arXiv subjects

Peter Gerstoft

Publications and source records attributed to Peter Gerstoft.

46 records · Page 3Linked to original sources

arXiv2017

Sparse Bayesian Learning for DOA Estimation in Heteroscedastic Noise

The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. This SBL approach is more flexible and performs better than high-resolution methods since they cannot estimate the heteroscedastic noise process. An alternative to SBL is simple data normalization, whereby only the phase across the array is utilized. Simulations demonstrate that taking the heteroscedastic noise into account improves DOA estimation.

eess.SP↗

arXiv2017

Source localization in an ocean waveguide using supervised machine learning

Source localization in ocean acoustics is posed as a machine learning problem in which data-driven methods learn source ranges directly from observed acoustic data. The pressure received by a vertical linear array is preprocessed by constructing a normalized sample covariance matrix (SCM) and used as the input. Three machine learning methods (feed-forward neural networks (FNN), support vector machines (SVM) and random forests (RF)) are investigated in this paper, with focus on the FNN. The range estimation problem is solved both as a classification problem and as a regression problem by these three machine learning algorithms. The results of range estimation for the Noise09 experiment are compared for FNN, SVM, RF and conventional matched-field processing and demonstrate the potential of machine learning for underwater source localization..

physics.ao-ph↗

arXiv2017

Eastern Arctic ambient noise on a drifting vertical array

Ambient noise in the eastern Arctic was studied from April to September 2013 using a 22 element vertical hydrophone array as it drifted from 89$^\circ$23'N, 64$^\circ$35'W to 83$^\circ$45'N, 4$^\circ$28'W. The hydrophones recorded for 108 min/day on six days/week with a sampling rate of 1953.125 Hz. After removal of data corrupted by non-acoustic transients, 19 days throughout the transit period were analyzed. Noise contributors identified include broadband and tonal ice noises, bowhead whale calling, seismic airgun surveys, and earthquake $T$ phases. The bowhead whale or whales detected are believed to belong to the endangered Spitsbergen population and were recorded when the array was as far north as 86$^\circ$24'N. Median power spectral estimates and empirical probability density functions (PDFs) along the array transit show a change in the ambient noise levels corresponding to seismic survey airgun occurrence and received level at low frequencies and transient ice ice noises at high frequencies. Median power for the same periods across the array show that this change is consistent in depth. The median ambient noise for May 2013 was among the lowest of the sparse reported observations in the eastern Arctic but comparable to the more numerous observations of western Arctic noise levels.

physics.geo-ph↗

arXiv2017

Sparse Bayesian learning with uncertainty models and multiple dictionaries

Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a signal model which accounts for dictionary mismatch and the presence of errors in the weight vector at low signal-to-noise ratios. A fixed point update equation is derived which incorporates the statistics of mismatch and weight errors. We also process observations from multiple dictionaries. Noise variances are estimated using stochastic maximum likelihood. The derived update equations are studied quantitatively using beamforming simulations applied to direction-of-arrival (DoA). Performance of SBL using single- and multi-frequency observations, and in the presence of aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively the advantages of SBL.

stat.AP↗

arXiv2017

Dictionary learning of sound speed profiles

To provide constraints on their inversion, ocean sound speed profiles (SSPs) often are modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on their coefficients, often yields low resolution SSP estimates. In this paper, it is shown that dictionary learning, a form of unsupervised machine learning, can improve SSP resolution by generating a dictionary of shape functions for sparse processing (e.g. compressive sensing) that optimally compress SSPs; both minimizing the reconstruction error and the number of coefficients. These learned dictionaries (LDs) are not constrained to be orthogonal and thus, fit the given signals such that each signal example is approximated using few LD entries. Here, LDs describing SSP observations from the HF-97 experiment and the South China Sea are generated using the K-SVD algorithm. These LDs better explain SSP variability and require fewer coefficients than EOFs, describing much of the variability with one coefficient. Thus, LDs improve the resolution of SSP estimates with negligible computational burden.

physics.ao-ph↗

arXiv2016

Multi Snapshot Sparse Bayesian Learning for DOA Estimation

The directions of arrival (DOA) of plane waves are estimated from multi-snapshot sensor array data using Sparse Bayesian Learning (SBL). The prior source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters the unknown variances (i.e. the source powers). For a complex Gaussian likelihood with hyperparameter the unknown noise variance, the corresponding Gaussian posterior distribution is derived. For a given number of DOAs, the hyperparameters are automatically selected by maximizing the evidence and promote sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against LASSO ($\ell_1$-regularization), conventional beamforming, and MUSIC

math.ST↗

arXiv2015

Using the LASSO's Dual for Regularization in Sparse Signal Reconstruction from Array Data

Waves from a sparse set of source hidden in additive noise are observed by a sensor array. We treat the estimation of the sparse set of sources as a generalized complex-valued LASSO problem. The corresponding dual problem is formulated and it is shown that the dual solution is useful for selecting the regularization parameter of the LASSO when the number of sources is given. The solution path of the complex-valued LASSO is analyzed. For a given number of sources, the corresponding regularization parameter is determined by an order-recursive algorithm and two iterative algorithms that are based on a further approximation. Using this regularization parameter, the DOAs of all sources are estimated.

math.ST↗

arXiv2015

Multiple and single snapshot compressive beamforming

For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an $\ell_1$-norm constraint renders the problem solvable with convex optimization, and promoting sparsity gives high-resolution DOA maps. Here, the sparse source distribution is derived using maximum a posteriori (MAP) estimates for both single and multiple snapshots. CS does not require inversion of the data covariance matrix and thus works well even for a single snapshot where it gives higher resolution than conventional beamforming. For multiple snapshots, CS outperforms conventional high-resolution methods, even with coherent arrivals and at low signal-to-noise ratio. The superior resolution of CS is demonstrated with vertical array data from the SWellEx96 experiment for coherent multi-paths.

math.ST↗

arXiv2015

Resolving Weak Sources within a Dense Array using a Network Approach

A non-parametric technique to identify weak sources within dense sensor arrays is developed using a network approach. No knowledge about the propagation medium is needed except that signal strengths decay to insignificant levels within a scale that is shorter than the aperture. We then reinterpret the spatial covariance matrix of a wave field as a matrix whose support is a connectivity matrix of a network of vertices (sensors) connected into communities. These communities correspond to sensor clusters associated with individual sources. We estimate the support of the covariance matrix from limited-time data using a robust hypothesis test combined with a physical distance criterion. The latter ensures sufficient network sparsity to prevent vertex communities from forming by chance. We verify the approach on simulated data and quantify its reliability. The method is then applied to data from a dense 5200 element geophone array that blanketed 7$\times$10 km of the city of Long Beach (CA). The analysis exposes a helicopter traversing the array, oil production facilities, and reveals that low-frequency events tend to occur near roads.

physics.data-an↗

arXiv2015

Grid-free compressive beamforming

The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve high-resolution imaging. On a discrete angular grid, the CS reconstruction degrades due to basis mismatch when the DOAs do not coincide with the angular directions on the grid. To overcome this limitation, a continuous formulation of the DOA problem is employed and an optimization procedure is introduced, which promotes sparsity on a continuous optimization variable. The DOA estimation problem with infinitely many unknowns, i.e., source locations and amplitudes, is solved over a few optimization variables with semidefinite programming. The grid-free CS reconstruction provides high-resolution imaging even with non-uniform arrays, single-snapshot data and under noisy conditions as demonstrated on experimental towed array data.

cs.IT↗