Studies on underwater acoustic vector sensor for passive estimation of direction of arrival of radiating acoustic signal

Transcription

1 Indian Journal of Geo-Marine Sciences Vol. XX(X), XXX 2015, pp. XXX-XXX Studies on underwater acoustic vector sensor for passive estimation of direction of arrival of radiating acoustic signal Arjun Kalgan *, Rajendar Bahl, Arun Kumar Centre for Applied Research in Electronics, Indian Institute of Technology, Delhi, New Delhi , India *[ Received 1 October 2014; revised 21 November 2014 A passive underwater surveillance system performs the function of detection and localisation by utilising the acoustic emissions from the source, whilst itself remaining concealed. The conventional technique employs an array of hydrophones (measure the scalar pressure), wherein the size of the array is dependent on the desired angular resolution and the wavelength of the signal to be monitored. The vector sensors, on the other hand, measure the scalar pressure as well as the orthogonal components of particle velocity using a co-located sensor and offer decided advantages over the traditional solution due to their smaller size and frequency independent performance (over the frequency range specified for constituent particle velocity sensors). This paper presents studies on a prototype underwater acoustic vector sensor. The present approach employs a tri-axial accelerometer as a co-located particle acceleration sensor, and along with a hydrophone it provides four sets of measurements of an acoustic field. The parameter (Direction of Arrival) estimation has been carried out using both subspace based methods as well as beamforming technique for demonstration of the acoustic vector sensor system in the lab environment and its performance analysis. [Keywords: Inertial vector sensor, MVDR, TLS-ESPRIT, cardioid processing] Introduction An Acoustic Vector Sensor (AVS) is a compact device that measures both the scalar and the vector component of acoustic field at a single point in space. The additional information provided by AVS, in the form of particle velocity estimate, results in significant advantages over a traditional pressure sensor array. AVS in its most general form comprises of three orthogonally oriented velocity hydrophones plus (an optional) pressure hydrophone, all of which are spatially co-located. Each constituent velocity sensor has an inherent directional response to the incident acoustic particle velocity wave field and estimates one Cartesian component of the threedimensional (3D) particle velocity vector of the incident wave field. A single-vector sensor thus possesses an inbuilt directionality in azimuth and elevation that is independent of signal frequency, signal bandwidth, and the source s location in the near field as opposed to the far field. In contrast, the beam pattern obtainable from an array of hydrophones is a function of frequency, inter element spacing and radial distance from the source. By utilizing additional information embedded in an acoustic wave field, the vector sensors offer numerous advantages over pressure sensor arrays for practical applications 1,2. These advantages include: 1) Better estimation of source direction with a compact sensor, thus, making them amenable for mounting from floats, hull etc., wherein, there is a constraint on the size of the sensor. 2) Ability to provide three dimensional localisation whilst alleviating the problematic left/right ambiguity. 3) The complicating effects of spatial under sampling are avoided. 4) Creation of a pseudo-sensor through linear combination of the four elements. This pseudo-sensor can be utilised to form many different response patterns 3. By appropriate weighting, patterns can null any direction. Thus, acoustic vector sensors have the ability to effectively replace pressure sensors while providing better and reliable results as compared to the existing systems. A generic implementation is illustrated in Fig. 1. There are a number of ways in which constituent velocity sensors can be implemented e.g. accelerometer, directional hydrophone or pressure gradient sensor. In this paper, tri-axial accelerometer has been employed as particle velocity sensor and hydrophone as an omnidirectional pressure sensor.

