Phase-shift-based time-delay estimators for proximity acousticsensors

Time-delay estimation is important in a wide range of applications in oceanic engineering. In this paper, we present a novel time-delay estimation algorithm based on maximum likelihood theory for the case that the measurements are corrupted by colored or nonuniform zero-mean Gaussian noise. It turns out that the likelihood function associated with the problem is highly oscillatory, and we propose a computationally efficient technique to maximize this function. Our algorithm first obtains an initial estimate based on a smooth approximate cost function, and then refines this estimate based on the true cost function. Simulation results show that our estimator outperforms a traditional phaseshift based estimator, and that the estimation error approaches the Cramer-Rao bound when the SNR increases without bound     

Depth measurement of remote sources using multipath propagation

A submerged acoustic source radiates narrowband Gaussian noise. Its signal propagates to a remote, large aperture vertical array over a multipath channel whose characteristics may or may not be fully known. The primary concern of this study is the accuracy of source depth estimates obtainable from the array output. Cramer-Rao bounds for the depth estimate are calculated. When the velocity profile is known exactly, the value of the bound is quite insensitive to the precise form of the velocity profile. A bound calculated from a constant velocity profile yields an excellent approximation for many situations likely to be encountered in practice. Introduction of an unknown parameter into the velocity profile has little effect on the Cramer-Rao bound for depth. However, a maximum likelihood estimator of depth working with an inaccurate value of the unknown parameter performs poorly. To obtain satisfactory performance, one must estimate the unknown parameters along with the source depth. Simulations demonstrate the success of this approach     

Effects of sensor placement on acoustic vector-sensor arrayperformance

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     

Narrowband line-array beamforming: practically achievableresolution limit of unbiased estimators

Based on an approximation to the Cramer-Rao lower bound, it is demonstrated that meaningful resolution with an unbiased narrowband estimator requires a source separation of at least about 1/10 of a Rayleigh beamwidth, even under ideal circumstances, with 1/4 beamwidth being a more practically achievable figure     

Towed array shape estimation using frequency-wavenumber data

Towed array beamforming algorithms require accurate array shape information in order to perform properly. Very often, these algorithms assume the array is linear. Unfortunately, the mechanical forces on the array due to ship motion and sea dynamics can change the shape of the array, which degrades the performance of the beamforming algorithm. A data-driven approach to estimating the relative shape of a nominally linear array is presented. The algorithm is robust in that it optimally combines information contained in a wide band of frequencies and source bearings. At the heart of the algorithm is a maximum-likelihood (ML) estimation scheme. The Cramer-Rao lower bound is derived and compared to the performance of the ML estimator. The utility of the algorithm is verified using both simulated and actual towed array data experiments     

The maximum likelihood estimator for acoustic synthetic apertureprocessing

The maximum likelihood estimator of source amplitude, bearing, and frequency for a moving towed line array of equispaced elements is discussed. A two-dimensional search in equivalent phase and frequency variables is found to yield the best estimates of the unknown parameters. Application to a physical experiment and comparison with the Cramer-Rao bound verify the unity of the approach     

A minimum variance unbiased estimator for ocean surface currentsbased on multifrequency microwave radar observations

This paper presents a minimum variance unbiased (MVU) estimator for estimating an ocean surface current using the multifrequency microwave radar technique. In this technique the current information is obtained by finding the difference between the measured phase velocities of some specific surface gravity waves and the phase velocities calculated from the dispersion relation for still water. By defining the problem as a linear estimation problem, we develop an unbiased estimator for the current component along the radar look direction, which has a variance that is inversely proportional to the sum of the squared wavenumbers of the gravity waves used in the measurements. We also study the performance of an MVU vector estimator based on radar observations along two directions. Our analysis shows that the confidence region of this estimator has the shape of an elongated ellipse with semi-axes and orientation which are dependent on the angle between the observation directions, but independent on the true current vector. Furthermore, the theoretical models are thoroughly tested using both simulated and real radar data, and these tests show very good agreement with the model predictions     

Range and bearing estimation using polynomial rooting

Simultaneous estimation of the range and bearing of near-field emitters usually involves a multidimensional search. The authors examine an alternative algorithm which involves search in the range direction combined with polynomial rooting, which replaces the search in the azimuth direction. The proposed algorithm requires a smaller amount of computation than algorithms based on two-dimensional search. The performance of the algorithm is evaluated by Monte Carlo simulation, and is compared to the Cramer-Rao bound on the bearing/range estimation errors. Formulas for computing the bound are derived     

Analysis of swath bathymetry sonar accuracy

The practical limitations of many bottom mapping sonars lie in their ability to accurately estimate the angle of arrival. This paper addresses the accuracy of angle estimation when employed to determine the location of an extended target such as the bottom. A Gaussian model is assumed for the bottom backscatter and the corresponding Cramer-Rao lower bound for the variance of the angle estimate is determined for multi-element linear arrays. The paper focuses on determining the performance of high-resolution swath bathymetry sonars and, therefore, concentrates on the ability to determine bottom location with short pulses. Two error mechanisms, footprint shift and uncorrelated noise, are identified as important contributors to measurement errors. The two-element interferometric sonar configuration is investigated in detail. It is shown through the use of probability distributions, the Cramer-Rao bound, and simulation that it is difficult to get a good estimate of performance through simulation alone. Performance enhancement through pre-estimation and post-estimation averaging of multiple snapshots and changes in performance with pulse length and pulse rise time are also considered. Bottom estimation performance employing multi-element arrays is compared and contrasted with that of the two-element interferometric array. It is determined that there is little benefit associated with the multi-element array in terms of angle estimation performance alone. However, when other considerations such as angle ambiguities, multiple angles of arrival, and physical shortcomings associated with practical arrays are taken into account, the multi-element array is favored.     

