Vector Sensor Arrays in Underwater Acoustic Applications

Transcription

1 Vector ensor Arrays in Underwater Acoustic Alications Paulo antos 1, Paulo Felisberto 1 and érgio M. Jesus 1, 1 Institute for ystems and Robotics, University of Algarve, Camus de Gambelas, Faro, Portugal. {jsantos, felis, sjesus}@ualg.t Abstract. Traditionally, ocean acoustic signals have been acquired using hydrohones, which measure the ressure field and are tyically omnidirectional. A vector sensor measures both the acoustic ressure and the three comonents of article velocity. Assembled into an array, a vector sensor array (VA) imroves satial filtering caabilities when comared with arrays of same length and same number of hydrohones. The objective of this work is to show the advantage of the use of vector sensors in underwater acoustic alications such as direction of arrival (DOA) estimation and geoacoustic inversion. Beyond the imrovements in DOA estimation, it will be shown the advantages of using the VA in bottom arameters estimation. Additionally, is tested the ossibility of using high frequency signals (say 8-14 kz band), acquired during the MakaiEx 2005, to allow a small aerture array, reducing the cost of actual sub-bottom rofilers and roviding a comact and easy-to-deloy system. Keywords: Vector sensor array, Direction of arrival estimation, Bottom roerties estimation. 1 Introduction Acoustic vector sensors measure both the acoustic ressure and the three comonents of article velocity. Thus a single device has satial filtering caabilities not available with ressure hydrohone. A Vector ensor array (VA) has the ability to rovide information in both vertical and azimuthal directions allowing for a high directivity not ossible with arrays of traditional hydrohone with same length and the same number of sensors. These characteristics have been exlored during the last decade but most of the studies are related to direction of arrival (DOA) estimation. owever, due to the VA ability to rovide directional information, this device can be used with advantage in other alications such as geoacoustic inversion. In this work it is shown that a reliable estimation of ocean bottom arameters can be obtained using a small aerture VA and high-frequency signals. This aer is organized as follows: in ection 2 is made a descrition of the contribution of this work to technological innovation. The state of the art and the related literature is resented in ection 3. ection 4 describes the vector sensor

2 measurement model and the theory related to the Bartlett estimator based on article velocity for generic arameter estimation, enhancing the advantages of the VA. In ection 5, the discussion of the results is made, showing that the VA remarkably reduces the ambiguities resents in DOA estimation obtained with a hydrohone array and rovide information both in vertical and azimuthal direction. Also, it is shown that VA imroves the resolution of bottom arameters estimation, such as sediment comressional seed, density and comressional attenuation based in matched-field inversion (MFI) techniques. The data herein considered was acquired by a four element vertical VA in the 8-14 kz band, during the Makai exeriment 2005 sea trial, off Kauai I., awaii (UA) [1]. Finally ection 6 concludes this work. 2 Contribution to technological innovation Vector sensors are long time used in underwater acoustic surveillance systems, mainly for DOA estimation. Only from the last decade the interest in VA rose exonentially, influenced by electromagnetic vector sensor alications and develoments in sensor technology that allowed building comact arrays for acoustic alications in the air. It is exected that in a near future will be also commercially available vector sensor devices well suited to develo comact underwater VA at a reasonable costs. Beyond DOA estimation, it is likely that these new comact systems can be used with advantage over traditional hydrohone arrays in other underwater alication fields, thanks to inherent satial filtering caabilities of vector sensors. Although the advantage of use a VA in DOA estimation is also considered in this work to show the enhanced satial filtering caabilities of a short aerture (4 elements) VA, the main focus is on using the short aerture VA to imrove inversion roblems found in underwater acoustics, in articular geoacoustic inversion. The roosed geoacoustic inversion method based on MFI techniques shows the advantage of including article velocity information that contributes to a better resolution of the estimated arameters, some of them with difficult estimation with traditional hydrohone arrays, even with larger aerture arrays. These methods were tested with field data acquired during Makai Ex 2005 [1], where robe signals in the 8-14 kz band were used. The bottom estimates obtained are in line with the bottom characteristics known for the area. The band of the robe signal used is well above the band traditionally used in geoacoustic inversion (bellow 1 kz), thus a systems based on a few elements VA oerating at such frequency band can be very comact, easyto-deloy or to install in a light mobile latform like AUV, becoming a good alternative to actual rofilers. 3 tate of the art During the last decade, several authors have been conducting research on vector sensors rocessing, most of them theoretical works, suggesting that this tye of device has advantage in DOA estimation and giving rise to an imroved resolution. Nehorai and Paldi [2] develoed an analytical model, initially for electromagnetic sources