2 520 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 2015 Fig. 1 Generalised representation of acoustic vector sensor The aim of this paper is to present the studies on an accelerometer based underwater Vector Sensor for bearing estimation of an acoustic source through passive surveillance of source emissions. An integral part of the implementation has been the development of a suitable suspension system and extensive testing of the setup in lab environment using various Direction of Arrival (DoA) estimation algorithms. The present investigation discusses the results obtained whilst using a single source by varying the angle of incidence in the azimuth plane keeping the elevation fixed. However, the present 2D implementation can easily be extended for a 3D scenario, albeit with minor modifications. The paper covers introduction to the vector sensor, fundamentals of inertial vector sensor, description of implemented signal processing algorithms, results and conclusion. Inertial (p-u method) vector sensor In accordance with the Euler's description of fluid mechanics, the field variables (i.e. pressure, density, momentum and energy) are continuous functions of the three-dimensional space (x, y, z) and time (t). In addition to the three components of particle velocity (u) in the three-dimensional space, two field variables pressure (p) and density (ρ) can be used to formulate the equations based on conservation laws for study of the acoustic field. The resulting equations can be suitably combined to derive one dimensional wave equation which governs acoustic propagation in elastic media 4. (, ) (, ) = 0 (1) The one-dimensional wave equation serves as a starting point for understanding the acoustical wave propagation and by utilising the interdependence between various field variables, suitable relations can be formulated towards estimation of the parameters of interest. For instance, the particle velocity in a given direction can be related to the pressure gradient in that direction (the rate at which the instantaneous pressure changes with distance) by, (, ) = (, ) (2) The particle velocity can thus be measured in three orthogonal directions and the resultant particle velocity vector can provide the 3D direction of arrival of the incident acoustic wave. There are two ways in which this can be done. Firstly, it is possible to estimate particle velocity by measuring pressure gradient with two closely spaced pressure sensors (p-p method), which, however, suffers from numerous inherent disadvantages namely, finite difference approximation, scattering and diffraction, and instrumentation phase mismatch. Secondly, an alternate methodology can be based on directly sensing the particle velocity in the three orthogonal directions at a single point in space using a suitable co-located sensor. The motivation for such a technique is based on the fact that acoustically small bodies immersed in the medium and free to move, respond directly to the acousticc particle motion. If the body is neutrally buoyant, then the body's motion is the same as that of the surrounding fluid. If the body is negatively buoyant, the amplitude of the motion of the body is reduced compared to that of the fluid; if the body is positively buoyant, the amplitude of the body's motion is larger than that of the fluid. Consequently, if an inertial transducer (an accelerometer) is embedded in the body, a signal is producedd that can be related to the acoustic particle motion 5. Because the particle velocity is measured directly, there is no approximation error associated with the subtraction of nearly equal signals common with gradient (p-p method) sensors. The dynamics of an unconstrained sphere can be considered as the basis to understand the implementation of particle velocity probe based on inertial sensor. For a rigid sphere of radius and density immersed in an infinite viscous fluid medium having density and viscosity, and is ensonified with a plane traveling wave having a velocity, the resulting velocity of the sphere is given by,

3 KALGAN et al.: STUDIES ON UNDERWATER ACOUSTIC VECTOR SENSOR 521 = (3) where, = is the specific gravity of the sphere and = 2 is the viscous penetration depth. The equation above is only valid for the case when the size of the sphere is small compared to a wavelength. However, if the sphere is sufficiently large compared to the viscous penetration depth (e.g., a<<1), then its motion will be purely a function of the specific gravity such that 6, = (4). It follows from this analysis that an inertial sensor embedded inside the sphere will produce an electrical output that corresponds to the velocity (acceleration) of the acoustic wave, as long as the effects of viscosity and scattering can be ignored and the sphere is neutrally buoyant. If the sphere deviates from neutral buoyancy, then the amplitude is adjusted by a factor of 3 (2γ+1), but the phase is preserved. In the present implementation, the tri-axial accelerometer (Piezotronics - ICP356A17) is embedded inside the sphere and therefore responds directly to the incident acoustic wave. The output of accelerometer is an electrical