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Hodgkiss, WS, Anderson VC.  1983.  Acoustic positioning for an array of freely drifting infrasonic sensors. IEEE Journal of Oceanic Engineering. 8:116-119.   10.1109/joe.1983.1145567   AbstractWebsite

Initial testing of the prototype element of a freely drifting infrasonic sensor array is described. The intent of this measurement system is to gather wide aperture data sets which will be used both to characterize ambient noise in the region 1-10 Hz and to assess the gains possible from beam forming utilizing a collection of very low frequency (VLF) sensors. Coherent processing (beam forming) of the infrasonic sensor data is made possible by relative position measurements derived from mutual acoustic interrogation of the elements at a higher frequency. Surface echo data from a recent sea test of the prototype buoy are used to illustrate the type of pulse processing which will be implemented as a first step in the localization procedure.

Richards, EL, Song HC, Hodgkiss WS.  2018.  Acoustic scattering comparison of Kirchhoff approximation to Rayleigh-Fourier method for sinusoidal surface waves at low grazing angles. The Journal of the Acoustical Society of America. 144:1269-1278.   10.1121/1.5052256   Abstract

The Fourier series method for implementing the Rayleigh hypothesis [Rayleigh-Fourier method (RFM)] is used as a reference solution to assess the Kirchhoff approximation of the Helmholtz integral [Helmholtz-Kirchhoff approximation (HKA)] for modeling broadband scatter from sinusoidal surfaces at low grazing angles. The HKA is a valuable solution because it has an eigen-ray interpretation without unbounded caustic amplitudes and discontinuous shadow zones. Plane wave studies of the HKA, however, show it becomes inaccurate at low grazing angles. This study quantifies how this limitation manifests with increasing transmission distance for time domain scattering simulations. Scattering results are compared over a complete surface wave cycle with parameters modeling sea surface-swell. The HKA agrees reasonably well with the RFM in point source calculations for limited extensions of transmission distances beyond where plane wave comparisons begin to diverge. Past these distances, HKA solutions begin to show significant over-prediction of the acoustic amplitude around late arrivals. This over-prediction is frequency dependent and eigen-ray interference offers an explanation of this behavior. Further extending the transmission range leads to a significant HKA error, and a range is found at which flat surface reflections have less error.

Hodgkiss, WS, Alexandrou D.  1986.  An adaptive algorithm for array processing. IEEE Transactions on Antennas and Propagation. 34:454-458.   10.1109/tap.1986.1143835   AbstractWebsite

A mathematical summary of the joint complex least squares lattice (JCLSL) adaptive algorithm is presented. The algorithm has as inputs two scalar discrete time series (primary. and reference channels). Output consists of the filtered reference channel subtracted from the primary channel. The convergence characteristics of the algorithm are illustrated experimentally for a problem where the reference channel time series consists of dual constant frequency sinusoids which undergo an instantaneous step in frequency. The primary channel time series consists of dual constant frequency sinusoids whose frequencies coincide with those of the reference channel after the step. Lastly, an application of the JCLSL algorithm to the rejection of ocean acoustic boundary reverberation is described.

Gemba, KL, Hodgkiss WS, Gerstoft P.  2017.  Adaptive and compressive matched field processing. Journal of the Acoustical Society of America. 141:92-103.   10.1121/1.4973528   AbstractWebsite

Matched field processing is a generalized beamforming method that matches received array data to a dictionary of replica vectors in order to locate one or more sources. Its solution set is sparse since there are considerably fewer sources than replicas. Using compressive sensing (CS) implemented using basis pursuit, the matched field problem is reformulated as an underdetermined, convex optimization problem. CS estimates the unknown source amplitudes using the replica dictionary to best explain the data, subject to a row-sparsity constraint. This constraint selects the best matching replicas within the dictionary when using multiple observations and/or frequencies. For a single source, theory and simulations show that the performance of CS and the Bartlett processor are equivalent for any number of snapshots. Contrary to most adaptive processors, CS also can accommodate coherent sources. For a single and multiple incoherent sources, simulations indicate that CS offers modest localization performance improvement over the adaptive white noise constraint processor. SWellEx-96 experiment data results show comparable performance for both processors when localizing a weaker source in the presence of a stronger source. Moreover, CS often displays less ambiguity, demonstrating it is robust to data-replica mismatch. (C) 2017 Acoustical Society of America.

