Charles F. Gaumond

Beamforming using compressive sensing

Compressive sensing (CS) is compared with conventional beamforming using horizontal beamforming of at-sea, towed-array data. They are compared qualitatively using bearing time records and quantitatively using signal-to-interference ratio. Qualitatively, CS exhibits lower levels of background interference than conventional beamforming. Furthermore, bearing time records show increasing, but tolerable, levels of background interference when the number of elements is decreased. For the full array, CS generates signal-to-interference ratio of 12 dB, but conventional beamforming only 8 dB. The superiority of CS over conventional beamforming is much more pronounced with undersampling.

Identification and synthesis of acoustic scattering components via the wavelet transform

An acoustic scatterer can be described in the time domain by its impulse response function, or in the frequency domain by its form function. Both functions will contain several complementary and distinct components, none of which is fully separable in either the time or frequency domain. This renders Fourier based methods ineffective in identifying and extracting one component from all the others. However, it is possible to do this using the wavelet transform, a transform that yields a two‐dimensional (two‐parameter) representation of a signal. In this paper, this transform is used to identify and extract the acoustic components from physical model data.

Demonstration at sea of the decomposition-of-the-time-reversal-operator techniquea)

This paper presents a derivation of the time reversal operator decomposition (DORT) using the sonar equation. DORT is inherently a frequency-domain technique, but the derivation is shown in the time-frequency domain to preserve range resolution. The magnitude of the singular values is related to sonar equation parameters. The time spreading of the time-domain back-propagation image is also related to the sonar equation. Noise-free, noise-only, and signal-plus-noise data are considered theoretically. Contamination of the echo singular component by noise is shown quantitatively to be very small at a signal-to-noise ratio of 0dB. Results are shown from the TREX-04 experiment during April 22 to May 4, 2004 in 94m deep, shallow water southwest of the Hudson Canyon. Rapid transmission of short, 500Hz wide linear frequency modulated beams with center frequencies of 750, 1250, 1750, 2250, 2750, and 3250Hz are used. Degradation caused by a lack of time invariance is found to be small at 750Hz and nearly complete a...

Reconstruction of the acoustic field over a limited surface area on a vibrating cylinder

The acoustic field on a small region on the surface of a radiating cylindrical shell is reconstructed from measurements of pressure made on a limited nearby surface. The boundary‐element method is applied to compute an operator relating the pressure on a small measurement surface located near the structure to the normal velocity at all points on the structure surface. Since the inverse problem of the reconstruction of the surface field is ill posed, singular value decomposition is applied to invert the operator. It is demonstrated that the surface field may be reconstructed over the portion of the structure surface located under the measurement surface.

T‐matrix implementation of forward scattering from rigid structures

The T‐matrix method is applied to compute forward scattering from rigid structures. The method requires evaluation of matrix elements Qmmlk whose imaginary parts with l<k are difficult to evaluate for long, slender, nonellipsoidal structures because the evaluation involves integrations of large oscillatory functions. A new approach for the evaluation of these elements is shown for finite cylinders where the antisymmetric part of the matrix is written in a form involving integrals that are easier to compute. Forward scattering results are shown for spheroids and cylinders with spheroidal endcaps where the length of the cylindrical section is shown to have little effect on forward scattering. The magnitude of the forward scattering at the high‐frequency limit is seen to be proportional to the cross‐sectional area, which is in agreement with the high‐frequency Kirchhoff approximation.

Comparison of a subrank to a full-rank time-reversal operator in a dynamic ocean

This paper investigates the application of time-reversal techniques to the detection and ensonification of a target of interest. The focusing method is based on a generalization of time-reversal operator techniques. A subrank time-reversal operator is derived and implemented using a discrete set of transmission beams to ensonify a region of interest. In a dynamic ocean simulation, target focusing using a subrank matrix is shown to be superior to using a full-rank matrix, specifically when the subrank matrix is captured in a period shorter than the coherence time of the modeled environment. Backscatter from the point target was propagated to a vertical 64-element source-receiver array and processed to form the sub-rank time-reversal operator matrix. The eigenvector corresponding to the strongest eigenvalue of the time-reversal operator was shown to focus energy on the target in simulation. Modeled results will be augmented by a limited at-sea experiment conducted on the New Jersey shelf in April-May 2004 measured low-frequency backscattered signal from an artificial target (echo repeater).