signal corresponding to the particle acceleration of the medium particles, in response to the incident acoustic wavefield. The obtained electrical signal is conditioned using an associated signal conditioner (Piezotronics Signal Conditioner- 480B21) and output from different axes is acquired using a suitable data acquisition system. The acquired signal is thereafter integrated in the computing environment, to provide the voltage corresponding to particle velocity, without the use of any additional electronic circuitry. The premise of employing an inertial sensor as sensing element is based on its directional capabilities. In case of an accelerometer it stems from the dipole behavior of its individual axes. Each accelerometer axis is most sensitive along a specific dimension in the 3D co-ordinate geometry whilst being relatively insensitive along the other two. This results in a dipole beam pattern along each axis of an accelerometer. The three sets of measurement provided by each of three axes of the tri-axial accelerometer can be used to compute particle velocity vector corresponding to an incident signal and in turn its direction of arrival. However, the resultant DoA so obtained will suffer from a 180 (left-right) ambiguity (in the azimuth plane for a 2D case) owing to the dipole response of individual axis of the accelerometer. The solution lies in the inclusion of pressure sensor (possibly co-located) along with the tri-axial accelerometer for computation of sound intensity to help resolve the ambiguity in the DoA estimate. The sound intensity in a given direction at a point is the average rate of transfer of sound energy through a unit area perpendicular to that direction at that point. It is a vector quantity and is given as, ( / ) = ( ). ( ) (5). The DoA of the acoustic plane wave can thereafter be estimated by calculating the unit vector associated with the intensity vector, (, ) = (6). Such a sensor which measures both pressure as well as particle velocity is termed as an inertial (p-u method) vector sensor. Importance of suspension system Inertial sensors are sensitive to any motion. Besides the desired motion that results from acoustic waves, structure-borne vibration, and flow-turbulence forces can produce undesired output. Consequently, the vector sensor suspension system should be designed in a way that isolates the sensors from all non-acoustic vibration. It is important that the suspension system have the following properties: 1) It should have a natural frequency well below the intended range of acoustic sensing. 2) It should fix the average position and orientation of the sensor body whilst permitting movement of the sensor body in response to the acoustic field. 3) It should isolate the sensor from structure-borne vibration and have the ability to withstand operational shock. 4) It should not distort the response of the sensor in magnitude, phase, or apparent sound incidence angle. The implementation of the Vector Sensor complete with the associated suspension system consists of Triaxial accelerometer, a spherical dome encasing the accelerometer, suspended rigidly using suitable mounting arrangement 7. The design whilst being simple circumvents the problems associated with the more popular implementations such as suspending the sphere inside a ring with the help of springs 8 (the motion of the sphere in this case has to be

4 522 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 2015 approximated with a lumped parameter circuit model of the system and would deviate from the simplistic model described above). In practice, inertial sensors have to be suspended from some host platform and therefore, it is critical that the suspension system and/ or the host platform not contaminate the measurement. Signal model and processing algorithms Inertial sensors are sensitive to any motion. A vector sensor comprising of three co-located (and mutually orthogonal) velocity sensors and pressure sensor (optional) is considered for formulation of signal model. The four sensors would in effect measure all three Cartesian components of the particle velocity vector and the scalar pressure. This ability to perceive the vector nature of the incident acoustic wavefield sets it apart from the conventional technique of spatial measurement of pressure (scalar). The conventional method of direction of arrival relies on measuring the phase difference between spatially displaced components of an array. The vector sensor on the other hand makes use of the directional nature of its constituent velocity sensors in computation of angle of arrival of an acoustic signal. Thus, the 3 1 array manifold at the vector sensor (comprising of only velocity sensors) is given as sin cos (, ) sin sin (, ) (7) cos ( ) where, the subscript k denotes the steering vector corresponding to the k th acoustic wave out of multiple acoustic waves incident on the vector sensor. The incident acoustic waves are constrained to be uncorrelated and distinct in frequency for the purpose of the present investigation. The three components of the steering vector essentially represent the velocity sensor aligned along the three Cartesian axes. An inspection of the vector sensor array manifold leads to following important observations, 1) A single vector sensor provides 3 sets of measurements of an acoustic field and effectively manifests as a three-element array in and of itself. 