Gerstoft, P, Hodgkiss WS, Kuperman WA, Song H, Siderius M, Nielsen PL.  2003.  Adaptive beamforming of a towed array during a turn. IEEE Journal of Oceanic Engineering. 28:44-54.   10.1109/joe.2002.808203   AbstractWebsite

During maneuvering, towed array beamforming degrades if a straight array is assumed. This is especially true for high-resolution adaptive beamforming. It is experimentally demonstrated that adaptive beamforming is feasible on a turning array, provided that array shape is estimated. The array shape can be inferred solely from the coordinates of the tow vessel's Global Positioning System (GPS) without any instrumentation in the array. Based on estimated array shape from the GPS, both the conventional beamformer and the white noise constrained (WNC) adaptive beamformer are shown to track the source well during a turn. When calculating the weight vector in the WNC approach, a matrix inversion of the cross-spectral density matrix is involved. This matrix inversion can be stabilized by averaging the cross-spectral density matrix over neighboring frequencies. The proposed algorithms have been tested on real data with the tow-vessel making 45degrees turns with a 500-m curvature radius. While turning, the improvement in performance over the assumption of a straight array geometry was up to 5 dB for the conventional beamformer and considerably larger for the WNC adaptive beamformer.

Hodgkiss, WS, Nolte LW.  1977.  Adaptive optimum array processing. Journal of the Acoustical Society of America. 61:763-775.   10.1121/1.381365   AbstractWebsite

A global approach to the processing of information from an array of sensors when uncertain parameters exist is proposed. Although an ad hoc estimate and plug structure is appealing due to its explicit adaptive characteristics, it is shown that the Bayes optimal array processor exhibits natural learning or adaptive features when implemented sequentially.

Siderius, M, Song HC, Gerstoft P, Hodgkiss WS, Hursky P, Harrison C.  2010.  Adaptive passive fathometer processing. Journal of the Acoustical Society of America. 127:2193-2200.   10.1121/1.3303985   AbstractWebsite

Recently, a technique has been developed to image seabed layers using the ocean ambient noise field as the sound source. This so called passive fathometer technique exploits the naturally occurring acoustic sounds generated on the sea-surface, primarily from breaking waves. The method is based on the cross-correlation of noise from the ocean surface with its echo from the seabed, which recovers travel times to significant seabed reflectors. To limit averaging time and make this practical, beamforming is used with a vertical array of hydrophones to reduce interference from horizontally propagating noise. The initial development used conventional beamforming, but significant improvements have been realized using adaptive techniques. In this paper, adaptive methods for this process are described and applied to several data sets to demonstrate improvements possible as compared to conventional processing.

Hodgkiss, WS, Presley JA.  1981.  Adaptive tracking of multiple sinusoids whose power levels are widely separated. IEEE Transactions on Acoustics Speech and Signal Processing. 29:710-721.   10.1109/tassp.1981.1163601   AbstractWebsite

The behavior of the gradient transversal filter (LMS), the gradient lattice (GL), and the least squares lattice (LSL) when used to track multiple sinusoidal (or narrow-band) components whose power levels are widely separated is investigated. These approaches to the realization of the pth-order one-step linear predictor of the time series are recursive in time. The lags of the instantaneous frequency estimates from their actual underlying values are of particular interest. The frequency tracking characteristics of the LMS, GL, and LSL algorithms are illustrated in several situations. Included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech.

Hursky, P, Porter MB, Cornuelle BD, Hodgkiss WS, Kuperman WA.  2004.  Adjoint modeling for acoustic inversion. Journal of the Acoustical Society of America. 115:607-619.   10.1121/1.1636760   AbstractWebsite

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used. (C) 2004 Acoustical Society of America.

