Nicholas C. Makris
Naval Res. Lab., Washington, DC 20375
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.