We consider the passive direction-of-arrival (DOA) estimation problem using arrays of acoustic ve... more We consider the passive direction-of-arrival (DOA) estimation problem using arrays of acoustic vector-sensors located in a fluid, at or near a plane boundary. We formulate a general measurement model applicable to most surfaces, and derive an expression for the Cramer-Rao bound (CRB) of a single source. The CRB is used to analyze the practically important cases of ideal rigid and pressure-release surfaces in detail. An important quantitative comparison is made between a stand-off array of pressure sensors and a surface-mounted array of velocity sensors for the latter surface. In particular, we define and find an expression for the critical distance, at which the arrays have an equivalent performance
We consider the role played by the sensor locations in the optimal performance of an array of aco... more We consider the role played by the sensor locations in the optimal performance of an array of acoustic vector sensors, First we derive an expression for the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous wholespace and show that it has a block diagonal structure, i.e., the source location parameters are uncoupled from the signal and noise strength parameters. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled from each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or “canonical” location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptotic normalization, which are useful measures in three-dimensional bearing estimation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations. We then show that our previously derived geometrical conditions are also sufficient to ensure that this bound is independent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic
This dissertation examines the ability of acoustic vector sensors to solve the passive direction-... more This dissertation examines the ability of acoustic vector sensors to solve the passive direction-of-arrival (DOA) estimation and 3-D localization problems. These sensors measure the three-dimensional acoustic particle velocity vector, as well as the acoustic pressure, at one location. By preserving directional information that is present in the structure of the velocity field, they gain a number of advantages over traditional arrays of scalar sensors, such as hydrophones and microphones. We compute and examine, through the Cramér-Rao bound and beam-forming based methods, the ability of arrays of acoustic vector sensors to estimate direction. We first consider the case of an array in free space then extend these results to account for the presence of a reflecting boundary, such as the seabed or a vessel's hull, located near the array. Next, we derive expressions for the noise correlation structure induced by various ambient noise fields, isotropic and anisotropic, at an acoustic vector sensor array, and use them to examine its localization performance. We then propose a decentralized processing scheme to rapidly locate a wideband target in three dimensions. Finally, we present a general framework for the analysis of errors associated with the estimation of a vector, or system of vectors, that has geometrical interpretations in terms of length, angle, etc. The framework is employed throughout the thesis.
We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic ... more We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic vector sensors. We derive an expression for the Cramer-Rao bound (CRB) on the DOA parameters of a single source. Using this, we give conditions that minimize the lower bound on the asymptotic mean-square angular error, and conditions that ensure it is isotropic. The asymptotic performance of the Capon (1969, 1971) and beamforming estimators is analyzed and compared with a scalar-sensor array. The vector-sensor array is seen to have improved performance due to its elements' directional sensitivity. Large sample approximations for the mean-square error (MSE) matrices of the estimators are derived. Throughout, we compare vector-sensor arrays with their scalar-sensor counterparts
We propose a framework of performance measures for analyzing estimators of geometrical vectors th... more We propose a framework of performance measures for analyzing estimators of geometrical vectors that have intuitive physical interpretations, are independent of the coordinate frame and parameterization, and have no artificial singularities. We obtain finite-sample and asymptotic lower bounds on them for large classes of estimators and show how they may be used as system design criteria. We determine a simple asymptotic relationship that is applicable to both the measures and their bounds
... 1 (4) p(r) = ei(kyY+kz,)(e-iksz + R e & X w(r) = 1058-6393/96 $5.00 0 1996 IEEE Proceedin... more ... 1 (4) p(r) = ei(kyY+kz,)(e-iksz + R e & X w(r) = 1058-6393/96 $5.00 0 1996 IEEE Proceedings of ASILOMAR-29 ... The input impedance of the boundary is de-fined and the ratio of the (complex) pressure to the (complex) normal component of particle velocity at the surface [7], ...