Roux, P, Kuperman WA, Cornuelle BD, Aulanier F, Hodgkiss WS, Song HC.  2013.  Analyzing sound speed fluctuations in shallow water from group-velocity versus phase-velocity data representation. Journal of the Acoustical Society of America. 133:1945-1952.   10.1121/1.4792354   AbstractWebsite

Data collected over more than eight consecutive hours between two source-receiver arrays in a shallow water environment are analyzed through the physics of the waveguide invariant. In particular, the use of vertical arrays on both the source and receiver sides provides source and receiver angles in addition to travel-times associated with a set of eigenray paths in the waveguide. From the travel-times and the source-receiver angles, the eigenrays are projected into a group-velocity versus phase-velocity (Vg-Vp) plot for each acquisition. The time evolution of the Vg-Vp representation over the 8.5-h long experiment is discussed. Group speed fluctuations observed for a set of eigenrays with turning points at different depths in the water column are compared to the Brunt-Vaisala frequency. (C) 2013 Acoustical Society of America.

Hodgkiss, WS, Nolte LW.  1978.  Array processor performance under directional uncertainty. IEEE Transactions on Aerospace and Electronic Systems. 14:826-832.   10.1109/taes.1978.308638   AbstractWebsite

Detection performance of four candidate receiver structures for the signal known except for direction (SKED) array problem is investigated. Included are the Bayes optimal detector, two estimate and plug structures, and a fixed estimate structure. Estimators considered are the maximum likelihood (ML) and maximum a posteriori (MAP). Performance degradation from optimal for the estimate and plug structures considered is shown to be significantly more severe the larger the array size.

Tran, J-MQD, Hodgkiss WS.  1993.  Array surveying using matched‐field processing. Journal of the Acoustical Society of America. 94:2851-2858.   10.1121/1.407342   AbstractWebsite

In this paper, the problem of localizing a vertical line array of sensors is studied in the context of matched-field processing. A broadcasting source is assumed deployed in a known environment at a known location from a vertical line array. Array surveying is discussed and a simple procedure using a correlation measure and a standard multidimensional optimization algorithm is proposed to resolve the array shape. First, this procedure is used on simulated data and convergence is demonstrated. Then, the method is used on data collected at wa in September 1987 with a 900-m-long array with 120 sensors. The derived array sensor positions are found consistent with previous analysis results. The positions found by the optimization procedure have a noisy character which is thought to be due to deviations of the individual array element gain and phase characteristics from their nominal calibrations.

Menon, R, Gerstoft P, Hodgkiss WS.  2012.  Asymptotic eigenvalue density of noise covariance matrices. IEEE Transactions on Signal Processing. 60:3415-3424.   10.1109/tsp.2012.2193573   AbstractWebsite

The asymptotic eigenvalues are derived for the true noise covariance matrix (CM) and the noise sample covariance matrix (SCM) for a line array with equidistant sensors in an isotropic noise field. In this case, the CM in the frequency domain is a symmetric Toeplitz sinc matrix which has at most two distinct eigenvalues in the asymptotic limit of an infinite number of sensors. Interestingly, for line arrays with interelement spacing less than half a wavelength, the CM turns out to be rank deficient. The asymptotic eigenvalue density of the SCM is derived using random matrix theory (RMT) for all ratios of the interelement spacing to the wavelength. When the CM has two distinct eigenvalues, the eigenvalue density of the SCM separates into two distinct lobes as the number of snapshots is increased. These lobes are centered at the two distinct eigenvalues of the CM. The asymptotic results agree well with analytic solutions and simulations for arrays with a small number of sensors.

Cho, SE, Song HC, Hodgkiss WS.  2012.  Asynchronous multiuser underwater acoustic communications (L). Journal of the Acoustical Society of America. 132:5-8.   10.1121/1.4726029   AbstractWebsite

An asynchronous multiuser system is proposed to support multiple-access underwater communications without the use of code-division multiple-access or a feedback channel. The rich multipath channels experienced by spatially separated users will be sufficient to ensure separation of collided packets at the base station. The iterative receiver will employ a combination of adaptive time-reversal processing, matching pursuit, and successive interference cancellation in a block-wise fashion to achieve multiuser separability. Data collected during the KAM11 experiment are used to illustrate the system's capability in a dynamic, time-varying environment. (C) 2012 Acoustical Society of America. []

