Colorado College OVAL Project

We have tried three different algorithms for localizing underwater sounds. These are

(1) a linear algebra approach

(2) intersecting hyperboloids

(3) matched field processing

We have settled on the last as the best. Matched field refers to a nonlinear minimization of an error function composed of a comparison between the measured time intervals and those predicted via straight line ray sound wave propagation from a hypothetical underwater location to each of the hydrophones in the array. Using a simplex algorithm, this hypothetical location is moved around until the error between the measured time differences and those predicted for the hypothetical location is minimized. It typically takes a few hundred error function evaluations to find the minimum and this takes less than ~1/2 sec on our Pentium III computer.

In the case of four hydrophones, there are 6 time differences, or equivalently travel distances, that can be compared between the observed and predicted hydrophone signals (3-0, 3-1, 3-2, 2-0, 2-1, 1-0). In this figure four of these are shown: 3-0, 3-1, 3-2, and 1-2. The error function that we minimize is: where D is the "extra travel distance" which is equal to the speed of sound in water times the time difference between when a sound wave reaches one hydrophone and a second one.