- Email: [email protected]
Software for neutrino acoustic detection and localization
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 604 (2009) S230–S232
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Software for neutrino acoustic detection and localization B. Bouhadef a,b, a b
INFN Sezione Pisa, Polo Fibonacci, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy Dipartimento di Fisica, ‘‘E. Fermi’’ University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
a r t i c l e in f o
a b s t r a c t
Available online 21 March 2009
The evidence of the existing of UHE ðE41019 eVÞ cosmic rays and its possible connection to UHE neutrino suggests the building of an acoustic telescope for neutrino, exploiting thermo-acoustic effect. We present software for neutrino acoustic signal detection and localization. The main points discussed here are the sea noise model, the determination of time differences of arrival (TDOA) between hydrophones signals, the source localization algorithm, and the telescope geometry effect. The effect of TDOAs errors and telescope geometry on the localization accuracy is also discussed. & 2009 Elsevier B.V. All rights reserved.
Keywords: Neutrino astronomy Acoustic detection Source localization Matched filter
1. Introduction Towards the detection of neutrinos with energies above EeV in the sea via an acoustic detection technique as predicted by Askarjan [1] and proven for a proton flux [2]. The acoustic detection is considered as a complementary part to optic and radio detections and an hybrid telescope is a promising tool for neutrino astronomy study following Auger experiment [3]. Here we want to present our first version of software for neutrino acoustic detection and localization. The software composed of sea noise parametrization, a signal detection, and source location using the estimated time differences of arrivals (TDOAs). These parts are considered separately and can be improved as well. In this paper we will focus on sea noise parametrization, detection technique using matched filter and the effect of hydrophone positions scattering as well as detector geometry effect.
2. Sea noise model Aiming to study a possibility of acoustic neutrino detection, many attempts are carrying on for sea noise background measurements [4,5]. The noise study gives us a sight about the threshold fixation and the expected probability of false alarm events. The NEMO collaboration [6] are employing an OnDE station at 25 km offshore the port of Catania (Sicily) at 2000 m depth, for more details one could see Ref. [7]. Based on noise measurement data given by OnDE Station, we have modeled the sea noise at low frequency (in the range 0.1–15 kHz) using an auto-regressive (AR) model (order p ¼ 7) which is defined by Corresponding author at: INFN Sezione Pisa, Polo Fibonacci, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy. E-mail address: [email protected]
0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.03.067
Eq. (1). The parameters of the model (a0 ; . . . ; aP ) are estimated using a burg method [8] which we find it better (presents less bias, stable model, and computationally efficient) then the covariance method and others. The estimated parameters are used then, to generate the sea noise, where, the sea state will be defined by an appropriate input s, which is the standard deviation of the input white noise of the model. The power spectrum density (PSD) of an AR model is given by Eq. (2). Fig. 1 shows spectrum of the simulated sea noise at different sea states compared to the theoretical sea noise spectrum given by [9]. AðzÞ ¼
Pðf Þ ¼
s
(1)
1 þ a1 z þ þ aP z P
j1 þ
PP
s2
j2pfk j2 k¼1 ak e
.
(2)
Moreover, after filtering out the low frequency from OnDE data (10–48 KHz), we have found that the noise can be considered as white noise with 99% confidence interval (CI) with mean zero. The simulated sea noise will be included in the software neutrino detection for trigger efficiency study.
3. Neutrino signal detection The fact that many theories predict an acoustic bipolar signal for UHE neutrino interaction, the first optimum detector (in the case where the signal shape is known) is the matched filter, which is an inverse version of the correct signal in time. Fig. 2 shows the receiver performances, where the true shape of the bipolar signal was used (solid line) and an approximate shape. As it is expected there will be a degradation of the receiver performances, which leads to more false events and a difficulty to identify a neutrino signal as well as localize it. Another simulation has been done
ARTICLE IN PRESS B. Bouhadef / Nuclear Instruments and Methods in Physics Research A 604 (2009) S230–S232
hydrophones. This plane presents the middle of the pancake and the angles of direction can be estimated using least square method. However, we still have a pour precisions of angles as expected. For position location, we adopt at this version of software the spherical interpolation (SI) method which desired in real time applications, and in the case where more complicated method such as the likelihood (which is a nonlinear optimization) the SI method could be considered as a good one for giving the initial values. For more detail about SI one could see Ref. [10], we present their basic idea, define: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3) Ri ¼ x2i þ y2i þ z2i ; Pi ¼ ½xi ; yi ; zi T
90
PSD (dB re. 1 µPa2/Hz)
80
4
70
1
60
S231
0
50 40 30
R¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 þ z2 ;
20
di;j ¼ di dj .
