Application of A Zero-latency Whitening Filter to Compact Binary - PowerPoint PPT Presentation

Application of A Zero-latency Whitening Filter to Compact Binary Coalescence GW Searches Leo Tsukada RESCEU, Univ. of Tokyo The Third KAGRA International Workshop May 21, 2017 1 /24 THE 3RD KAGRA INTERNATIONAL WORKSHOP

This talk is based on … Application of a zero-latency whitening filter to compact binary coalescence gravitational-wave searches Leo Tsukada, 1, 2, ∗ Chad Hanna, 3 Cody Messick, 3 Drew Keppel, 4 Duncan Meacher, 3 and Kipp Cannon 1, † 1 Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan 2 Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan 3 The Pennsylvania State University, University Park, Pennsylvania 16802, USA 4 (Dated: April 23, 2017) We examine the performance of a zero-latency whitening filter in a detection pipeline for compact binary coalescence (CBC) gravitational-wave (GW) signals. We find that the filter reproduces su ffi ciently consistent signal-to-noise ratio (SNR) for both noise and artificial GW signals (called injections ) with the results of the original high latency and phase preserving filter. Additionally, we demonstrate that these two filters have a great agreement of squared-chi value, χ 2 , a discriminator for gravitational wave signals. Keywords: gravitational waves, compact binary coalescence, whitening filter, low latency LIGO Document Number “LIGO-P1700094” (In preparation) 2 /24 THE 3RD KAGRA INTERNATIONAL WORKSHOP

Outline ▸ Background ▸ Introduction ▸ Improvements ▸ Performance tests ▸ Summary 3 /24 OUTLINE THE 3RD KAGRA INTERNATIONAL WORKSHOP

Outline ▸ Background ▸ Introduction ▸ Improvements ▸ Performance tests ▸ Summary 4 /24 BACKGROUND THE 3RD KAGRA INTERNATIONAL WORKSHOP

NS-NS Coalescence ▸ Several emissions ๏ Gravitational radiation Chirp signal - Short gamma-ray burst (SGRB) Δ t ~ seconds - Radio afterglow Δ t ~ weeks, years - Kilonova (optical) Δ t ~ days Metzger & Berger 2012, ApJ 746, 48 5 /24 BACKGROUND THE 3RD KAGRA INTERNATIONAL WORKSHOP

Multi-messenger Astronomy ▸ Electromagnetic waves + Gravitational waves Signal association ▸ latency problem GRB theory : <10s (X.Li. et al . 2016, ApJ 827, 75) Pipeline latency : ~30s ← Need to be reduced ! 6 /24 BACKGROUND THE 3RD KAGRA INTERNATIONAL WORKSHOP

