### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 3aUW9. The dependence of ocean acoustic parameter resolution bounds on
sample size.

**Nicholas C. Makris
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*Naval Res. Lab., Washington, DC 20375
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It is currently common practice in theoretical ocean acoustics to derive
``fundamental'' parameter resolution bounds for a monochromatic measurement of
the temporally fluctuating field received on a hydrophone array. However, a
monochromatic measurement corresponds to a single random sample. In applied
ocean acoustics, single samples are seldom if ever used for parameter estimation
because the associated error can be unnecessarily large. Instead estimates are
derived from ensemble averages such as the sample covariance. To bridge the gap
between these two approaches, the Fisher information for the sample covariance
is examined and found to be equal to the number of independent and stationary
samples times the Fisher information for a single sample. Therefore, there are
no practical limits on parameter resolution if (1) the bound for a single sample
is finite, which is generally the case of interest, (2) a sufficiently large
populatin of independent samples can be found. The parameter resolution issue
then becomes one of determining the maximum number of such samples. This number
is set by physical variables that do not appear in the monochromatic or
instantaneous measurement. A means of determining this number from the temporal
coherence of the received field and the measurement time is given.