(4)
Then, based on Fig. 3 and from Phthagonerean, we have
10 102
103 Frequency (Hz)
104
Fig. 1. Sea noise model: simulated spectrum noise (dash lines) and approximated spectrum presented in Urick [9] (solid lines).
i ¼ 2; 3; . . . ; N.
(5)
In the presence of measurement errors, Eq. (5) becomes
ei ¼ R2i R2i;1 2Pi P
(6)
where ei is the equation error. Eq. (6) can be written in compact form as
1
e ¼ d 2Rd 2Pi P
0.9 SNR = 5 dB Probability of Detection PD
ðR þ di;1 Þ2 ¼ R2i 2Pi P þ R2 ;
(7)
where e is the equation error vector and
0.8
½Ai;1 ¼ xiþ1 ;
½Ai;2 ¼ yiþ1
½Ai;3 ¼ yiþ1 ;
i ¼ 1; 2; . . . ; N 1
0.5
½Ai;3 ¼ yiþ1 ;
i ¼ 1; 2; . . . ; N 1
0.4
d ¼ ½R22 d22;1 ; R23 d23;1 ; . . . ; R2N d2N;1
0.7
SNR = 0 dB
0.6
SNR = -5 dB
0.3 d ¼ ½d2;1 ; d2;1 ; . . . ; dN;1 T .
0.2
The stand least square solution to P, given R, is
0.1
P ¼ 12ðAT AÞ1 AT ðd 2RdÞ.
0 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Probability of false alarm PFA
(8)
The key idea of SI approach is to substitute Eq. (8) into Eq. (7) and minimize the equation error again but with respect to R. This
Fig. 2. Matchef filter performances for true (solid lines) and approximate bipolar pulse (dash lines).
z
(not presented here) showing the performances of the matched filter for a bipolar signal detection using two hydrophones will also improve the performance of an acoustic neutrino telescope. Once an event occurs, the source identification proceeds, but here a knowledged of all kind of sources (bio-activities and all spices) that might generate an acoustic sound. So, a database will be needed to better identification and selection. This version, we consider that any detected event is believed to be a neutrino event and the neutrino source location will proceed.
d
1
=
R
(x, y, z)
di
(x1, y1, z1) = (0, 0, 0)
y
4. Neutrino source localization Given the fact that neutrino interaction at HE (E41019 eV) generates an acoustic such that the total acoustic radiation is confined to a narrow, so-called ‘‘pancake’’ with an opening angle y of about 5 . So, to localize neutrino sources via an acoustic technique, we need to know five parameters that to say: the position ðxs ; ys ; zs Þ of interaction and the direction of neutrino ðys ; fs Þ. For angles, one can fit a plane using the positions of hit
Ri
(xi, yi, zi) x Fig. 3. Illustration for spherical interpolation approach.
ARTICLE IN PRESS S232
B. Bouhadef / Nuclear Instruments and Methods in Physics Research A 604 (2009) S230–S232
of CC) and conserving its phase which contains the TDOA information. Fig. 4 shows variance (blue) and bias (red) of the estimated TDOA versus signal to noise ratio (SNR) using PHAT algorithm.
0.8
TDOA’s errors (samples)
0.7 0.6
6. Detector geometry effect
0.5 0.4
ttrue-tasr Variance on mean
0.3 0.2 0.1 0 -10
-8
-6
-4
-2
0
2
4
6
8
10
To test whether the precision of a source location depends on detector structure, we have done a Monte Carlo simulation using a detector of 10 hydrophones. The simulation was done for four detectors: 1, 4, 7, and 10 times the original structure. Fig. 5 shows the effect of detector geometry and the hydrophone uncertainly, as much as the geometry is zoom out the error on position goes down, and the error on position increase with uncertainly on hydrophone position. We must notice here that, the uncertainly on hydrophones affects the precision of neutrino source location more than TDOA errors.
Signal to noise ratio (dB) 7. Conclusion
Fig. 4. Variance and error on the mean of TDOAs.
