### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 2aUW6. Fisher information for fluctuating intensity and the efficiency of
logarithmic measures.

**Nicholas C. Makris
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*Naval Res. Lab., Washington, DC 20375
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The optimal resolution of a set of parameters to be estimated from a set
of measurements of fluctuating intensity can be determined by computing the
respective Fisher information matrix. This matrix is dependent upon the
conditional distribution of the fluctuating intensity measurements, given the
parameters to be estimated. It is assumed that fluctuating intensity is
measured from circular complex Gaussian random (CCGR) fields. Such fields are
commonly measured in acoustics, optics, and radar. For example, CCGR fields
typically arise in scattering from fluctuating targets and surfaces, random
sources, and ocean-acoustic propagation scintillation. Distributions for
intensity, log-intensity, and acoustic flow (analogous to optical flow) are
derived as a function of the measurement-system averaging time and the temporal
coherence of the fluctuating field under the CCGR field assumption. (This
advances previous work in ocean-acoustic propagation scintillation that was
limited to instantaneous measurements.) It is shown that the Fisher information
for a measurement of fluctuating intensity is expressed in terms of parameter
variations over the expectation value of a logarithmic measure of intensity.
This gives a mathematical justification for the engineering intuition that
fluctuating intensity should be measured in logarithmic units to efficiently
convey information. A generalized Fisher information matrix is derived for the
estimation of parameters from intensity images.