Chi-squared 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.

1 General Target Model
2 Swerling Target Models
3 References

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 $σ a v$ refers to the mean value of $σ$ . 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 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 $m$ 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 $m$ ^-1/2, larger values of $m$ will result in less fluctuations. If $m$ equals infinity, the target's RCS is non-fluctuating.

Swerling Target Models

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:

Swerling I

A model where the RCS varies according to a Chi-squared 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.

Swerling II

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

Swerling III

A model where the RCS varies according to a Chi-squared 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

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

Swerling IV

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

Swerling V (Also known as Swerling 0)

Constant RCS ( $m\to\infty$ ).

References

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

Categories:

Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

Chi-squared — In statistics, the term chi squared has different uses: chi squared distribution, a continuous probability distribution; chi squared statistic, a statistic used in some statistical tests; chi squared test, name given to some tests using chi… … Wikipedia
Species distribution — A species range maps represents the geographical region where individuals of a species can be found. This is a range map of Juniperus communis, the common juniper. Species distribution is the manner in which a biological taxon is spatially… … Wikipedia
Kullback–Leibler divergence — In probability theory and information theory, the Kullback–Leibler divergence[1][2][3] (also information divergence, information gain, relative entropy, or KLIC) is a non symmetric measure of the difference between two probability distributions P … Wikipedia
Control chart — One of the Seven Basic Tools of Quality First described by Walter A. Shewhart … Wikipedia
Regression toward the mean — In statistics, regression toward the mean (also known as regression to the mean) is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on a second measurement, and a fact that may… … Wikipedia
Decision tree learning — This article is about decision trees in machine learning. For the use of the term in decision analysis, see Decision tree. Decision tree learning, used in statistics, data mining and machine learning, uses a decision tree as a predictive model… … Wikipedia
Official statistics — on Germany in 2010, published in UNECE Countries in Figures 2011. Official statistics are statistics published by government agencies or other public bodies such as international organizations. They provide quantitative or qualitative information … Wikipedia
Sample size determination — is the act of choosing the number of observations to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample … Wikipedia
Data collection — is a term used to describe a process of preparing and collecting data, for example, as part of a process improvement or similar project. The purpose of data collection is to obtain information to keep on record, to make decisions about important… … Wikipedia
Hash table — Not to be confused with Hash list or Hash tree. Unordered map redirects here. For the proposed C++ class, see unordered map (C++). Hash Table Type unsorted dictionary Invented 1953 Time complexity in big O notation Average Worst case Space … Wikipedia

Academic Dictionaries and Encyclopedias

Chi-squared target models

Contents

General Target Model