We have presented here the first version of software for neutrino source detection and localization, we give also a model for sea noise simulation based on an AR model. The efficiency of neutrino detection will be based mainly on the algorithm of detection to be used at a single hydrophone as well as the algorithm for source selection. As first step we used matched filter which is optimum unless the shape of the signal is unknown. In addition, the precision of neutrino point location is based mainly on uncertainly of hydrophones locations as we have shown, our future work will focus on more robust algorithm such as maximum likelihood for detection and localization. The software developed here could be tested in an underwater optical neutrino detection telescope such NEMO experiment [6] for acoustic positioning calibration.
106
Variance on position (m)
105 104 103 102 101 100 Detector 4X Detector 7X Detector 10X Detector
10-1 10-2 10-3 10-2
10-1
Acknowledgments
100
Noise std (m) Fig. 5. Geometric effect on position estimation.
solution leads to a closed form location from range difference measurements.
5. Time differences of arrival The TDOA is considered as a first step for sources localization, there are many proposed algorithms for TDOA estimation using a modified version of the cross-correlation (GC) known as general CC (see for example Ref. [11]), in our software we used the PHAse Transform (PHAT) algorithm which easy to implement and is robust then many other algorithm. The PHAT algorithm normalizes the magnitude of cross-spectrum (the Fourier transform
The author is grateful to the Dipartimento di Fisica di Pisa, Ph.D. school Galileo Galilei, INFN Sezione Pisa, and NEMO Collaboration.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
G. Askarjan, Atomnaya Energia 3 (1957) 153. G. De Bonis, this issue. A.M. Jaime, this issue. K. Kurahashi, this issue. G. Riccobene, this issue. hhttp://nemoweb.lns.infn.iti. G. Riccobene, et al., submitted for publication, available at: http://arxiv.org/ abs/0804.2913v1, 17 April 2008. J.G. Proakis, D.G. Manolakis, Digital Signal Processing, third ed., Prentice-Hall, Englewood Cliffs, NJ, 1996. R.J. Urick, Principles of Underwater Sound, McGraw-Hill, New York, 1983. J.S. Abel, J.O. Smith, Proceedings of the IEEE ICASSP 1 (1987) 471. J. Chen, Journal of Applied Signal Processing (2006) 1 (Article 26503).
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Software for neutrino acoustic detection and localization B. Bouhadef a,b, a b
INFN Sezione Pisa, Polo Fibonacci, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy Dipartimento di Fisica, ‘‘E. Fermi’’ University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
a r t i c l e in f o
a b s t r a c t
Available online 21 March 2009
The evidence of the existing of UHE ðE41019 eVÞ cosmic rays and its possible connection to UHE neutrino suggests the building of an acoustic telescope for neutrino, exploiting thermo-acoustic effect. We present software for neutrino acoustic signal detection and localization. The main points discussed here are the sea noise model, the determination of time differences of arrival (TDOA) between hydrophones signals, the source localization algorithm, and the telescope geometry effect. The effect of TDOAs errors and telescope geometry on the localization accuracy is also discussed. & 2009 Elsevier B.V. All rights reserved.
Keywords: Neutrino astronomy Acoustic detection Source localization Matched filter
1. Introduction Towards the detection of neutrinos with energies above EeV in the sea via an acoustic detection technique as predicted by Askarjan [1] and proven for a proton flux [2]. The acoustic detection is considered as a complementary part to optic and radio detections and an hybrid telescope is a promising tool for neutrino astronomy study following Auger experiment [3]. Here we want to present our first version of software for neutrino acoustic detection and localization. The software composed of sea noise parametrization, a signal detection, and source location using the estimated time differences of arrivals (TDOAs). These parts are considered separately and can be improved as well. In this paper we will focus on sea noise parametrization, detection technique using matched filter and the effect of hydrophone positions scattering as well as detector geometry effect.