2) This array manifold contains no time-delay phase factor that makes it independent of the incident signal's frequency spectra, unlike that of a spatially displaced array. 3) The co-location of the constituent element in a vector sensor obviates the complicating effects of a near-field wave-front s curvature. Azimuth-elevation estimates can thus be found without any a priori knowledge of the incident signal's spectra with a single vector sensor. However, the estimates obtained with the use of a single triaxial accelerometer would suffer from 180 ambiguity in the azimuth plane (for 2D case) as has been brought out earlier. In the present implementation the ambiguity has been resolved with the help of a pressure sensor (hydrophone) placed close to the sensor body which helps resolve the quadrant for angle of arrival by providing reference for phase comparison. Extensive study of various methods for DoA estimation using the vector sensor signal model was undertaken, and three different approaches have been investigated in greater detail and subsequently implemented in MATLAB. 1) TLS-ESPRIT- the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm can be employed to obtain the azimuth and elevation estimates with a single vector sensor 9. This method has been explored due to reduced computational load and a superior performance when there is constraint on the duration of signal and signal to noise ratio. The traditional ESPRIT employs spatial invariance, in that it uses two subarrays which are identical in all respects but are spatially displaced, since, this is not possible using a single vector sensor, an alternative is to form temporal invariance i.e. two (overlapping) data sets can be formed out of a single set by timedelaying one w.r.t another. The sets can be expressed as, (, ) = 1, (8) and ( +, ) = (, ) = 1, (9). The signal is defined as, (, ), = 1.. (10) where, b k - amplitude of k th signal; f k - frequency of k th signal; φ k - phase and ΔT - arbitrary but fixed timedelay between two sets. The array output is given as, ( ) ( ) + ( )

5 KALGAN et al.: STUDIES ON UNDERWATER ACOUSTIC VECTOR SENSOR 523 = si n ( + ) = cos (18) = ( + ) (19) = ( ) + ( ) (11) where, [ ] [ ] = (12). The entire set of observations given as: [ ( ) ( )] = (13) Z is formed from Z 1 containing data sampled at {t 1...t N- L} and Z 2 containing data sampled at {t L+1.t N }. Let E S = [E 1 T E 2 T ] T denote the matrix formed corresponding to eigenvectors lying in the signal space obtained by decomposition of ZZ H matrix. By separating the E S matrix into E 1 and E 2 and noting that we can articulate, E 1 = A 1 T T and E 2 = A 2 T T (where T is a non singular matrix), the total least squares solution can thus be found out by introduction of Φ and ψ. Where, ψ = T -1 ΦT and E 1 ψ = E 2 and noting that Φ is a diagonal matrix with its non-zero elements equal to eigenvalues of ψ. The TLS fit is given by ψ TLS = V 1,2 V 2,2-1, where the matrices V 1,2 and V 2,2 are implicitly defined by the eigen-decomposition of [ ] = (14). The computation of matrices Φ and T gives us, A 1 =1/2 (E 1 T -1 +E 2 T -1 Φ -1 ). Where, A 1 ={a 1, a k }, and the direction cosines can be found out using relation [ ] (15) Fig. 2 Cardioid response of a vector sensor. [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Elevation and Azimuth angles are computed as, (16) (17). 2) Computation of Principal Eigen Vector of Data Correlation Matrix - From the velocity-sensor triplet s data, a 3 3 correlation matrix can be formed. Eigendecomposition of the resulting correlation matrix yields the eigenvector corresponding to the largestmagnitude eigenvalue. This principal eigenvector is related to the direction cosines corresponding to the incident signal and provides the elevation and azimuth angle estimates 10. 3) Minimum Variance Distortionless Response (MVDR) Beamformer - MVDR a robust adaptive beamformer employing a single constraint designed to pass a signal of given direction and frequency with unit gain 11. The weights are chosen to minimize output variance or power subject to the response constraint. This has the effect of preserving the desired signal while minimizing contributions to the output due to interfering signals and noise arriving from directions other than the direction of interest. Mathematically output can be expressed as, ( ) = ( ) ( ) (20) where, -array steering vector and R uu -covariance matrix of the received signal. The direction of arrival can be found out by steering across all the values of, and are given by the peaks obtained in the MVDR spectra. 4) Cardioid Processing-The constituent dipoles of accelerometer i.e. the axes, have a directional amplitude response proportional to cos α, where, α is the angle measured from the axis of the dipole. Therefore, by summing the dipole with an omnidirectional sensor having the same sensitivity as the maximum of the dipole's directional response, we can obtain a cardioid amplitude response 12 (essentially heart-shaped) pattern proportional to 1 + cos α (shown in Fig. 2). The constituent dipoles are broadband i.e. their response pattern is frequency independent over the band for which they are small in size compared to an acoustic wavelength. Further, they are superdirective in that they provide directional information and directivity gain in a configuration which is much smaller than a wavelength. Thus, the resulting Cardioid is also superdirective, providing directivity gain in a very small package. In effect, for a two-dimensional scenario, a pair of

