Model-independent range localization of a moving source in shallow water

Abstract

A method for range localization with a single sensor in an ocean waveguide is derived. Range localization typically requires an accurate environmental acoustics model used for processing acoustic data on a multi-element array. Recently, an alternative method for estimating range has emerged based on the waveguide invariant which still requires either an array of sufficient horizontal extent or data from a moving source for which range rate is known. In analogy to the waveguide invariant derivation, it is shown that the magnitude of the square of the difference between the acoustic field at two different ranges contains information about the range interval, Δr. Since the range interval is manifest in the time interval, Δt between field measurements, range rate can be ascertained. Experimental results confirm this single sensor localization method.

Range Localization of a Moving Source Based on Synthetic Aperture Beamforming Using a Single Hydrophone in Shallow Water

“…and the wavenumbers can be expressed as k m = k + δk m , where k is the average horizontal wavenumber of the modes since δk m k (typically, δk m /k ∼ O(10 −2 ) for discrete mode wavenumbers, which are between k min = ω/c b and k max = ω/min(c w ) where c b and c w are the sound speeds at the bottom surface and in the water, respectively [14]. For some lower frequencies' cases, δk m /k ∼ 10 −1 ).…”

“…It can be seen from Equation 7that the approximation of the average horizontal wavenumber by the wavenumber in water causes a bias on the estimation of the average radial velocity, which will in turn affect the accuracy of the range estimation. Assuming that the error of the average horizontal wavenumber is δk, then the estimation error of the average radial velocity is given here [14] ∆v…”

“…This method calculates the slope of interference patterns in different regions on the range-frequency plane and uses the principle of waveguide invariance to achieve robust range measurement. Rakotonarivo and Kuperman [14] pointed out that the magnitude of the square of the difference between the acoustic field at two different ranges contains information about the range interval, and the range rate can be ascertained. Bonnel et al [15] developed a single-hydrophone ranging method using the nonlinear signal processing method warping transform to filter the modes.…”

Joint Estimation of Source Range and Depth Using a Bottom-Deployed Vertical Line Array in Deep Water

“…The sinusoidal modulation exhibits periods of π, which yields the following: $z_s=\frac{c}{2\mathrm{normal\Delta }f\sin \phi },$ where Δ f is the width of the modulation between nulls. The interference pattern can be transformed into source depth information by the Fourier transform scheme [18,19]. The process involves the following steps: (a) obtaining of the time series y ( t ) by CBF, (b) Fourier transforming y ( t ) to frequency domain g ( f ), and (c) Fourier transforming g ( f ) to the depth and range domain:$bold-italicnormalx\left(t\right)\underset{\mathrm{CBF}}{\to }y\left(t\right)\underset{fft}{\to }g\left(f\right)\underset{fft}{\to }h\left(z_s,r\right)$…”

Deep-learning source localization using multi-frequency magnitude-only data

“…(2) The magnitudes of multi-frequency data from a single sensor are used for localization, showing the remarkable capability of DNNs. Note that the localization methods [29][30][31] based on waveguide invariant also use just the magnitude pressure.…”