2. Sea noise model Aiming to study a possibility of acoustic neutrino detection, many attempts are carrying on for sea noise background measurements [4,5]. The noise study gives us a sight about the threshold fixation and the expected probability of false alarm events. The NEMO collaboration [6] are employing an OnDE station at 25 km offshore the port of Catania (Sicily) at 2000 m depth, for more details one could see Ref. [7]. Based on noise measurement data given by OnDE Station, we have modeled the sea noise at low frequency (in the range 0.1–15 kHz) using an auto-regressive (AR) model (order p ¼ 7) which is defined by Corresponding author at: INFN Sezione Pisa, Polo Fibonacci, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy. E-mail address: [email protected]
0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.03.067
Eq. (1). The parameters of the model (a0 ; . . . ; aP ) are estimated using a burg method [8] which we find it better (presents less bias, stable model, and computationally efficient) then the covariance method and others. The estimated parameters are used then, to generate the sea noise, where, the sea state will be defined by an appropriate input s, which is the standard deviation of the input white noise of the model. The power spectrum density (PSD) of an AR model is given by Eq. (2). Fig. 1 shows spectrum of the simulated sea noise at different sea states compared to the theoretical sea noise spectrum given by [9]. AðzÞ ¼
Pðf Þ ¼
s
(1)
1 þ a1 z þ þ aP z P
j1 þ
PP
s2
j2pfk j2 k¼1 ak e
.
(2)
Moreover, after filtering out the low frequency from OnDE data (10–48 KHz), we have found that the noise can be considered as white noise with 99% confidence interval (CI) with mean zero. The simulated sea noise will be included in the software neutrino detection for trigger efficiency study.
3. Neutrino signal detection The fact that many theories predict an acoustic bipolar signal for UHE neutrino interaction, the first optimum detector (in the case where the signal shape is known) is the matched filter, which is an inverse version of the correct signal in time. Fig. 2 shows the receiver performances, where the true shape of the bipolar signal was used (solid line) and an approximate shape. As it is expected there will be a degradation of the receiver performances, which leads to more false events and a difficulty to identify a neutrino signal as well as localize it. Another simulation has been done
ARTICLE IN PRESS B. Bouhadef / Nuclear Instruments and Methods in Physics Research A 604 (2009) S230–S232
hydrophones. This plane presents the middle of the pancake and the angles of direction can be estimated using least square method. However, we still have a pour precisions of angles as expected. For position location, we adopt at this version of software the spherical interpolation (SI) method which desired in real time applications, and in the case where more complicated method such as the likelihood (which is a nonlinear optimization) the SI method could be considered as a good one for giving the initial values. For more detail about SI one could see Ref. [10], we present their basic idea, define: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3) Ri ¼ x2i þ y2i þ z2i ; Pi ¼ ½xi ; yi ; zi T
90
PSD (dB re. 1 µPa2/Hz)
80
4
70
1
60
S231
0
50 40 30
R¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 þ z2 ;
20
di;j ¼ di dj .
(4)
Then, based on Fig. 3 and from Phthagonerean, we have
10 102
103 Frequency (Hz)
104
Fig. 1. Sea noise model: simulated spectrum noise (dash lines) and approximated spectrum presented in Urick [9] (solid lines).
i ¼ 2; 3; . . . ; N.
(5)
In the presence of measurement errors, Eq. (5) becomes
ei ¼ R2i R2i;1 2Pi P
(6)
where ei is the equation error. Eq. (6) can be written in compact form as
1
e ¼ d 2Rd 2Pi P
0.9 SNR = 5 dB Probability of Detection PD
ðR þ di;1 Þ2 ¼ R2i 2Pi P þ R2 ;
(7)
where e is the equation error vector and
0.8
½Ai;1 ¼ xiþ1 ;
½Ai;2 ¼ yiþ1
½Ai;3 ¼ yiþ1 ;
i ¼ 1; 2; . . . ; N 1
0.5
½Ai;3 ¼ yiþ1 ;
i ¼ 1; 2; . . . ; N 1
0.4
d ¼ ½R22 d22;1 ; R23 d23;1 ; . . . ; R2N d2N;1
0.7
SNR = 0 dB
0.6
SNR = -5 dB
0.3 d ¼ ½d2;1 ; d2;1 ; . . . ; dN;1 T .
0.2
The stand least square solution to P, given R, is
0.1
P ¼ 12ðAT AÞ1 AT ðd 2RdÞ.
