Spectral and modal formulations for the Doppler-shifted field scattered by an object moving in a stratified medium

Abstract

Spectral and normal mode formulations for the three-dimensional field scattered by an object moving in a stratified medium are derived using full-field wave theory. The derivations are based on Green's theorem for the time-domain scalar wave equation and account for Doppler effects induced by target motion as well as source and receiver motion. The formulations are valid when multiple scattering between the object and waveguide boundaries can be neglected, and the scattered field can be expressed as a linear function of the object's plane wave scattering function. The advantage of the spectral formulation is that it incorporates the entire wave number spectrum, including evanescent waves, and therefore can potentially be used at much closer ranges to the target than the modal formulation. The normal mode formulation is more computationally efficient but is limited to longer ranges. For a monochromatic source that excites N incident modes in the waveguide, there will be roughly N2 distinct harmonic components in the scattered field. The Doppler shifts in the scattered field are highly dependent upon the waveguide environment, target shape, and measurement geometry. The Doppler effects are illustrated through a number of canonical examples.

Estimating the instantaneous velocity of randomly moving target swarms in a stratified ocean waveguide by Doppler analysis

“…(14) and (15) cannot typically be analytically evaluated. A significant simplification is however possible in the case of some specially designed source spectra, such as Costas sequences, which can be written in the form of Eq.…”

“…It is known, for example, that for a waveguide supporting N modes, N 2 Doppler shifts as opposed to the single shift will occur in free-space for the same motion. 14 We show here that by applying a statistical formulation to the even more complicated problem of sensing multiple randomly moving targets in an ocean waveguide within a single imaging system resolution cell, the analysis can be greatly simplified.…”

“…For active sensing of a single deterministic target in a waveguide where N 2 Doppler shifts occur, it has been shown that a relatively accurate estimate of the target velocity can be obtained from the Dopplershifted spectrum of its scattered field. 14,15 Here, we show that, for a group of random targets within a resolution cell, accurate simultaneous estimates can be obtained for the instantaneous velocity and position means of the group, as well as their standard deviations through the Moment Method. In Sec.…”

ONR Acoustic Observatory Science Plan Workshop

“…Targets moving in a waveguide lead to multiple Doppler shifts at a receiver due to multimodal propagation. This theory has been developed for both passive [6] and active sonar [7], where Doppler distortion is greatly compounded in the latter case but the original source signal is always known, which is advantageous for target velocity estimation. The observatory array could be used to isolate targets in range azimuth and depth and also perform modal processing to determine the target's instantaneous velocity via application of waveguide Doppler theory.…”

“…For data where path identification is not applicable, approximations relying on modal decompositions will be examined. Time-frequency techniques (in combination with simultaneous deconvolution, since the source waveform is unknown) will be tested on the identification of distinct components of the field [7] that can be subsequently employed for localization. Josko Catipovic, Dan Nagle Naval Undersea Warfare Center Undersea acoustic communication (acomms) at ranges of several hundred to several thousand kilometers will support new civilian and Navy applications of both manned and autonomous underwater systems.…”