Outline ▸ Background ▸ Introduction ▸ Improvements ▸ Performance tests ▸ Summary 7 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Inspiral Search Pipeline ▸ Matched filter Whitening transformation s ( t ) : data stream h ( t ) : a template waveform ( m 1 , m 2 , D eff ... ) S n ( f ) : noise power spectrum density 8 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Statistics ▸ Signal-to-Noise Ratio : (SNR) ≡ σ SNR ≡ z � ∞ | ˜ h ∗ ( f ) | 2 σ 2 ≡ 4 where S n ( f ) d f σ 0 Loudness of the trigger χ 2 ▸ Chi square : � p 1 χ 2 ≡ � | z i − z/p | 2 � σ 2 /p i =1 � f i ˜ h ∗ ( f )˜ s ( f ) f, st ⟨ z 1 ⟩ = ⟨ z 2 ⟩ · · · = ⟨ z p ⟩ = ⟨ z ⟩ where z i = 4 d S n ( f ) p f i − 1 Discriminator of glitches from chirp signals 9 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Latency ▸ Three bottlenecks } - Data calibration ~30s - Data distribution ๏ Whitening transformation : 16s Essential to improve the whitening filter 10 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Whitening filter ▸ Flatten the power spectrum ▸ Apply to the both of a template and data � � � � ∞ ˜ � ∞ ˜ h ∗ ( f )˜ s ( f ) h ∗ ( f ) s ( f ) ˜ ( s ( t ) , h ( t )) ∝ f = · d d f � � S n ( f ) S n ( f ) S n ( f ) 0 0 11 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Whitening filter ▸ Flatten the power spectrum ▸ Apply to the both of a template and data 12 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Current Algorithm � -��D��53�3� !(#) � ▸ Discrete Fourier Transform (DFT) �� � )����� 3������3���F��5�F� - Applied to 32s blocks every 16s !(#)×& ' (#) � �� � - Latency of 16s ~ 32s ���� (!×& ' )(*) � �� � � � 1�53�6�AD������ �� � 2���6��F���� 3�6A3�6����� ��6����� Whitening ( ) (*) � (!×& ' )(*) � +( ) (*) filter �� � -���� ,!×& ' - (#) � +( ) ▸ Frequency-domain whitening �� � )����� 3��D�6��F��5�F� - Conserve the phase of data ,!×& ' - (#)×& . (#) � +( ) Switch into time-domain processing! �( � )55���6��3��� F��������64����7��� 13 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Current Algorithm � -��D��53�3� !(#) � ▸ Discrete Fourier Transform (DFT) �� � )����� 3������3���F��5�F� - Applied to 32s blocks every 16s !(#)×& ' (#) � �� � - Latency of 16s ~ 32s ���� (!×& ' )(*) � �� � � � 1�53�6�AD������ �� � 2���6��F���� 3�6A3�6����� ��6����� ( ) (*) � (!×& ' )(*) � +( ) (*) �� � -���� ,!×& ' - (#) � +( ) ▸ Frequency-domain whitening �� � )����� 3��D�6��F��5�F� - Conserve the phase of data ,!×& ' - (#)×& . (#) � +( ) Switch into time-domain processing! �( � )55���6��3��� F��������64����7��� 14 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Outline ▸ Background ▸ Introduction ▸ Improvements ▸ Performance tests ▸ Summary 15 /24 IMPROVEMENTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Time-domain Processing Freq.-domain Time-domain ∞ IDFT ∑ ! f [ m − n ] Convolution g [ n ] F [ m ] · G [ m ] n = −∞ theorem DFT F [ m ] ≡ DFT { f } G [ m ] ≡ DFT { g } ∞ IDFT 1 ∑ ! ! [ m ] ⋅ Whitening s [ m − n ] s w [ n ] S n [ m ] transformation n = −∞ DFT ⎛ ! ( f ) ⎞ s ⎜ ⎟ ⎝ ⎠ S n ( f ) 16 /24 IMPROVEMENTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Time-domain Processing Freq.-domain Time-domain ∞ IDFT ∑ ! f [ m − n ] Convolution g [ n ] F [ m ] · G [ m ] n = −∞ theorem DFT F [ m ] ≡ DFT { f } G [ m ] ≡ DFT { g } ∞ IDFT 1 ∑ ! ! [ m ] ⋅ Whitening s [ m − n ] s w [ n ] S n [ m ] transformation n = −∞ DFT ⎛ ! ( f ) ⎞ s ⎜ ⎟ ⎝ ⎠ S n ( f ) Finite Impulse Response (FIR) 17 /24 IMPROVEMENTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Linear-phase FIR filter Amplitude response Linear-phase filter Latency 16s 18 /24 IMPROVEMENTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Minimum-phase FIR Filter Linear-phase filter Minimum-phase filter Zero latency filter ! 19 /24 IMPROVEMENTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Outline ▸ Background ▸ Introduction ▸ Whitening filter ▸ Improvements ▸ Performance tests ▸ Summary 20 /24 PERFORMANCE TESTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Statistical tests Auto-correlation Amplitude histogram Good whitening quality ! 21 /24 PERFORMANCE TESTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

New Whitener vs Old Whitener ▸ Data - 45,056 s during S5 at the Hanford LIGO detector ▸ Noise-based test - Trigger-trigger (only noise) association χ 2 - and comparison SNR ▸ Injection-based test - Simulated chirp signals injected every 31.4s - Injection-injection association χ 2 - and comparison SNR 22 /24 PERFORMANCE TESTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Noise-based test 23 /24 PERFORMANCE TESTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Injection-based test Agreement between the old and new whiteners ! 24 /24 PERFORMANCE TESTS THE 3RD KAGRA INTERNATIONAL WORKSHOP

Improved latency ▸ Three bottlenecks } - Data calibration 18s - Data distribution ๏ Whitening transformation : 16s 0s Significant role in the whole latency reduction 25 /24 INTRODUCTION THE 3RD KAGRA INTERNATIONAL WORKSHOP

Outline ▸ Background ▸ Introduction ▸ Whitening filter ▸ Improvements ▸ Performance tests ▸ Summary 26 /24 SUMMARY THE 3RD KAGRA INTERNATIONAL WORKSHOP

Summary ▸ Dawn of multi-messenger astronomy - Signal association from NS-NS merger ▸ Latency problem - Need to be ~ 10s ▸ FIR whitening transformation - Zero latency whitening by minimum-phase filter - Good agreement between the old and new whiteners ▸ Improved latency of 18s - The new whitener will be implemented soon. 27 /24 SUMMARY THE 3RD KAGRA INTERNATIONAL WORKSHOP

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