Track Parameter Estimation from Multipath Delay Information

It is desired to track the location of an underwater acoustic source with range difference measurements from a stationary passive array. Many times, the array has only one or two sensors, and the multipath and intersensor range difference measurements are insufficient to localize and track a source moving along an arbitrary path [1]. Here, we propose to track sources with one- or two-sensur stationary passive arrays by making the simplifying assumption that the source's path can be described by a small set of so-called track parameters. Range difference information can then be used to estimate the track parameter set rather than the source location as a function of time. In this paper, we choose the track parameters to specify a straight-line constant-velocity constant-depth path. Cramer-Rao bounds are presented for estimating these track parameters from the time history of multipath and intersensor range difference measurements. It is shown that this track parameter set cannot be accurately estimated from the time history of a single multipath range difference without side information (an independent velocity estimate, for instance), although multipath and intersensor range difference measurements from a two-sensor array are generally sufficient to estimate the track parameter set. Computationally efficient techniques are presented which estimate track parameters from range difference measurements taken from one- and two-sensor arrays. Monte-Carlo simulations are presented which show that these techniques have sample mean-square error approximately equal to the Cramer-Rao bound when a single multipath range difference and an independent velocity estimate are available. The sample mean-square error is shown to be in the range of two to ten times the corresponding Cramer-Rao bounds when these techniques are applied to two-sensor range difference data.     

Acoustic vector-sensor correlations in ambient noise

Most array-processing methods require knowledge of the correlation structure of the noise. While such information may sometimes be obtained from measurements made when no sources are present, this may not always be possible. Furthermore, measurements made in-situ can hardly be used to analyze system performance before deployment. The development of models of the correlation structure under various environmental assumptions is therefore very important. In this paper, we obtain integral and closed form expressions for the auto- and cross-correlations between the components of an acoustic vector sensor (AVS) for a wideband-noise field, under the following assumptions concerning its spatial distribution: 1) azimuthal independence; 2) azimuthal independence and elevational symmetry; and 3) spherical isotropy. We also derive expressions for the cross-covariances between all components of two spatially displaced AVSs in a narrowband-noise field under the same assumptions. These results can be used to determine the noise-covariance matrix of an array of acoustic vector sensors in ambient noise. We apply them to a uniform linear AVS array to asses its beamforming capabilities and localization accuracy, via the Cramer-Rao bound, in isotropic and anisotropic noise     

Time-delay estimation via optimizing highly oscillatory costfunctions

In sonar and many other applications, time-delay estimation is an important problem. When bandpass probe signals are used, the correlation function between the received and the known transmitted signals oscillates near the carrier frequency of the transmitted signal. In this case, many existing time-delay estimation algorithms perform poorly due to converging to local optimum points. In this paper, two efficient algorithms, Hybrid-WRELAX and EXIP-WRELAX, are proposed to deal with the above problem. They are relaxation-based global minimizers of a highly oscillatory nonlinear least-squares cost function. Both algorithms are shown to achieve the Cramer-Rao bound and require only a sequence of weighted Fourier transforms     

Pressure image assimilation for atmospheric motion estimation

The complexity of the laws of dynamics governing 3-D atmospheric flows associated with incomplete and noisy observations make the recovery of atmospheric dynamics from satellite image sequences very difficult. In this paper, we address the challenging problem of estimating physical sound and time-consistent horizontal motion fields at various atmospheric depths for a whole image sequence. Based on a vertical decomposition of the atmosphere, we propose a dynamically consistent atmospheric motion estimator relying on a multilayer dynamic model. This estimator is based on a weak constraint variational data assimilation scheme and is applied on noisy and incomplete pressure difference observations derived from satellite images. The dynamic model is a simplified vorticity-divergence form of a multilayer shallow-water model. Average horizontal motion fields are estimated for each layer. The performance of the proposed technique is assessed using synthetic examples and using real world meteorological satellite image sequences. In particular, it is shown that the estimator enables exploiting fine spatio-temporal image structures and succeeds in characterizing motion at small spatial scales.     

Theoretical accuracy of Doppler navigation sonars and acoustic Doppler current profilers

This paper addresses the problem of Doppler shift estimation in Doppler sonar systems. The analysis focuses on the single-beam geometry formed by a circular planar array and considers both narrow-band (or so-called incoherent) and wide-band (or coherent) Doppler sonars, transmitting, respectively, one long continuous-wave pulse and a train of short continuous-wave pulses. The correlation function of the reverberation signal at the beam output is derived for volume reverberation. Directive transmission or reception and a combination of both is considered. Estimation theory is applied to derive the Cramer-Rao bound of the Doppler parameter estimate. The effect of pulse duration, sonar geometry, beamwidth, and signal-to-noise ratio are discussed. The accuracy of coherent and incoherent systems is compared for a specific case.     