3 extending then to the acoustic case, to comare the DOA estimation erformance of a VA to that of an array that measures only scalar acoustic ressure. At the beginning of 2000 s, Cray and Nuttall [3], erformed comarisons of directivity gains of VA to conventional ressure arrays. ource bearing estimation was exlored in [4], where the lane wave beamformer was alied to real data acquired by a four element VA in the 8-14 kz band, during Makai Exeriment 2005, off Kauai I., awaii (UA). Increased satial filtering caabilities gave rise to new alications where the VA could be used with advantage over hydrohone arrays. Due to these characteristics the VA is aearing in different fields like ort and waterway security [5], underwater communications [6], underwater acoustic tomograhy and geoacoustic inversion [7,8]. The bottom arameter estimation results [9,10] using high-frequency signals acquired by the VA during the Makai Ex 2005 are of considerable interest due to their uniqueness in this research area. Recently, some theoretical works [11,12] were ublished using quaternion based algorithms in order to more effectively rocess VA data. These works are concerned to DOA estimation but in [10] it was suggested that quaternion based algorithms can be used with advantage also in geoacoustic inversions. 4 The measurement model 4.1 Particle velocity model formulation olving inversion roblems by MFI techniques, a roagation model to generate field relicas is required. erein a ray tracing model TRACE [13] is considered to generate the article velocity comonents, beyond the acoustic ressure. Using the analytical aroximation of the ray ressure [13], the article velocity v ( Θ0 ) for a generic set of environmental arameters ( Θ 0 ) can be written as [14]: v Θ ) = u( ), (1) ( 0 Θ0 where the vector u is a unit vector related to the ressure gradient. The environmental arameter deends on the characteristics of the acoustic channel, including ocean bottom arameters. 4.2 Data model Assuming that the roagation channel is a linear time-invariant system, is the ressure and v x, v y and v z are the three article velocity comonents, a narrowband signal at frequency ω (omitting the frequency deendency in the following formulas) due to a source signal s, for a articular set of channel arameters Θ 0, measured with an array of L vector sensors, can be written, for acoustic ressure as: T y ( Θ0) = [ y 1( Θ0),..., y L( Θ0)], (2)

4 where y Θ ) is the acoustic ressure at l ( 0 for the acoustic ressure is: y s + n th l vector sensor. The linear data model ( Θ 0 ) = h ( Θ0), (3) where h Θ ) is the channel frequency resonse measured on L ressure sensors and n ( 0 is the additive noise. In the following formulation it is assumed that the additive noise is zero mean, white, both in time and sace, with variance σ, uncorrelated between each sensor and uncorrelated with the signal s. A similar definition has been adated for the article velocity: T y v( Θ0) = [ y v x ( Θ0),..., yv xl ( Θ0), yv y ( Θ0),..., yv yl ( Θ0), yv z ( Θ0),..., yv zl ( Θ0)] (4) becoming the data model for the article velocity comonents, taking in account (1): y v s + n ( Θ 0 ) = u( Θ0) h ( Θ0) v, (5) where is the Kronecker roduct and n v is additive noise. Taking into account (3) and (5), the VA data model defined for a signal measured on L elements can be written as: y ( Θ0) 1 n y v ( Θ ) = = h ( Θ0) s + yv ( Θ0) u( Θ0) n 0. v Data model (6) exands data model for the article velocity comonents with acoustic ressure. 2 n (6) 4.3 Bartlett estimator The classical Bartlett estimator is ossibly the most widely used estimator in MFI arameter identification, maximizing the outut ower for a given inut signal [15]. The Bartlett arameter estimate ˆΘ 0 is given as the argument of the maximum of the functional: { eˆ y( Θ ) y ( Θ )ˆ( e Θ) } = eˆ R( Θ )ˆ( e ) P B = E Θ (7) where the relica vector estimator e ˆ( Θ) is determined as the vector e (Θ) that maximizes the mean quadratic ower: eˆ = arg max{ e R( Θ0) e( Θ)}, (8) e where reresents the comlex transosition conjugation oerator, E {}. denotes statistical exectation and E{ Θ 0 ) y ( Θ )} y is the correlation matrix R Θ ). The ( 0 ( 0