The effect of coherence and noise on the decomposition of the time reversal operator

Active sonar in shallow water in shallow water is often reverberation-limited and the detectability is often limited by the presence of too many false alarms. The decomposition of the time reversal operator (DORT) is a method that potentially alleviates this problem by separating echoes from different depths in the water column. For example, DORT can separate a target in the water column from reverberation on the bottom. DORT requires a set of echoes recorded on a line array that result from a set of independent transmissions from a source array. A short derivation of DORT using the sonar equation is given. Because DORT is inherently a frequency-domain method, the time-frequency domain is derived to implement the algorithm on the data. Lastly, the similarity of DORT to adaptive beam forming is shown. In this paper, data taken on the Atlantic shelf, east of Cape May, NJ, during Geoclutter 03 and TREX-04 experiments, is processed and shown. The data was taken with a 64 element vertical line array of source-receiver elements. The target was an echo repeater using an XF4 source from 500 to 2500 Hz or an ITC 200 source from 2500 to 3500 Hz. The data cover six 500 Hz-bands from 500 Hz to 3500 Hz. The data are processed using DORT in the time-frequency domain. The analysis produces singular values in the time-frequency domain and in the time-delay domain. It also produces singular vectors that are used with a broad-band propagation model to form back-propagation images in the range, depth, frequency or range, depth, time domain. The analysis shows that the limiting factors in this data set arise from 1) motion that causes a lack of time-invariance, 2) additive noise and 3) the independent transmission scheme. The lack of time invariance is shown to spread the echo energy into several singular indices. Additive noise is shown to contaminate the singular values and back-propagation images. The particular transmission scheme used, time division multiplexed LFMs, is shown to create large side lobes in the time domain. Alternative transmission sequences, as well as alternative source and receiver orientations, are discussed

Application of DORT to active sonar

Active sonar in shallow water is often reverberation-limited and the detectability is often limited by the presence of too many false alarms. The problem of improving detection, and classification, in shallow water is being worked on in several different ways. The time reversal operator decomposition (DORT) is a technique that has recently been applied to the problem of discriminating echoes in shallow water based on the different depths of the scatterers. DORT uses scattering data from a multiple source and multiple receiver sonar arrangement to separate scatterers that are resolvable by the source and receiver arrays. DORT is the application of the singular value decomposition of the frequency-domain data. This paper presents a derivation of DORT from the sonar equation. DORT is inherently a frequency-domain technique. In order to preserve range-resolution, the sonar equation is transformed into the time-frequency domain. With that representation, DORT can be applied to the frequency domain signal within a range resolution cell. Following the derivation of DORT from the sonar equation, numerical simulations are shown that demonstrate the depth resolution of a vertical line array of sources and receivers. Sufficient depth resolution is shown using few sources at frequencies near 500 Hz in water with a depth of 100 m. Problems that are encountered with the implementation of the technique are discussed. Target motion causes leakage of signal energy into several singular values. Motion of the source or receiver is shown to have little effect. The problems and constraints that arise from different multiplexing techniques, including frequency, code and time division, are shown. Results are shown with data taken on the Atlantic shelf, east of Cape May, NJ, during Geoclutter 03 and TREX-04 experiments

On the structural acoustic modeling of cetacean mammals by the finite element method

Requirements for the computational modeling of a mammal are presented. In general, meticulous attention to details of its anatomy is needed. The extent of detail must go beyond size and shape to include an inventory of each organ and bone. Also, some components are unique to a species, such as the melon in dolphins. The elastic properties of several biological materials must be determined. A few of these materials are bone, connective tissue, and fat. The compressional sound speeds of the above materials in humans are easily available. Transverse sound speeds and anisotropic information are somewhat less abundant. The compressional and transverse sound speeds are sufficient to model isotropic materials, such as fat, but anisotropic information is necessary for materials that have a grain, such as connective tissue. The modeling of bone may require an understanding of the separate layers of bone, which are quite different from each other. A simple FEM model of a dolphin is presented. The model is run over ...

Echo components for aspect-independent detection and classification

Data from a numerical target scattering model are described in the time and frequency domains. These echoes are separated into physics-based components called wavepackets, which are aspect-dependent. These individual components are made stochastic by the assumption of random aspect. Each physical component is then decomposed with a statistically independent basis via the Karhunen-Loeve Expansion (KLE). It is shown that the echo is well described by a collection of a few terms of the KLE. The statistically independent expansion amplitudes are then used to generate detection statistics.