Chi-squared Target Models - General Target Model

General Target Model

Swerling target models give the RCS of a given object using a distribution in the location-scale family of the chi-squared distribution.

p(\sigma) = \frac{m}{\Gamma(m) \sigma_{av}} \left ( \frac{m\sigma}{\sigma_{av}} \right )^{m - 1} e^{-\frac{m\sigma}{\sigma_{av}}} I_{[0,\infty)}(\sigma)

where refers to the mean value of . This is not always easy to determine, as certain objects may be viewed the most frequently from a limited range of angles. For instance, a sea-based radar system is most likely to view a ship from the side, the front, and the back, but never the top or the bottom. is the degree of freedom divided by 2. The degree of freedom used in the chi-squared probability density function is a positive number related to the target model. Values of between 0.3 and 2 have been found to closely approximate certain simple shapes, such as cylinders or cylinders with fins.

Since the ratio of the standard deviation to the mean value of the chi-squared pdf is equal to -1/2, larger values of will result in less fluctuations. If equals infinity, the target's RCS is non-fluctuating.

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