Waveguide Invariant Parameter Research Articles

Bayesian navigation in shallow water using passive acoustics

Autonomous underwater vehicle (AUV) navigation relying on active acoustic sources causes noise pollution, while dead reckoning leads to a localization error that increases with time. Therefore, AUV navigation based on passive acoustics is appealing. However, for AUV navigation, extracting location information with passive acoustics is a challenging signal processing task. Due to the small form factor of an AUV as a sensing platform, only a single hydrophone or a small aperture hydrophone array can be used as an acoustic sensor. Furthermore, the acoustic signals originate from uncooperative sources. Here, we propose a Bayesian navigation approach for an AUV that exploits acoustic signals generated from sources of opportunity (SOOs) in a shallow water environment. The waveguide invariant (WI) parameter is estimated from cross-correlation coefficients of non-linearly transformed tonal signals of an SOO. It is assumed that the location information of the SOO is transmitted by an automatic identification system. Additionally, the range rate is inferred using the spectrum of cross-correlatedacoustic fields over a time interval. The WI parameter estimate, the range rate estimate, and inertial measurements are fused in a Bayesian parameter estimation approach. The navigation capability is demonstrated using simulated and real data from the SwellEx-96 experiment.

Waveguide-Invariant-Based Ranging and Receiver Localization Using Tonal Sources of Opportunity

Acoustic emissions from cargo ships transiting coastal waterways, measured by a single hydrophone, can be exploited to estimate both the time-varying source–receiver range and receiver location. In this paper, two parameter-search-based maximum-likelihood estimators are presented: one for $\beta$ , the waveguide invariant parameter, and one for source range. $\beta$ characterizes the interference structure inherent to ducted acoustic propagation and is central to the spectral analysis involved in the range estimation. The source ranging method extends prior work by the authors and focuses on the strong narrowband tonals that typically dominate the acoustic spectra of cargo ships. Source ranging results are presented using real data from the SWellEx-96 experiment and are shown to be in close agreement with simulation results obtained using the KRAKEN normal mode program. A technique for estimating the position of a receiver, which can be stationary or moving, is also proposed. The localization technique requires knowledge of the source track, hydrophone data, and an initial estimate of the receiver's position. An application to autonomous underwater vehicle (AUV) navigation is included in which the waveguide-invariant-based range estimates are used to mitigate the position estimation error due to drift in inertial measurement units on submerged AUVs. A specific scenario is examined, using SWellEx-96 data, in which an initial position error of 3 km is reduced to under 1 km using the proposed technique.

Frequency Striations Induced by Moving Nonlinear Internal Waves and Applications

Modal interferences are evident in the spectrogram of broadband signals propagated over distances and received on a single receiver. Plotted against range and frequency, the spectrogram displays striated bands of constant acoustic intensity levels as explained by the waveguide-invariant theory, the slope of which can be used to estimate the source range by the waveguide-invariant parameter “beta.” Given a vertical array of receivers, one finds, however, no frequency striation in the depth-integrated acoustic energy, as the total energy corrected for geometrical spreading remains “conserved” except for mode attenuations. When nonlinear solitary internal waves (SIWs) are present in the propagation path, one finds a different phenomenon: the depth-integrated energy will display striations with respect to time and frequency. In this case, the striation slope is related to the source-to-SIW range, and not the source–receiver range. The striation is caused predominantly by mode coupling (as opposed to mode interference), which changes the mode amplitudes as the SIWs move. Theory and simulations are developed in this paper. As an application, one can use the SIW-induced striations to monitor the positions (and wavefronts) of nonlinear internal waves on a continuous time basis. This method is evaluated using the SWARM95 experimental environment to address the real-world issues.

Extension of the array invariant to deep-water environments

The array invariant utilizes multiple arrivals separated in beam angle and travel time for broadband signals, achieving robust source-range estimation without detailed knowledge of the environments in shallow water. This approach includes the waveguide invariant parameter β, which is close to one for surface/bottom-interacting shallow-water environments. In deep water, however, β significantly varies from large negative to positive values depending on the group of modes, while being sensitive to the sound speed variation within the water column. In this paper, two different approaches are investigated: 1) an extension of the array invariant by integrating multiple arrivals with varying β and 2) the use of dispersion relationship between several pairs of arrivals. These two approaches will be applied to a deep-water environment (4-km deep) using a 13-m aperture vertical array deployed to the sound channel axis (e.g., 330-m) from the Medium Frequency Noise experiment (MFN), where a high-frequency source (above 1 kHz) also was positioned around the sound channel axis.

