A method of range and depth estimation by modal decomposition

Abstract

Normal mode amplitudes are definite functions of depth and have a characteristic phase as a function of source range rs [i.e., exp(−ikirs), where ki is the ith mode wavenumber]. The range and depth of an acoustic source in the ocean can then be determined by decomposing array data and beamforming on the mode amplitudes. In particular, the product of the normal mode amplitudes with the steering vector Ui [where Ui=exp(ikir) ] is maximum for the true source range (r=rs). Similarly, the correlation of the measured (decomposed) mode amplitudes with the theoretically calculated mode amplitudes is maximum at the source depth. Accurate range and depth estimation with this approach, however, requires reliable estimates of the mode amplitudes. In this article, an eigenvector decomposition technique is used to extract the mode amplitudes for data received on a long (1-km) vertical array. Range and depth are successfully estimated both for simulated data and for data from the 1982 FRAM IV experiment in the Arctic Ocean. The effect of the number of modes on the estimates is also illustrated.

Clutter depth discrimination using the wavenumber spectrum

“…Some of these methods include matched field processing which attempts to maximize an objective function which correlates the modeled and measured acoustic fields (Bucker, 1976;Baggeroer et al, 1988;Fawcett et al, 1996); modal decomposition methods which seek to match the modeled and measured modal amplitudes as a function of depth (Shang, 1985;Yang, 1987;Glattetre et al, 1989); matched mode methods which endeavor to match modeled and observed mode amplitudes as measured on a horizontal line array by use of the frequency-wavenumber (f-k) transform (Nicolas et al, 2006); and waveguide invariant approaches which are based on Chuprov's (1982) parameterization relating range and frequency to the slope of the striations in acoustic pressure in a frequency-range plot (Brekhovskikh and Lysanov, 1991;D'Spain and Kuperman, 1999). The waveguide invariant is commonly interpreted in terms of constructive and destructive interference of propagating normal modes (Turgut and Orr, 2010), but it has also been described in terms of ray theory (Gerstoft et al, 2001) and variations in eigenray arrival times (Harrison, 2011), and related to the wavenumber integration technique (Cockrell and Schmidt, 2010).…”

Data-based depth estimation of an incoming autonomous underwater vehicle

“…5 Equation (6a) is the same as the MMP ambiguity function evaluated at the source range 4 except for a slightly different shading coefficient. The depth z j where the ambiguity function is maximum yields the approximate source depth so long as the source depth is within the depth span of the VLA.…”

Low-frequency broadband sound source localization using an adaptive normal mode back-propagation approach in a shallow-water ocean

“…(6) will approach E H mx b ð ÞA m ; and it still has the capability to resolve the source location. This mode conjugate formula is used in Matched Mode Processing (Yang, 1987;Yang, 1990). The principal criterion for ranging the source is phase conjugation, and the closure relation of the normal modes, i.e.,…”

“…Shang (1985) and Shang et al (1985) recognized that the source range and depth can be determined from the phase difference between modes and the closure relation of normal modes, respectively. Yang (1987) utilized jointly the phase conjugation and the closure relation for normal mode beamforming to source locations, which can also be considered as Matched Mode Processing (MMP). Yang (1990) showed that when the sampled-mode-shape mode filter (Ferris, 1972) is used, MMP is equivalent to MFP.…”