Song, HC, Kuperman WA, Hodgkiss WS.  2009.  Basin-scale time reversal communications. Journal of the Acoustical Society of America. 125:212-217.   10.1121/1.3021435   AbstractWebsite

During November 1994, broadband acoustic signals were transmitted from a 75-Hz source to a 20-element, 700-m vertical array at approximately 3250 km range in the eastern North Pacific Ocean as part of the acoustic engineering test (AET) of the acoustic thermometry of ocean climate program [Worcester , J. Acoust. Soc. Am. 105, 3185-3201 (1999)]. The AET tomography signal can be treated as a binary-phase shift-keying communication signal with an information rate of 37.5 bits/s. With the multipath arrivals spanning 5-8 sec, these data represent an extreme case of intersymbol interference. The AET array data are processed using time reversal combined with frequent channel updates to accommodate channel variations over the 20-min long reception, followed by a single channel decision-feedback equalizer. The almost error-free performance using all 20 array elements demonstrates the feasibility of time reversal communications at basin scale. Further, comparable performance of single receive element communications integrating over multiple transmissions indicates that the ocean provided temporal diversity that is as effective as the spatial diversity provided by the array.

Hodgkiss, WS, Nolte LW.  1975.  Bayes optimum and maximum-likelihood approaches in an array processing problem. IEEE Transactions on Aerospace and Electronic Systems. 11:913-916.   10.1109/taes.1975.308004   AbstractWebsite

A comparison of the structure and performance of two detectors for an array processing problem is discussed. The first is optimal for detection performance in the Bayesian sense and the second models a maximum-likelihood (beam-forming) approach. Of particular interest is the loss in performance due to nonoptimal processing.

Battle, DJ, Gerstoft P, Hodgkiss WS, Kuperman WA, Nielsen PL.  2004.  Bayesian model selection applied to self-noise geoacoustic inversion. Journal of the Acoustical Society of America. 116:2043-2056.   10.1121/1.17855671   AbstractWebsite

Self-noise geoacoustic inversion involves the estimation of bottom parameters such as sound speeds and densities by analyzing towed-array signals whose origin is the tow platform itself. As well as forming inputs to more detailed assessments of seabed geology, these parameters enable performance predictions for sonar systems operating in shallow-water environments. In this paper, Gibbs sampling is used to obtain joint and marginal posterior probability distributions for seabed parameters. The advantages of viewing parameter estimation problems from such a probabilistic perspective include better quantified uncertainties for inverted parameters as well as the ability to compute Bayesian evidence for a range of competing geoacoustic models in order to judge which model explains the data most efficiently. (C) 2004 Acoustical Society of America.

Richardson, AM, Hodgkiss WS.  1994.  Bispectral analysis of underwater acoustic data. Journal of the Acoustical Society of America. 96:828-837.   10.1121/1.410321   AbstractWebsite

Estimates of the power spectral density have been found to be very useful in a variety of signal processing applications over the last several decades. Higher-order spectra contain information not present in the power spectrum and recently, estimates of higher-order spectra have been shown to be useful in certain signal processing problems. In particular, estimates of the bispectrum and bicoherence have been found useful in detecting non-Gaussianity and nonlinearity in system identification, and in detecting transient signals. This paper is concerned with the estimation of the bispectrum and bicoherence of underwater acoustic signals. Some of the properties of the bispectrum and bicoherence are introduced and described. Estimates of bispectra of actual data taken from a freely drifting Swallow float and also from an element of a moored acoustic array are presented and discussed. In the results portion of the paper, three particular properties of bispectrum estimation are focused on. It is demonstrated how the bispectrum estimate can be used to detect non-Gaussianity, nonlinearity, and harmonic coupling. The detection of harmonic coupling is shown to be a useful property of the particular bispectrum estimation algorithm employed here.

