Physically constrained maximum likelihood (PCML) mode filtering and its application as a pre-processing method for underwater acoustic communication

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2009Mode filtering is most commonly implemented using the sampled mode shape or pseudoinverse algorithms. Buck et al placed these techniques in the context of a broader maximum a posteriori (MAP) framework. However, the MAP algorithm requires that the signal and noise statistics be known a priori. Adaptive array processing algorithms are candidates for improving performance without the need for a priori signal and noise statistics. A variant of the physically constrained, maximum likelihood (PCML) algorithm is developed for mode filtering that achieves the same performance as the MAP mode filter yet does not need a priori knowledge of the signal and noise statistics. The central innovation of this adaptive mode filter is that the received signal's sample covariance matrix, as estimated by the algorithm, is constrained to be that which can be physically realized given a modal propagation model and an appropriate noise model. The first simulation presented in this thesis models the acoustic pressure field as a complex Gaussian random vector and compares the performance of the pseudoinverse, reduced rank pseudoinverse, sampled mode shape, PCML minimum power distortionless response (MPDR), PCML-MAP, and MAP mode filters. The PCML-MAP filter performs as well as the MAP filter without the need for a priori data statistics. The PCML-MPDR filter performs nearly as well as the MAP filter as well, and avoids a sawtooth pattern that occurs with the reduced rank pseudoinverse filter. The second simulation presented models the underwater environment and broadband communication setup of the Shallow Water 2006 (SW06) experiment. Data processing results are presented from the Shallow Water 2006 experiment, showing the reduced sensitivity of the PCML-MPDR filter to white noise compared with the reduced rank pseudoinverse filter. Lastly, a linear, decision-directed, RLS equalizer is used to combine the response of several modes and its performance is compared with an equalizer applied directly to the data received on each hydrophone

Sensor Array Processing with Manifold Uncertainty

<p>The spatial spectrum, also known as a field directionality map, is a description of the spatial distribution of energy in a wavefield. By sampling the wavefield at discrete locations in space, an estimate of the spatial spectrum can be derived using basic wave propagation models. The observable data space corresponding to physically realizable source locations for a given array configuration is referred to as the array manifold. In this thesis, array manifold ambiguities for linear arrays of omni-directional sensors in non-dispersive fields are considered. </p><p>First, the problem of underwater a hydrophone array towed behind a maneuvering platform is considered. The array consists of many hydrophones mounted to a flexible cable that is pulled behind a ship. The towed cable will bend or distort as the ship performs maneuvers. The motion of the cable through the turn can be used to resolve ambiguities that are inherent to nominally linear arrays. The first significant contribution is a method to estimate the spatial spectrum using a time-varying array shape in a dynamic field and broadband temporal data. Knowledge of the temporal spectral shape is shown to enhance detection performance. The field is approximated as a sum of uncorrelated planewaves located at uniform locations in angle, forming a gridded map on which a maximum likelihood estimate for broadband source power is derived. Uniform linear arrays also suffer from spatial aliasing when the inter-element spacing exceeds a half-wavelength. Broadband temporal knowledge is shown to significantly reduce aliasing and thus, in simulation, enhance target detection in interference dominated environments. </p><p>As an extension, the problem of towed array shape estimation is considered when the number and location of sources are unknown. A maximum likelihood estimate of the array shape using the field directionality map is derived. An acoustic-based array shape estimate that exploits the full 360$^\circ$ field via field directionality mapping is the second significant contribution. Towed hydrophone arrays have heading sensors in order to estimate array shape, but these sensors can malfunction during sharp turns. An array shape model is described that allows the heading sensor data to be statistically fused with heading sensor. The third significant contribution is method to exploit dynamical motion models for sharp turns for a robust array shape estimate that combines acoustic and heading data. The proposed array shape model works well for both acoustic and heading data and is valid for arbitrary continuous array shapes.</p><p>Finally, the problem of array manifold ambiguities for static under-sampled linear arrays is considered. Under-sampled arrays are non-uniformly sampled with average spacing greater than a half-wavelength. While spatial aliasing only occurs in uniformly sampled arrays with spacing greater than a half-wavelength, under-sampled arrays have increased spatial resolution at the cost of high sidelobes compared to half-wavelength sampled arrays with the same number of sensors. Additionally, non-uniformly sampled arrays suffer from rank deficient array manifolds that cause traditional subspace based techniques to fail. A class of fully agumentable arrays, minimally redundant linear arrays, is considered where the received data statistics of a uniformly spaced array of the same length can be reconstructed in wide sense stationary fields at the cost of increased variance. The forth significant contribution is a reduced rank processing method for fully augmentable arrays to reduce the variance from augmentation with limited snapshots. Array gain for reduced rank adaptive processing with diagonal loading for snapshot deficient scenarios is analytically derived using asymptotic results from random matrix theory for a set ratio of sensors to snapshots. Additionally, the problem of near-field sources is considered and a method to reduce the variance from augmentation is proposed. In simulation, these methods result in significant average and median array gains with limited snapshots.</p>Dissertatio

