## Iterative range estimation in a sloping-bottom shallow-water waveguide using the
generalized array invariant"

**C. Cho**, chomgun@gmail.com

**H.C. Song**, hcsong@ucsd.edu

Scripps Institution of Oceanography, La Jolla, California 92093-0238, USA

**P. Hursky**, hursky@hlsresearch.com

Heat, Light and Sound Research, Incorporated, San Diego, California, 92130, USA

and

**S.M. Jesus**, sjesus@ualg.pt

LARSyS, University of Algarve, Campus de Gambelas, PT-8005-139 Faro, Portugal

**Comments:** download pdf.

** Ref.:** Journal of Acoustical Society of America, Vol**142**(1), pp. 55-60, June **2017**
(doi).

**Abstract:**
The array invariant theory was generalized by incorporating the waveguide invariant Beta, referred to
as the generalized array invariant. In this paper, the generalized array invariant is extended
to mildly range-dependent environments with a sloping bottom where the waveguide invariant is
variable in range. Assuming knowledge of the bottom slope, the array invariant can be applied
iteratively to estimate the source range starting with Beta=1 (i.e., range-independent),
which converges toward the correct source range by updating Beta at the previously estimated range.
The iterative array invariant approach is demonstrated using a short-aperture vertical array
(2.8-m) in a sloping-bottom shallow-water waveguide from the Random Array of Drifting Acoustic
Receivers 2007 experiment, where a high-frequency source (2–3.5 kHz) close to the surface (6-m)
was towed between 0.5 and 5 km in range with the water depth varying from 80 to 50 m