Brienzo, RK, Hodgkiss WS.  1993.  Broadband matched‐field processing. Journal of the Acoustical Society of America. 94:2821-2831.   10.1121/1.407339   AbstractWebsite

Acoustic energy in the ocean propagates from a source to an array of sensors via multiple pathways. Conventional time-delay-and-sum beamforming does not utilize energy contained in the multipath arrivals. In this paper, a generalized beamformer is presented which coherently recombines the multipaths to provide enhanced detectability of broadband transients as well as range and depth localization of the source. Modeling of the wave field at the array due to a broadband source is accomplished with a normal mode model using 1.0-Hz increments across the 1- to 100-Hz band. These results are combined to yield the impulse response from a specified source location to each of the array elements. The set of calculated impulse responses is used in the generalized beamformer to coherently recombine energy arriving along multipaths that exist from that source range and depth to the array. The location of a source is determined by examining the beamformer output at a number of candidate range/depth cells; a peak in the output gives the location of the source. Experimental data, consisting of multiple arrivals at a hydrophone array from an explosive source at mid-depth in 2800 m of water, are processed using the generalized-beamformer.

Tan, BA, Gerstoft P, Yardim C, Hodgkiss WS.  2013.  Broadband synthetic aperture geoacoustic inversion. Journal of the Acoustical Society of America. 134:312-322.   10.1121/1.4807567   AbstractWebsite

A typical geoacoustic inversion procedure involves powerful source transmissions received on a large-aperture receiver array. A more practical approach is to use a single moving source and/or receiver in a low signal to noise ratio (SNR) setting. This paper uses single-receiver, broadband, frequency coherent matched-field inversion and exploits coherently repeated transmissions to improve estimation of the geoacoustic parameters. The long observation time creates a synthetic aperture due to relative source-receiver motion. This approach is illustrated by studying the transmission of multiple linear frequency modulated (LFM) pulses which results in a multi-tonal comb spectrum that is Doppler sensitive. To correlate well with the measured field across a receiver trajectory and to incorporate transmission from a source trajectory, waveguide Doppler and normal mode theory is applied. The method is demonstrated with low SNR, 100-900 Hz LFM pulse data from the Shallow Water 2006 experiment. (C) 2013 Acoustical Society of America.

Yuan, Z, Richards EL, Song HC, Hodgkiss WS, Yan S.  2018.  Calibration of vertical array tilt using snapping shrimp sound. The Journal of the Acoustical Society of America. 144:1203-1210.: Acoustical Society of America   10.1121/1.5054089   Abstract

Snapping shrimp are the dominant biological source of high-frequency (>2 kHz) ambient noise in warm coastal waters. In a recent experiment, the highly impulsive signals produced by shrimp snaps were recorded continually by a large-aperture vertical array (56 m) that was bottom-moored in 100-m deep shallow water. Assuming the array vertical, initial localization of individual snaps based on wavefront curvature along the array indicated that all snaps came from either above or beneath the flat seabed. By constraining all snaps to originate from the seabed, several hundred snaps within a radius of 500 m from the array over a 20-s window were detected successfully and localized in the three-dimensional space of time-of-arrival, range, and array tilt. Since the estimated array tilt for each snap is a projection of the absolute array tilt onto the nominal array-snap plane, the maximal tilt in the range and tilt domain corresponds to the absolute array tilt. Both simulations and data demonstrate that snapping shrimp can be exploited as a source of opportunity for calibration of vertical array tilt.

Tan, BA, Gerstoft P, Yardim C, Hodgkiss WS.  2015.  Change-point detection for recursive Bayesian geoacoustic inversions. Journal of the Acoustical Society of America. 137:1962-1970.   10.1121/1.4916887   AbstractWebsite

In order to carry out geoacoustic inversion in low signal-to-noise ratio (SNR) conditions, extended duration observations coupled with source and/or receiver motion may be necessary. As a result, change in the underlying model parameters due to time or space is anticipated. In this paper, an inversion method is proposed for cases when the model parameters change abruptly or slowly. A model parameter change-point detection method is developed to detect the change in the model parameters using the importance samples and corresponding weights that are already available from the recursive Bayesian inversion. If the model parameters change abruptly, a change-point will be detected and the inversion will restart with the pulse measurement after the change-point. If the model parameters change gradually, the inversion (based on constant model parameters) may proceed until the accumulated model parameter mismatch is significant and triggers the detection of a change-point. These change-point detections form the heuristics for controlling the coherent integration time in recursive Bayesian inversion. The method is demonstrated in simulation with parameters corresponding to the low SNR, 100-900 Hz linear frequency modulation pulses observed in the Shallow Water 2006 experiment [Tan, Gerstoft, Yardim, and Hodgkiss, J. Acoust. Soc. Am. 136, 1187-1198 (2014)]. (c) 2015 Acoustical Society of America.

