Bearing Estimation with Acoustic Vector-Sensor Arrays

1 I N T R O D U C T I O N The pass ive d i rec t ion-of-ar r iva l (DOA) e s t ima t ion p rob lem, in which the bea r ings of a n u m b e r of far-field acous t ic sources are d e t e r m i n e d , is of g rea t i m p o r t a n c e in m a n y unde rwa te r appl ica t ions . Tradi t iona l ly , the solut ion is to use a spa t i a l l y d i s t r i b u t e d a r ray of omnid i r ec t iona l pressure-sensors , and m a n y e s t i m a t i o n techniques have evolved for th is scenario. As emphas i s has shif ted to low in -wa te r costs, d e m a n d for b e t t e r pe r fo rmance at lower s ignal to-noise ra t ios (SNRs) and wi th smal le r a r rays has increased. This has lead to the idea of using acous t ic vec tor sensors. A vec tor sensor measures the acoust ic pressure and all t h ree c ompone n t s of t he acous t ic pa r t i c l e veloci ty at a pa r t i cu l a r po in t in space. Ar r ays of acous t ic vec tor sensors are, therefore , in con t ras t to t r ad i t i ona l pressure-sensor a r rays s ince t hey s a m p l e the ve loc i ty field, as well as the pressure field, at a n u m b e r of f ixed locat ions . The i r name der ives f rom the fact t ha t t hey measu re a c o m p l e t e vec to r phys ica l quant i ty . By mak ing use of more of the avai lable i n fo rma t ion in t he acous t ic field, vector-sensor a r rays are ab le to improve source loca l i za t ion accuracy. In pa r t i cu l a r , since each vec tor sensor measures the s t ruc tu re of the © 1996 American Institute of Physics 345 Downloaded 06 Feb 2012 to 128.252.255.140. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions acoustic field as well as its magnitude, the improvement is more than a simple increase in SNR associated with taking a greater number of measurements. A theoretical framework for DOA estimation using acoustic vector-sensor arrays has recently been developed in [1] and preliminary studies for free-space and hull-mounted arrays made in [2] and [3]. In addition, acoustic vector sensors have already been constructed [4] and linear arrays of them built and been subject to sea trials [5], [6]. We consider an array of vector sensors, illuminated by n narrowband Gaussian signals in spatially and temporally uncorrelated Gaussian noise. The Cram6r-Rao bound (CRB) for a single source scenario is derived and examined. We are able to distinguish and quantify two distinct improvements of the vector-sensor array over the pressure-sensor array: one associated with the greater number of measurements and one with the inherent directionality of the vector sensors themselves. Examination of these expressions shows that the use of vector sensors is most advantageous in small array, low SNR situations. We examine the performance of the conventional beamforming and Capon [7] DOA estimators, when used with the vector-sensor array. It is seen that even the simplest yector-sensor array can fully resolve both azimuth and elevation, and further advantages are revealed with regard to reduced aliasing and removal of ambiguities in undersampled arrays. A diversely-oriented array consisting of spatially distributed velocity sensors with various orientations is proposed and analyzed. Although only having the same hardware and computational requirements as a pressure-sensor array, it gains some of the directional capabilities of a vector-sensor array at the expense of SNR. In addition, it may be used in the presence of non-isotropic spatially correlated noise and still provide uncorrelated outputs if the correlation distance is shorter than the inter-sensor spacing or the sensors are placed at nulls of the spatial correlation function. This is in contrast to the vectorsensor array where the noise of co-located measurements will be correlated in the presence of a non-isotropic noise field, thus reducing performance.