An Doppler estimators performance losses in the presence of noiseand equivocation

Doppler estimation accuracy for current profiling is discussed, with comparison with the Cramer-Rao bound (CRB). The apparent decrease in estimation accuracy at low SNR is introduced by the estimate equivocation, due to noise structure and not accounted by the CRB. The actual error is assessed by analysis and simulations     

On the ability to estimate narrow-band signal parameters usingtowed arrays

Using the Cramer-Rao lower bound (CRLB) as an indicator of potential performance, the limits on the estimation and resolution capabilities of a towed line array of uniformly spaced hydrophones to provide frequency and bearing information about narrowband signals are examined. It is assumed that a monochromatic plane wave arrives at the array for each source. Several versions of the bounds are computed using different assumptions about which parameters have known values and about the way in which the samples are taken in space and in time. It is shown that the CRLB values for different situations can be compared to provide information about the effective use of a moving aperture for estimation of the parameters of narrowband signals arriving at the array. It is also shown that adding at least one hydrophone occupying a fixed position in space can improve the bearing estimates of a towed array by supplying additional frequency information if both the bearings and frequencies of the sources are unknown     

The scattering of regular surface waves by a fixed,half-immersed,circular cylinder

A train of regular surface waves is incident upon a fixed, half-immersed, circular cylinder; the waves are partially reflected and partially transmitted, and also induce hydrodynamic forces on the cylinder. In order to give a theoretical study of this problem, we make the familiar assumptions of classical hydrodynamics and then solve the linear, two-dimensional, diffraction boundary-value problem, using Ursell's multipole method. Accurate numerical results are presented (in the form of tables) for four important (complex) quantities; these are the reflection and transmission coefficients, and two dimensionless coefficients which describe the horizontal and vertical forces on the cylinder. We have also made an experimental study, in which we measured the forces on the cylinder, and the reflection coefficient. These measurements are compared with the linear theory, and also with other experimental data; discrepancies are noted and an attempt to analyse them is made. We have also measured the mean horizontal forces on the cylinder; these results are compared with the predictions of a simple formula obtained by Longuet-Higgins.     

Performance comparison of high resolution bearing estimationalgorithms using simulated and sea test data

The performance of both the Capon and the MUSIC high resolution bearing estimation algorithms is investigated using both simulated data and sea test data collected with an experimental planar array. The major problem with these estimators is their sensitivity to both system errors and deviations from the assumed noise model. To alleviate this problem, two methods for preprocessing the data before they are input into the high-resolution algorithm are investigated: beam space and sector focused stability. The performance of both high-resolution estimators is examined, using both types of preprocessing, and the results are compared with those for the standard element-space (ES) techniques, assuming both finite cross-spectral-matrix (CSM) averaging errors and weakening target strengths. For the Capon estimator the performance is only superior to the standard element space technique when the CSM is calculated using a small number of averages. For the MUSIC estimator, both preprocessing techniques give clearly superior results over standard space techniques, with the SFS preprocessor performing the best     

Two-Dimensional Spectral Estimation: A Radon Transform Approach

A new technique for two-dimensional (2-D) spectral estimation of a stationary random field (SRF) is investigated in this paper. This is based on the extension of the Radon transform theory to stationary random fields (SRF's), proposed by Jain and Ansari [19]. Using the Radon transform, the 2-D estimation problem is reduced to a set of one-dimensional (1-D) independent problems, which could then be solved using 1-D linear prediction (LP) or by any other high-resolution estimation procedure. This is unlike previous methods which obtain the 2-D power spectral density OPSD) estimate by using 1-D high-resolution techniques in the spirit of a separable estimator [2]. Examples are provided to illustrate the performance of the new technique. Various features of this approach are highlighted.     

Mitigation techniques for non-Gaussian sea clutter

This paper deals with the problem of coherent radar detection of targets embedded in clutter modeled as a compound-Gaussian process. We first provide a survey on clutter mitigation techniques with a particular emphasis on adaptive detection schemes ensuring the constant false-alarm rate (CFAR) property with respect to all of the clutter parameters. Thus, we propose a novel decision rule based on a recursive covariance estimator, which exploits the persymmetry property of the clutter covariance matrix. Remarkably, the devised receiver is fully CFAR in that its threshold can be set independently of the clutter distribution as well as of its covariance, even if the environment is highly heterogeneous; namely, the disturbance distributional parameters vary from cell to cell. At the analysis stage, we compare the performance of the novel detector with some classical radar receivers such as that of Kelly and the adaptive matched filter both in the presence of simulated as well as on real radar data, which statistical analysis has shown to be compatible with the compound-Gaussian model. The results show that the new receiving structure generally provides higher detection performance than the others and, for a fluctuating target, it uniformly outperforms the counterparts. We also provide a discussion on the CFAR behavior of the analyzed receivers as well as on their computational complexity.