Chi-square target models

Swerling models were introduced by Peter Swerling and are used to describe the statistical properties of the radar cross-section of complex objects.

General Target Model

Swerling target models give the RCS of a given object based on the chi-square probability density function, which has the following form:

:p(sigma) = frac{m}{Gamma(m) sigma_{av left ( frac{msigma}{sigma_{av ight )^{m - 1} e^{-frac{msigma}{sigma_{av}

sigma_{av} refers to the mean value of sigma. 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. m is the number of degrees of freedom divided by 2. While the number of degrees of freedom used in the chi-square probability density function is an integer value in statistics, it can assume any positive real number in the target model. Values of m between .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-square pdf is equal to m-1/2, larger values of m will result in less fluctuations. If m equals infinity, the target's RCS is non-fluctuating.

werling Target Models

Swerling target models are special cases of the Chi-Square target models with specific degrees of freedom. There are five different Swerling models, numbered I through V:

werling I

A model where the RCS varies according to a Chi-square probability density function with two degrees of freedom (m = 1). 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

:p(sigma) = frac{1}{sigma_{av e^{-frac{sigma}{sigma_{av}

Swerling I has been shown to be a good approximation when determining the RCS of objects in aviation.

werling II

Similar to Swerling I, except the RCS values returned are independent from pulse to pulse, instead of scan to scan.

werling III

A model where the RCS varies according to a Chi-square probability density function with four degrees of freedom (m = 2). 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

:p(sigma) = frac{4sigma}{sigma_{av}^2} e^{-frac{2sigma}{sigma_{av}

werling IV

Similar to Swerling III, but the RCS varies from pulse to pulse rather than from scan to scan.

werling V (Also known as Swerling 0)

Constant RCS (m o infinity).


* Skolnik, M. Introduction to Radar Systems: Third Edition. McGraw-Hill, New York, 2001.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Ho Chi Minh trail — Infobox Military Structure name=Ho Chi Minh Trail location=Southeastern Laos caption= The Ho Chi Minh Trail, 1967 type=Logistical system built=1959 1975 in use=1959 1975 controlledby=People s Army of Vietnam garrison=5,000 60,000 commanders=Vo… …   Wikipedia

  • Peter Swerling — Infobox Scientist name = Peter Swerling caption = birth date = birth date|1942|8|15 birth place = New York City, New York death date = death date and age|2000|8|25|1929|3|4 death place = Pacific Palisades, California residence = United States… …   Wikipedia

  • Radar cross section — (RCS) is a measure of how detectable an object is with a radar. For example a stealth aircraft (which is designed to be undetectable) will have design features that give it a low RCS, as opposed to a passenger airliner that will have a high… …   Wikipedia

  • china — /chuy neuh/, n. 1. a translucent ceramic material, biscuit fired at a high temperature, its glaze fired at a low temperature. 2. any porcelain ware. 3. plates, cups, saucers, etc., collectively. 4. figurines made of porcelain or ceramic material …   Universalium

  • China — /chuy neuh/, n. 1. People s Republic of, a country in E Asia. 1,221,591,778; 3,691,502 sq. mi. (9,560,990 sq. km). Cap.: Beijing. 2. Republic of. Also called Nationalist China. a republic consisting mainly of the island of Taiwan off the SE coast …   Universalium

  • arts, East Asian — Introduction       music and visual and performing arts of China, Korea, and Japan. The literatures of these countries are covered in the articles Chinese literature, Korean literature, and Japanese literature.       Some studies of East Asia… …   Universalium

  • international relations — a branch of political science dealing with the relations between nations. [1970 75] * * * Study of the relations of states with each other and with international organizations and certain subnational entities (e.g., bureaucracies and political… …   Universalium

  • japan — japanner, n. /jeuh pan /, n., adj., v., japanned, japanning. n. 1. any of various hard, durable, black varnishes, originally from Japan, for coating wood, metal, or other surfaces. 2. work varnished and figured in the Japanese manner. 3. Japans,… …   Universalium

  • Japan — /jeuh pan /, n. 1. a constitutional monarchy on a chain of islands off the E coast of Asia: main islands, Hokkaido, Honshu, Kyushu, and Shikoku. 125,716,637; 141,529 sq. mi. (366,560 sq. km). Cap.: Tokyo. Japanese, Nihon, Nippon. 2. Sea of, the… …   Universalium

  • Norden bombsight — The Norden bombsight at the Computer History Museum in Mountain View, California. This example does not have the associated autopilot attached …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.