Measured depth-dependence of waveguide invariant in shallow water with a summer profile.

Acoustic-intensity striation patterns were measured in the time-frequency domain using an L-shaped array and two simultaneously towed broadband (350-650 Hz) sources at depths above and below the thermocline under summer profile conditions. Distributions of the waveguide invariant parameter β, extracted from the acoustic striation patterns, peak at different values when receivers are above or below the thermocline for a source that is below the thermocline. However, the distributions show similar characteristics when the source is above the thermocline. Experimental results are verified by a numerical analysis of phase slowness, group slowness, and relative amplitudes of acoustic modes.

Shallow-water waveguide invariant parameter estimation and source ranging using narrowband signals

This paper concerns waveguide invariant parameter estimation using narrowband underwater acoustic signals from multiple sources at known range, or alternatively, the ranges of multiple sources assuming known waveguide invariant parameters. Previously, the waveguide invariant has been applied to estimate the range or bottom properties from intensity striations observed from a single broadband signal. The difficulty in separating striations from multiple broadband sources, however, motivates the use of narrowband components, which generally have higher signal-to-noise ratios and are non-overlapping in frequency. In this paper, intensity fluctuations of narrowband components are shown to be related across frequency by a time-warping (i.e., stretching or contracting) of the intensity profile, assuming constant radial source velocity and the waveguide invariant β. A maximum likelihood estimator for the range with β known or for the invariant parameter β with known source range is derived, as well as Cramer-Rao bounds on estimation accuracy assuming a Gaussian noise model. Simulations demonstrate algorithm performance for constant radial velocity sources in a representative shallow-water ocean waveguide. [Work supported by ONR.]

Passive multi-target localization by cross-correlating beams of a compact volumetric array

A technique is presented for passively localizing multiple noise-producing targets by cross-correlating the elevation beams of a compact volumetric array on separate bearings. A target's multipath structure inherently contains information about its range, however unknown, random noise waveforms make time separation of individual arrivals difficult. Ocean ambient noise has previously been used to measure multipath delays to the seabed by cross-correlating the beams of a vertical line array [Siderius et al., J. Acoust. Soc. Am. 127, 2193–2200 (2010)], but this methodology has not been applied to distant noise sources having non-vertical arrivals. In this paper, methods are presented for using a compact volumetric array mounted to an autonomous underwater vehicle to measure the directionality and time delays of multipath arrivals, while simultaneously rejecting clutter and interference. This is validated with results from the GLASS'12 experiment in which a small workboat maneuvered in shallow water. Short ranges could be estimated reliably using straight ray paths, but longer ranges required accounting for ray refraction effects. Further, this is related to striation patterns observed in spectrograms, and it is shown that measured multipath time delays are used to predict this pattern, as well as the waveguide invariant parameter, β.

Predicting range-frequency interference patterns from broadband sources in a range-dependent, continental shelf environment

The 2007 CALOPS dataset contains horizontal line array received signals from numerous surface vessels transiting an area off the coast of southeast Florida. Parabolic equation propagation models using measured bathymetric, sound velocity profile, and sediment parameter data suggest that substantial mode coupling should be occurring for several down-slope propagation scenarios in the dataset. However, received acoustical data for these scenarios, in the form of range-frequency interference patterns, are best described by adiabatic propagation. This discrepancy has implications that affect waveguide invariant parameter estimation, which is necessary for invariant-based passive ranging. The causes of the incongruous model output will be discussed, as well as their effects on estimating waveguide invariant distributions for these scenarios. [This research was supported by the Applied Research Laboratory, at the Pennsylvania State University through the Eric Walker Graduate Assistantship Program.]

Modal interference and frequency striations induced by moving nonlinear internal waves

Spectrogram of a broadband signal propagated over distances often displays striated bands of constant acoustic intensity levels plotted against the range and frequency. This phenomenon is due to modal interference and the slope of the striation is related to the source range and frequency by the waveguide invariant parameter “beta.” As an application, one can estimate the range to a moving source based on the striation of the spectrogram (as a function of frequency and time), knowing the source velocity and the waveguide invariant parameter. Conversely, no frequency striation is expected in the spectrogram of the received signal when both the source and receiver are fixed (the frequency content remains unchanged with respect to time). However, when nonlinear internal waves, appearing as a train of moving solitons, are present in the propagation path, the spectrogram of the received signal will display frequency striations (with respect to time) even for a fixed source and receiver. This paper applies the mode coupling equation to calculate the modal interference, intensity fluctuation and the striation slope. Broadband spectrograms are simulated to show the frequency striation as the solitons move from the receiver to the source. Results from at-sea data will be presented for comparison.

