Parameter Resolution Bounds that Depend on Sample Size

Abstract

It is currently common practice in theoretical ocean acoustics to derive parameter resolution bounds for a monochromatic measurement of the temporally fluctuating field received by 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 shown 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 population 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 presented.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1996
Accession Number
ADA640528

Entities

People

  • Nicholas C. Makris

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Sensors

DTIC Thesaurus Topics

  • Acoustic Tomography
  • Acoustic Waves
  • Acoustics
  • Data Science
  • Detection
  • Detectors
  • Frequency
  • Information Processing
  • Information Science
  • Internal Waves
  • Measurement
  • Pattern Recognition
  • Probability
  • Probability Distributions
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Readers

  • Acoustical Oceanography.
  • Image Processing and Computer Vision.
  • Regression Analysis.