The performance breakdown of subspace-based parameter estimation methods can be naturally related... more The performance breakdown of subspace-based parameter estimation methods can be naturally related to a switch of vectors between the estimated signal and noise subspaces (a “subspace swap”). We derive a lower bound for the probability of such an occurrence and use it to obtain a simple data-based indicator of whether or not the probability of a performance breakdown is significant. We also present a conceptually simple technique to determine from the data whether or not a subspace swap has actually occurred, and to extend the range of SNR values or data samples in which a given subspace method produces accurate estimates
We consider the passive direction-of-arrival (DOA) estimation problem using arrays of acoustic ve... more We consider the passive direction-of-arrival (DOA) estimation problem using arrays of acoustic vector-sensors located in a fluid, at or near a plane boundary. We formulate a general measurement model applicable to most surfaces, and derive an expression for the Cramer-Rao bound (CRB) of a single source. The CRB is used to analyze the practically important cases of ideal rigid and pressure-release surfaces in detail. An important quantitative comparison is made between a stand-off array of pressure sensors and a surface-mounted array of velocity sensors for the latter surface. In particular, we define and find an expression for the critical distance, at which the arrays have an equivalent performance
We consider the role played by the sensor locations in the optimal performance of an array of aco... more We consider the role played by the sensor locations in the optimal performance of an array of acoustic vector sensors, First we derive an expression for the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous wholespace and show that it has a block diagonal structure, i.e., the source location parameters are uncoupled from the signal and noise strength parameters. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled from each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or “canonical” location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptotic normalization, which are useful measures in three-dimensional bearing estimation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations. We then show that our previously derived geometrical conditions are also sufficient to ensure that this bound is independent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic
This dissertation examines the ability of acoustic vector sensors to solve the passive direction-... more This dissertation examines the ability of acoustic vector sensors to solve the passive direction-of-arrival (DOA) estimation and 3-D localization problems. These sensors measure the three-dimensional acoustic particle velocity vector, as well as the acoustic pressure, at one location. By preserving directional information that is present in the structure of the velocity field, they gain a number of advantages over traditional arrays of scalar sensors, such as hydrophones and microphones. We compute and examine, through the Cramér-Rao bound and beam-forming based methods, the ability of arrays of acoustic vector sensors to estimate direction. We first consider the case of an array in free space then extend these results to account for the presence of a reflecting boundary, such as the seabed or a vessel's hull, located near the array. Next, we derive expressions for the noise correlation structure induced by various ambient noise fields, isotropic and anisotropic, at an acoustic vector sensor array, and use them to examine its localization performance. We then propose a decentralized processing scheme to rapidly locate a wideband target in three dimensions. Finally, we present a general framework for the analysis of errors associated with the estimation of a vector, or system of vectors, that has geometrical interpretations in terms of length, angle, etc. The framework is employed throughout the thesis.
We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic ... more We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic vector sensors. We derive an expression for the Cramer-Rao bound (CRB) on the DOA parameters of a single source. Using this, we give conditions that minimize the lower bound on the asymptotic mean-square angular error, and conditions that ensure it is isotropic. The asymptotic performance of the Capon (1969, 1971) and beamforming estimators is analyzed and compared with a scalar-sensor array. The vector-sensor array is seen to have improved performance due to its elements' directional sensitivity. Large sample approximations for the mean-square error (MSE) matrices of the estimators are derived. Throughout, we compare vector-sensor arrays with their scalar-sensor counterparts
We propose a framework of performance measures for analyzing estimators of geometrical vectors th... more We propose a framework of performance measures for analyzing estimators of geometrical vectors that have intuitive physical interpretations, are independent of the coordinate frame and parameterization, and have no artificial singularities. We obtain finite-sample and asymptotic lower bounds on them for large classes of estimators and show how they may be used as system design criteria. We determine a simple asymptotic relationship that is applicable to both the measures and their bounds
... 1 (4) p(r) = ei(kyY+kz,)(e-iksz + R e & X w(r) = 1058-6393/96 $5.00 0 1996 IEEE Proceedin... more ... 1 (4) p(r) = ei(kyY+kz,)(e-iksz + R e & X w(r) = 1058-6393/96 $5.00 0 1996 IEEE Proceedings of ASILOMAR-29 ... The input impedance of the boundary is de-fined and the ratio of the (complex) pressure to the (complex) normal component of particle velocity at the surface [7], ...
The performance breakdown of subspace-based parameter estimation methods can be naturally related... more The performance breakdown of subspace-based parameter estimation methods can be naturally related to a switch of vectors between the estimated signal and noise subspaces (a “subspace swap”). We derive a lower bound for the probability of such an occurrence and use it to obtain a simple data-based indicator of whether or not the probability of a performance breakdown is significant. We also present a conceptually simple technique to determine from the data whether or not a subspace swap has actually occurred, and to extend the range of SNR values or data samples in which a given subspace method produces accurate estimates
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