal variable (statistics) for the net of GW- detectors has to be addressed.