5 maximization roblem is well described in [15], thus the Bartlett estimator when only ressure sensors are considered, can be written as: P B, (Θ) = h R ( Θ0) h h h. (9) Aling the above formulation to the data model (5), it was shown in [14] that an estimator for article velocity oututs is: where P 2 [ u u( Θ0) ] 2 P [ cos( )] P ( ) = B, θ B, u u( Θ) B, v Θ. (10) θ is the angle between the vector u(θ) from the relica and the vector u( Θ0 ) from the data. Based on this equation, one can conclude that the article velocity Bartlett estimator resonse is roortional to the ressure Bartlett estimator resonse by a directivity factor (gave by the inner roduct u u( Θ 0 ) ), which could rovide an imroved side lobe reduction or even suression when comared with the ressure resonse. For the data model (6), the VA Bartlett estimator is given by [14]: ( θ ) 2 B, v Θ P 2 [ 1+ cos( θ )] PB, 2cos PB, ( ). (11) 2 One can conclude that when the acoustic ressure is included a wider main lobe is obtained (11), comared to the estimator with only article velocity comonents (10). owever, including the ressure on the estimator, can lead to reduce ambiguities when frequencies higher then the working frequency of the array are used. 5 Discussion of results 5.1 DOA estimation One of the Bartlett estimator alications is the conventional beamformer for DOA estimation. The lane wave beamformer is alied to comare the erformance of the VA versus hydrohone arrays. In the case of lane wave DOA estimation, the search arameter Θ is the direction ( θ, φ ) and the relica vector is simle a combination of weights, which are direction cosines as weights for the article velocity comonents and a unit weight for the ressure and is given by [4]: r T r e ( θ, φ ) = 1,cos θ sinφ,sinθ sinφ,cosφ ex( k., (12) [ ] ) where r r is the osition vector of the VA elements (in this work the VA used has four elements equally saced with 10cm and located in the z-axis being the first one at the origin of the Cartesian coordinates system), i k r is the wavenumber vector

6 corresonding to the chosen steered, or look direction θ, ) of the is the azimuth angle and φ [ π, ] array, θ [ π, π ] Fig. 1. ( φ 2 π is the elevation angle, 2 Fig. 1. The array coordinates and the geometry of acoustic lane wave roagation, with azimuth θ and elevation φ angles. Fig. 2 resents the simulation results obtained for the working frequency of the array, 7500z, and for a DOA of (45º, 30º). Fig. 2 (a) shows that when the acoustic ressure sensors are considered (9), only the elevation angle is obtained due to omnidirectionality of the sensors. On the other hand, Fig. 2 (b) shows that when the article velocity comonents are introduced, the DOA is erfectly resolved due to the directivity factor obtained with the inner roduct in (10). Finally, when acoustic ressure is included, a wider main lobe is obtained, Fig. 2 (c), however the ambiguities are eliminated. This can be observed even when frequencies higher then the working frequency of the array are used. The main advantage of the VA in the DOA estimation is that it resolves both vertical and azimuthal direction when comared with traditional hydrohones arrays. The results of the real data DOA estimation can be seen in [4]. (a) (b) (c) Fig. 2. DOA estimation simulation results at frequency 7500z with azimuth 45º and elevation 30º for Bartlett beamformer considering: only ressure sensors resonse (a), only article velocity comonents resonse (b) and all elements of the VA ( + v) (c). 5.2 Bottom arameters estimation The ocean bottom arameters estimation is another subject where the VA can be used with advantage. Fig. 3 shows the sediment comressional seed estimation