Broadband source localization using horizontal-beam acoustic intensity striations

Waveguide invariant theory is applied to horizontal line array (HLA) beamformer output to localize moving broadband noise sources from measured acoustic intensity striation patterns. Acoustic signals emitted by ships of opportunity (merchant ships) were simultaneously recorded on a HLA and three hydrophones separated by 10 km during the RAGS03 (relationship between array gain and shelf-break fluid processes) experiment. Hough transforms are used to estimate both the waveguide invariant parameter "beta" and the ratio of source range at the closest point of approach to source speed from the observed striation patterns. Broadband (50-150-Hz) acoustic data-sets are used to demonstrate source localization capability as well as inversion capability of waveguide invariant parameter beta. Special attention is paid to bathymetric variability since the acoustic intensity striation patterns seem to be influenced by range-dependent bathymetry of the experimental area. The Hough transform method is also applied to the HLA beam-time record data and to the acoustic intensity data from three distant receivers to validate the estimation results from HLA beamformer output. Good agreement of the results from all three approaches suggests the feasibility of locating broadband noise sources and estimating waveguide invariant parameter beta in shallow waters.

Acoustic ranging and waveguide invariant parameter estimation using virtual arrays.

A method for estimating the range of an unknown broadband acoustic source in a waveguide [Thode et al., J. Acoust. Soc. Am. 108(4), 1582–1594 (2000)] is revisited and extended to estimate both waveguide invariant parameter “beta” and source range in shallow water. In the new method, two or more vertical arrays are used without requiring a signal sample from a guide‐source. It was shown that both methods are mathematically identical and they both provide robust range estimation even when the reference signal sample is used from different time and/or different vertical array location. It was also demonstrated that an image processing tool, Hough Transform method, provides robust parameter estimation from virtual array output data. In addition, the parameter estimation method was validated under both summer and winter conditions by using incoherent noise data to localize and track merchant vessels and to estimate waveguide invariant parameter. [Work supported by the Office of Naval Research.]

Investigation of bistatic invariance principles for active sonars.

Application of bistatic invariance principles to mid-frequency active sonar systems is investigated using data collected during two recent experiments conducted at the Malta Plateau and East China Sea. Low-frequency (350–650 Hz) and mid-frequency (1.5–3.5 kHz) LFM pulses were transmitted and direct-blast and return signals from an echo-repeater and several strong scatterers simultaneously recorded on a towed array, a drifting volumetric array, and a moored vertical line array. At low frequencies, application of bistatic invariance principles to target detection is demonstrated. At mid-frequencies, the spectrograms of the direct-blast signals showed regular striation patterns that were used to estimate the waveguide invariant parameter beta. However, both measured and simulated spectrograms of the signals scattered from an oil rig indicated the complexity of the striation patterns. More complex patterns of striations in the measured spectrograms might be due to azimuthal dependency of the scattering kernel, source/receiver motion, and low SNR. [Work supported by the Office of Naval Research.]

Beam intensity striations and applications.

The single-element spectrogram for a continuous broadband signal, plotted as a function of range, has been shown to exhibit striated bands of intensity maxima and minima. The slope of the striations is an invariant of the modal interference and is described by a waveguide invariant parameter "beta." The striation pattern is analyzed and modeled in this paper for the beam outputs of a horizontal line array obtained by conventional beamforming. Array beamforming makes it possible to measure the waveguide invariant parameter for weak signals due to the enhancement of signal levels by the array gain over that of a single element. It is shown that the signal beam spectrogram as a function of range exhibits the same striation pattern as that (predicted) for a single element. Specifically, for a broadside signal, the beam striation is identical to that of a single-element plus a constant signal gain. For a nonbroadside target, the signal beam intensity will be modified by a frequency-bearing dependent signal gain due to the signal spread over multiple beams, nevertheless the beam spectrogram retains the same striation pattern (slope) as for a single element. The sidelobe beams (outside the canonical cones containing the signal arrivals) exhibit an entirely different striation pattern as a function of frequency and range. For array processing, it is shown that a fast range-rate, close range target and a distant, slow range-rate interference source will have a different striation pattern (slope) in the corresponding beam spectrograms as a function of time, assuming no prior knowledge of the source ranges. The difference in the striations between the beam spectrograms can be used in array processing to suppress the interference contribution. A 5-7 dB interference suppression is demonstrated using simulated data.