6 524 INDIAN J. MAR. SCI., VOL. XX, NO. X XXXX 2015 matched orthogonal dipoles together can form a steerable equivalent dipole response, which when combined with an omni-directional sensor can provide a cardioid with a null steerable towards any azimuthal direction. Trials and Results The prototype acoustic vector sensor was tested in the underwater tank facility available in-house. The setup of the trials is as shown in Fig. 3. The source (underwater speaker) was placed at a distance of 35 cm from the sensor, comprising of rigidly suspended prototype vector sensor and a hydrophone placed in its proximity. The trials were conducted by rotating the sensor about its own axis in fixed steps of 10 to achieve the desired angle of arrival (AoA) with help of protractor and the pointer. The source signal was taken to be a sinusoid and tests weree carried out by varying the signal frequency from 2 to 3 khz. The results and analysis for the set of trials carried out at 2.4 and 2.6 khz is discussed. upright position, manual error in placement and reading off from scale. Reference step (in degrees) Angle (in degrees) Fig. 4 Linear plot showing variation of AoA from 0 to 350. Fig. 3 Set up for trial in underwater tank. The trials in underwater tank weree undertaken for the entire azimuth plane and observations and inferences are listed below: 1) The unambiguous DoA Estimate from all the algorithms for all orientations identical (with a difference < 1 ). 2) The results were found to be in-line w.r.t relative positioning of the source vis-a-vis sensor for most cases (Fig. 4 and 5). The deviations are attributable to the slight offset of the sensor sphere from its desired Fig. 5 Polar plot showing variation of AoA from 0 to 350 vis-a-vis reference 10 step. 3) MVDR algorithm gives 0.8 3dB Beamwidth 6 (Fig. 6). 4) There is a deviation from the ideal phase relationships between constituent elements of the sensor and is attributable to non co-location of acoustic centres of the constituent elements.

7 KALGAN et al.: STUDIES ON UNDERWATER ACOUSTIC VECTOR SENSOR 525 Fig. 6 Half power beamwidth obtained for AoA from 0 to MVDR. Conclusion The various trials conducted in underwater tank have established the efficacy of the design of Acoustic Vector Sensor prototype and veracity of associated DoA algorithms. The setup and variants have been rigorously tested for various scenarios and the prototype offers a robust and compact alternative to a conventional array, and as an example, to achieve the 3 db beamwidth (comparable to the worst case scenario of results obtained i.e. 6 ) the length of linear array (at frequency khz) would have to be approx. 4.8 m which is about 40 times the diameter of the prototype, whilst the prototype additionally offers advantage in terms of alleviating the problematic Left- Right ambiguity inherent to linear arrays. References 1. Shipps J.C. and Abraham B.M, The Use of Vector Sensors for underwater Port and Waterway security. IEEE Sensors for Industry Conference, (1994): Nehorai A. and Paldi E., Acoustic vector-sensor array processing. IEEE Transactions on Signal Processing, 42 (September 1994): Cox H. and Lai H., Performance of Line Arrays of Vector and Higher Order Sensors. Conference Record of the Forty- First Asilomar Conference on Signals, Systems, and Computers, (November 2007): Daniel R. Raichel, The Science and Applications of Acoustics. Springer, pp McConnell, J.A., Practical experiences with inertial type underwater acoustic intensity probes. Oceans '02 MTS/IEEE, 4(2002): Landau L.D. and Lifshitz E.M., Fluid Mechanics (Pergamon, Oxford, 1984), Secs. 11 and Cray Benjamin A., US Pat B1 (to The United States Of America as represented by The Secretary of the Navy), 09 Apr Gabrielson Thomas B., McEachern James F. and Lauchle Gerald C., US Pat (to The United States Of America as represented by The Secretary of the Navy), 21 Feb Wong K.T. and Zoltowski M.D., Uni-vector-sensor ESPRIT for multisource azimuth, elevation, and polarization estimation. IEEE Transactions on Antennas and Propagation, 45(1997): Yue Ivan Wu, Kainam Thomas Wong, Acoustic Near-Field Source-Localization by Two Passive Anchor-Nodes. IEEE Transactions on Aerospace and Electronic Systems, 48(Jan 2012): Barry D Van Veen, Kevin M. Buckley, Beamforming: A versatile approach to Spatial Filtering. IEEE ASSP Magazine, (Apr 1988): Cox H., Zeskind R.M., Adaptive cardioid processing. Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems, and Computers, (1992):