0 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Probability of false alarm PFA
(8)
The key idea of SI approach is to substitute Eq. (8) into Eq. (7) and minimize the equation error again but with respect to R. This
Fig. 2. Matchef filter performances for true (solid lines) and approximate bipolar pulse (dash lines).
z
(not presented here) showing the performances of the matched filter for a bipolar signal detection using two hydrophones will also improve the performance of an acoustic neutrino telescope. Once an event occurs, the source identification proceeds, but here a knowledged of all kind of sources (bio-activities and all spices) that might generate an acoustic sound. So, a database will be needed to better identification and selection. This version, we consider that any detected event is believed to be a neutrino event and the neutrino source location will proceed.
d
1
=
R
(x, y, z)
di
(x1, y1, z1) = (0, 0, 0)
y
4. Neutrino source localization Given the fact that neutrino interaction at HE (E41019 eV) generates an acoustic such that the total acoustic radiation is confined to a narrow, so-called ‘‘pancake’’ with an opening angle y of about 5 . So, to localize neutrino sources via an acoustic technique, we need to know five parameters that to say: the position ðxs ; ys ; zs Þ of interaction and the direction of neutrino ðys ; fs Þ. For angles, one can fit a plane using the positions of hit
Ri
(xi, yi, zi) x Fig. 3. Illustration for spherical interpolation approach.
ARTICLE IN PRESS S232
B. Bouhadef / Nuclear Instruments and Methods in Physics Research A 604 (2009) S230–S232
of CC) and conserving its phase which contains the TDOA information. Fig. 4 shows variance (blue) and bias (red) of the estimated TDOA versus signal to noise ratio (SNR) using PHAT algorithm.
0.8
TDOA’s errors (samples)
0.7 0.6
6. Detector geometry effect
0.5 0.4
ttrue-tasr Variance on mean
0.3 0.2 0.1 0 -10
-8
-6
-4
-2
0
2
4
6
8
10
To test whether the precision of a source location depends on detector structure, we have done a Monte Carlo simulation using a detector of 10 hydrophones. The simulation was done for four detectors: 1, 4, 7, and 10 times the original structure. Fig. 5 shows the effect of detector geometry and the hydrophone uncertainly, as much as the geometry is zoom out the error on position goes down, and the error on position increase with uncertainly on hydrophone position. We must notice here that, the uncertainly on hydrophones affects the precision of neutrino source location more than TDOA errors.
Signal to noise ratio (dB) 7. Conclusion
Fig. 4. Variance and error on the mean of TDOAs.
We have presented here the first version of software for neutrino source detection and localization, we give also a model for sea noise simulation based on an AR model. The efficiency of neutrino detection will be based mainly on the algorithm of detection to be used at a single hydrophone as well as the algorithm for source selection. As first step we used matched filter which is optimum unless the shape of the signal is unknown. In addition, the precision of neutrino point location is based mainly on uncertainly of hydrophones locations as we have shown, our future work will focus on more robust algorithm such as maximum likelihood for detection and localization. The software developed here could be tested in an underwater optical neutrino detection telescope such NEMO experiment [6] for acoustic positioning calibration.
106
Variance on position (m)
105 104 103 102 101 100 Detector 4X Detector 7X Detector 10X Detector
10-1 10-2 10-3 10-2
10-1
Acknowledgments
100
Noise std (m) Fig. 5. Geometric effect on position estimation.
solution leads to a closed form location from range difference measurements.
5. Time differences of arrival The TDOA is considered as a first step for sources localization, there are many proposed algorithms for TDOA estimation using a modified version of the cross-correlation (GC) known as general CC (see for example Ref. [11]), in our software we used the PHAse Transform (PHAT) algorithm which easy to implement and is robust then many other algorithm. The PHAT algorithm normalizes the magnitude of cross-spectrum (the Fourier transform
The author is grateful to the Dipartimento di Fisica di Pisa, Ph.D. school Galileo Galilei, INFN Sezione Pisa, and NEMO Collaboration.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
G. Askarjan, Atomnaya Energia 3 (1957) 153. G. De Bonis, this issue. A.M. Jaime, this issue. K. Kurahashi, this issue. G. Riccobene, this issue. hhttp://nemoweb.lns.infn.iti. G. Riccobene, et al., submitted for publication, available at: http://arxiv.org/ abs/0804.2913v1, 17 April 2008. J.G. Proakis, D.G. Manolakis, Digital Signal Processing, third ed., Prentice-Hall, Englewood Cliffs, NJ, 1996. R.J. Urick, Principles of Underwater Sound, McGraw-Hill, New York, 1983. J.S. Abel, J.O. Smith, Proceedings of the IEEE ICASSP 1 (1987) 471. J. Chen, Journal of Applied Signal Processing (2006) 1 (Article 26503).