7 obtained with ressure data only (a), article velocity only (b) and both ressure and article velocity (c). The estimation results for density and comressional attenuation can be found in [10]. (a) (b) (c) Fig. 3. Real data ambiguity surfaces for sediment comressional seed during the eriod of acquisition considering: ressure only (a), article velocity only (b) and both ressure and article velocity (c). The ambiguity surfaces illustrated in Fig. 3 were obtained for the maximum values of estimator functions during almost 2 hours of data acquisition, showing the stability of the results. Fig. 3 (a) shows a wider main lobe obtained when only ressure data is considered (9), with oor resolution of the arameter estimation. Fig. 3 (b) and (c) were obtained considering the VA Bartlett estimators (10) and (11), resectively without and with ressure. Comaring lots (b) and (c) clearly show that the estimate of sediment comressional seed is 1575 ± 5 m/s, but when the estimate function without ressure is considered, a narrower main lobe aears as well as some ambiguities, like in DOA estimation. The results obtained with the function that included all the vector sensor comonents are stable during the eriod of acquisition and show an increased resolution of the bottom arameters estimation, not ossible with hydrohone arrays of same number of sensors. 6 Conclusion This work shows the advantage of using a VA for DOA and bottom arameters estimation. It was seen that the VA reduces ambiguities in DOA estimation, when comared with hydrohone arrays, roviding information in both vertical and azimuthal directions. Also, the VA imroves the resolution of the bottom arameters estimation allowing to access arameters, usually with difficult estimation using traditional hydrohone arrays. One can remark that reliable estimates are obtained even with a small aerture array (4 elements only) and high frequency signals (say 8-14 kz band). Thus the usage of VA with high-frequencies can rovide an alternative for a comact and easy-to-deloy system in various underwater acoustical alications.

8 Acknowledgments The authors would like to thank Michael Porter, chief scientist for the Makai Exeriment, Jerry Tarasek at Naval urface Weaons Center for the use of the vector sensor array used in this work. The authors also thank Bruce Abraham at Alied Physical ciences for roviding assistance with the data acquisition and the team at L Research for their hel with the data used in this analysis. Research suorted by FCT IT/IR Plurianual funding rogram (U101/13). References 1. Porter, M. et al: The Makai exeriment: igh-frequency acoustic. In: 8 th ECUA, Jesus,. M., Rodríguez, O. C. (eds) vol. 1, Carvoeiro, Portugal (2006) 2. Nehorai, A., Paldi E.: Acoustic vector-sensor array rocessing. IEEE Trans. ignal Processing 42, (1994) 3. Cray, B. A., Nuttall, A..: Directivity factors for linear arrays of velocity sensors. J. Acoust. oc. Am. 110, (2001) 4. antos, P., Felisberto, P., ursky, P.: ource localization with vector sensor array during Makai exeriment. In: 2 nd International Conference and Exhibition on Underwater Acoustic Measurements, Technologies and Results, eraklion, Greece (2007) 5. his, J. C., Abraham, B. M.: The use of vector sensors for underwater ort and waterway security. In: ensors for Industry Conference, New Orleans, Louisiana, UA (2004) 6. Abdi, A., Guo,., utthiwan, P.: A new vector sensor receiver for underwater acoustic communication. In: Proceedings MT/IEEE Oceans, Vancouver, BC, Canada (2007) 7. Peng,., Li, F.: Geoacoustic inversion based on a vector hydrohone array. Chin. Phys. Lett. 24, (2007). 8. Lindwall, D.: Marine seismic surveys with vector acoustic sensors. In: Proceedings of oc. Exloration Geohysicists annual meeting. New Orleans, UA (2006) 9. antos, P., Felisberto, P., Jesus,. M.: Estimating bottom roerties with a vector sensor array during MakaiEx In: 2 nd International worksho on Marine Technology, MARTEC Vilanova I LA Geltrú, Barcelona, ain (2007) 10. antos, P., Rodríguez, O. C., Felisberto, P., Jesus,. M.: Geoacoustic Matched-field inversion using a vertical vector sensor array. In: 3 rd International Conference and Exhibition on Underwater Acoustic Measurements, Technologies and Results, Naflion, Greece (2009) 11. Miron,., Le Bihan, N., Mars, J. I.: Quaternion-MUIC for vector sensor array rocessing. IEEE Transactions on ignal Processing 54, (4), (2006) 12. Wang, Y.., Zhang, J. Q., u, B., e, J.: yercomlex model of acoustic vector sensor array with its alication for the high resolution two dimensional direction of arrival estimation. In: I 2 MTC 2008 IEEE International Instrumentation and Measurement Technology Conference, Victoria, Vancouver Island, Canada (2008) 13. Rodríguez, O. C.: The TRACE and TRACEO ray tracing rograms. Physics Deartment, iplab, FCT, University of Algarve (2008) 14. antos, P., Rodríguez, O. C., Felisberto, P., Jesus,. M.: Geoacoustic Inversion using a vertical vector sensor array. ubmitted to J. Acoust. oc. Am. (2009) 15. Krim,., Viberg, M.: Two decades of array signal rocessing research. IEEE ignal rocessing magazine, (1996)