Applied stochastic eigen-analysis

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2007The first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest (“signal”) eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded. The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) “free probability” theory. The class of “algebraic” random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting conditional “eigenvector distribution.” The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. The method is applied to predict the deterioration in the quality of the sample eigenvectors of large algebraic empirical covariance matrices due to sample size constraints.I am grateful to the National Science Foundation for supporting this work via grant DMS-0411962 and the Office of Naval Research Graduate Traineeship awar

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

Joint DOA and DOD Estimation in Bistatic MIMO Radar without Estimating the Number of Targets

Existing subspace-based direction finding methods for multiple-input multiple-output (MIMO) radar assume perfect knowledge about the dimension of the signal or noise subspace, which is hard to be established without prior knowledge of the signal environment. In this paper, an efficient method for joint DOA and DOD estimation in bistatic MIMO radar without estimating the number of targets is presented. The proposed method computes an estimate of the noise subspace using the power of R (POR) technique. Then the two-dimensional (2D) direction finding problem is decoupled into two successive one-dimensional (1D) angle estimation problems by employing the rank reduction (RARE) estimator

Sound propagation around underwater seamounts

Thesis (Ph. D.)--Joint Program in Applied Ocean Physics and Engineering (Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and the Woods Hole Oceanographic Institution), 2009.Includes bibliographical references (leaves 184-189).In the ocean, low frequency acoustic waves propagate with low attenuation and cylindrical spreading loss over long-ranges, making them an effective tool for underwater source localization, tomography, and communications. Underwater mountains, or seamounts, are ubiquitous throughout the world's oceans and can absorb and scatter acoustic energy, offering many interesting acoustic modeling challenges. The goal of the research performed in support of this thesis is to measure the acoustic scattered field of a large, conical seamount at long-range, and reconcile observations with 2-D range-dependent acoustic models, for the purpose of understanding the effects of highly range-dependent bathymetry. The Basin Acoustic Seamount Scattering Experiment (BASSEX) was conducted to measure the scattered fields of the two seamounts which form the Kermit-Roosevelt Seamount Complex in the Northeast Pacific Ocean during September and October of 2004. The experiment used fixed and ship-deployed acoustic sources transmitting m-sequence signals at 68.2 and 250 Hz carrier frequencies, with 35 and 83 Hz bandwidth, respectively. The receiver was a towed hydrophone array with 3 m sensor spacing, cut for 250 Hz. BASSEX is the first experiment to measure acoustic arrival patterns in the scattered field of a seamount at many locations at sound path ranges of order 500 km, utilizing a rich bathymetry and sound velocity database. Convergence zones in the forward-scattered field of seamounts at long-range are observed, created by higher order mode coupling and blockage. Acoustic ray arrival angles, travel times, and amplitudes show good agreement with parabolic equation (PE) acoustic modeling results inside the forward-scattered fields; in particular, simulated results are fairly accurate for weak surface-reflected-bottom-reflected acoustic rays. The width of the forward-scattered field is shown to span the projected width of a seamount.(cont.) Temporal coherence of ray amplitude inside a seamount scattered field could not be determined due to array movement issues, and should be the focus of future research to determine the stability of scattered acoustic rays for applications such as acoustic tomography. Robust adaptive beamforming methods are used to process hydrophone array data gathered in the BASSEX experiment. Non-stationarity in the observed noise field caused by array fluctuations and data acquisition system malfunctions motivate the use of a time varying Capon adaptive beam former, and strong acoustic harmonics from ship operations motivate the use of a frequency and steering angle dependent white noise gain constraint. In an effort to process snap-shot deficient data sets, the novel physically constrained maximum likelihood (PCML) beamformer was further developed and applied. By using orthonormal trigonometric eigenvector bases to determine the maximum likelihood spectral covariance matrix, the PCML beamformer computational efficiency is significantly increased.by Joseph J. Sikora, III.Ph.D