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Proceedings Paper

The heavy tailed distribution of a common CFAR detector
Author(s): Paul Frank Singer; Doreen M. Sasaki
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Paper Abstract

A CFAR detector commonly used for the detection of unresolved targets normalizes the background variance by dividing the detection filter output by the local sample standard deviation. A number of researchers have measured the experimental false alarm probability of this detector and found it to be higher than the probability predicted by a Gaussian density function. This is the case even when the filter output statistics are known to be Gaussian distributed. A number of attempts have been made to heuristically construct distributions which exhibit the heavy tails associated with the measured false alarm probability (e.g. sum of two Gaussian densities or the modified gamma density). This paper presents a first principle derivation of the detector false alarm density function based upon the assumption that the filter output is Gaussian distributed. The resulting false alarm density function is very nearly Gaussian out to about 3.5 standard deviations. Past 3.5 standard deviations the tails of the derived density function are markedly heavier than the corresponding Gaussian tails. The parameters of this new density function are easily estimated from the filter outputs. The analytic results are validated using a Chi-Square goodness-of-fit test and experimental measurements of the false alarm density.

Paper Details

Date Published: 1 September 1995
PDF: 17 pages
Proc. SPIE 2561, Signal and Data Processing of Small Targets 1995, (1 September 1995); doi: 10.1117/12.217699
Show Author Affiliations
Paul Frank Singer, Hughes Aircraft Co. (United States)
Doreen M. Sasaki, Hughes Aircraft Co. (United States)

Published in SPIE Proceedings Vol. 2561:
Signal and Data Processing of Small Targets 1995
Oliver E. Drummond, Editor(s)

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