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| {{one source|date=January 2014}}
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| '''Swerling models''' were introduced by [[Peter Swerling]] and are used to describe the statistical properties of the [[radar cross-section]] of complex objects.
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| ==General Target Model==
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| Swerling target models give the radar cross-section (RCS) of a given object using a distribution in the location-scale family of the [[chi-squared distribution]].
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| :<math>p(\sigma) = \frac{m}{\Gamma(m) \sigma_{av}} \left ( \frac{m\sigma}{\sigma_{av}} \right )^{m - 1} e^{-\frac{m\sigma}{\sigma_{av}}}
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| I_{[0,\infty)}(\sigma)</math>
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| where <math>\sigma_{av}</math> refers to the [[mean]] value of <math>\sigma</math>. 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. <math>m</math> is the [[Degrees of freedom (statistics)|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 <math>m</math> between 0.3 and 2 have been found to closely approximate certain simple shapes, such as cylinders or cylinders with fins.
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| Since the ratio of the standard deviation to the mean value of the chi-squared distribution is equal to <math>m</math><sup>-1/2</sup>, larger values of <math>m</math> will result in smaller fluctuations. If <math>m</math> equals infinity, the target's RCS is non-fluctuating.
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| ==Swerling Target Models==
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| '''Swerling target models''' are special cases of the Chi-Squared target models with specific degrees of freedom. There are five different Swerling models, numbered I through V:
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| ===Swerling I===
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| A model where the RCS varies according to a Chi-squared probability density function with two degrees of freedom (<math>m = 1</math>). This applies to a target that is made up of many independent scatterers of roughly equal areas. As little as half a dozen scattering surfaces can produce this distribution. Swerling I describes a target whose radar cross-section is constant throughout a single scan, but varies independently from scan to scan. In this case, the pdf reduces to
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| :<math>p(\sigma) = \frac{1}{\sigma_{av}} e^{-\frac{\sigma}{\sigma_{av}}}</math> | |
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| Swerling I has been shown to be a good approximation when determining the RCS of objects in aviation.
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| ===Swerling II===
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| Similar to Swerling I, except the RCS values returned are independent from pulse to pulse, instead of scan to scan.
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| ===Swerling III===
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| A model where the RCS varies according to a Chi-squared probability density function with four degrees of freedom (<math>m = 2</math>). This PDF approximates an object with one large scattering surface with several other small scattering surfaces. The RCS is constant through a single scan just as in Swerling I. The pdf becomes
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| :<math>p(\sigma) = \frac{4\sigma}{\sigma_{av}^2} e^{-\frac{2\sigma}{\sigma_{av}}}</math>
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| ===Swerling IV===
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| Similar to Swerling III, but the RCS varies from pulse to pulse rather than from scan to scan.
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| ===Swerling V (Also known as Swerling 0)===
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| Constant RCS (<math>m\to\infty</math>).
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| also known as infinite degree of freedom
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| ==References==
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| * Skolnik, M. Introduction to Radar Systems: Third Edition. McGraw-Hill, New York, 2001.
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| [[Category:Signal processing]]
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| [[Category:Radar]]
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