Lani, SW, Sabra KG, Hodgkiss WS, Kuperman WA, Roux P.  2013.  Coherent processing of shipping noise for ocean monitoring. Journal of the Acoustical Society of America. 133:EL108-EL113.   10.1121/1.4776775   AbstractWebsite

Ambient noise was recorded on two vertical line arrays (VLAs) separated by 450m and deployed in shallow water (depth similar to 150 m) off San Diego, CA continuously for 6 days. Recordings were dominated by non-stationary and non-uniform broadband shipping noise (250 Hz to 1.5 kHz). Stable coherent noise wavefronts were extracted from ambient noise correlations between the VLAs during all 6 days by mitigating the effect of discrete shipping events and using array beamforming with data-derived steering vectors. This procedure allows the tracking of arrival-time variations of these coherent wavefronts during 6 days and may help in developing future passive acoustic tomography systems. (C) 2013 Acoustical Society of America

Culver, RL, Hodgkiss WS.  1988.  Comparison of Kalman and least squares filters for locating autonomous very low frequency acoustic sensors. IEEE Journal of Oceanic Engineering. 13:282-290.   10.1109/48.9241   AbstractWebsite

The Marine Physical Laboratory has designed, fabricated, and taken to sea self-contained, freely drifting acoustic sensors which can measure signal propagation and ambient ocean noise in the 1-20-Hz band for up to 25-hour periods. The deployment of several freely drifting floats forms an array of sensors whose outputs can be combined after the experiment with a beamformer. A Kalman filter and a least-squares estimator have been developed to estimate float positions from travel-time measurements. Computer simulation is used to compare filter performance-under several deployment scenarios. Results show that the Kalman filter performs better than the least-squares filter when the floats are subjected to small-magnitude accelerations between measurements. Neither filter was sensitive to relatively major changes in deployment geometry as long as the sound-speed profile is known exactly

Worcester, PF, Cornuelle BD, Hildebrand JA, Hodgkiss WS, Duda TF, Boyd J, Howe BM, Mercer JA, Spindel RC.  1994.  A comparison of measured and predicted broadband acoustic arrival patterns in travel time–depth coordinates at 1000‐km range. Journal of the Acoustical Society of America. 95:3118-3128.   10.1121/1.409977   AbstractWebsite

Broadband acoustic signals were transmitted from a moored 250-Hz source to a 3-km-long vertical line array of hydrophones 1000 km distant in the eastern North Pacific Ocean during July 1989. The sound-speed field along the great circle path connecting the source and receiver was measured directly by nearly 300 expendable bathythermograph (XBT), conductivity-temperature-depth (CTD), and air-launched expendable bathythermograph (AXBT) casts while the transmissions were in progress. This experiment is unique in combining a vertical receiving array that extends over much of the water column, extensive concurrent environmental measurements, and broadband signals designed to measure acoustic travel times with 1-ms precision. The time-mean travel times of the early raylike arrivals, which are evident as wave fronts sweeping across the receiving array, and the time-mean of the times at which the acoustic reception ends (the final cutoffs) for hydrophones near the sound channel axis, are consistent with ray predictions based on the direct measurements of temperature and salinity, within measurement uncertainty. The comparisons show that subinertial oceanic variability with horizontal wavelengths shorter than 50 km, which is not resolved by the direct measurements, significantly (25 ms peak-to-peak) affects the time-mean ray travel times. The final cutoffs occur significantly later than predicted using ray theory for hydrophones more than 100-200 m off the sound channel axis. Nongeometric effects, such as diffraction at caustics, partially account for this observation.