Department of Electrical and Computer Eng.,

University of Sharjah, 27272 UAE

LARSyS, University of Algarve, 8005-139 Faro, Portugal

**Comments:** download pdf

** Ref.:** OCEANS MTS/IEEE, Marseille (France), June **2019**

**Abstract**:
Propagation of acoustic waves in a shallow water is modeled using the normal mode
model. Reliable and fast estimation of the model parameters is of the utmost importance
to many underwater observation systems. A vertical linear array is deployed that partially
covers the water column, with the objective to estimate the model functions at the sensor
depths, as well as the wavenumbers relative to the different modes.

For this purpose, a monochromatic source is placed at a given range from the array. It
is activated successively at the same sensor depths. Pressure field measurements are
collected and grouped into a first data matrix. Then, the source is moved to another location
at a different range, and the experiment is repeated. A second data matrix is collected.

We design a subspace algorithm that computes the sought-after model parameters. Unlike
existing subspace algorithms, the presented algorithm is not based on the decomposition
of the array data matrix, and consequently, does not require full and dense coverage of
the water column. This unpractical condition is, unfortunately, needed to obtain orthogonal
columns that could be identified by means of a singular vector decomposition. We
manage to design a subspace algorithm that does not require this condition because we
do not process the brute data matrix. Instead, we introduce a non-trivial combination
of the two data matrices collected as mentioned above. In this matrix, sampled modal
functions appear as eigenvectors and wavenumbers appear as eigenvalues. Contrarily to
singular vectors, eigenvectors do not have to be orthogonal, explaining why the proposed
algorithm does not require orthogonality (of modal functions).

Not only does the resulting algorithm operate under realistic conditions, it also
computes the model parameters in a closed-form, search-free and fully-automatic manner,
that contrasts with many of the existing heuristic techniques. It, also, does not make
any assumption about the statistical distribution of observation noise. The computation
burden is that of one eigenvector decomposition and one singular vector decomposition,
where the matrix size is determined by the number of array sensing elements.

By a proper theoretical development, we prove that the so-obtained estimates are exact if
pressure measurements are error-free. From this point-of-view, we propose a truly
high-resolution algorithm whose accuracy is not limited by the size of the sensing array, but
rather by the observation noise. In the presence of noise, estimation accuracy can be
improved by collecting more field measurements, over longer periods of time and/or using
longer arrays.

The developed algorithm was tested with two different 300m deep waveguides: a Pekeris
waveguide and a lossy waveguide with an underlying sediment layer, both excited by a
source emitting at 60 Hz. Pressure field was generated using the KRAKEN propagation
model and computer-generated random noise was artificially added. The estimation algorithm
was run with different combinations of SNR levels, source-to-VLA separation,
inter-sensor spacing, array length and depth. Good estimation performance is obtained,
more difficultly for the lossy waveguide, naturally. Below, we show typical estimation
performance for the modal functions expressed in terms of an averaged normalized mean
square error, for the two waveguides, as function of the number of sensors and the depth
of the bottom sensor.

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