Peter Swerling
Encyclopedia
Peter Swerling was one of the most influential radar
theoreticians in the second half of the 20th century. He is best known for the class of statistically "fluctuating target" scattering models he developed at the RAND Corporation in the early 1950s to characterize the performance of pulsed radar systems, referred to as Swerling Target I, II, III, and IV in the literature of radar. He also made significant contributions to the optimal estimation orbits and trajectories of satellites and missiles, later refined by Rudolph Kalman as the Kalman filter
.
in Mathematics
from the California Institute of Technology
in 1947 and a B.A.
in Economics
from Cornell in 1949. He then attended the University of California, Los Angeles
, where he received an M.A.
in Mathematics in 1951 and a Ph.D.
in Mathematics in 1955. His thesis Families of Transformations in the Function Spaces H^p was advised by Angus Taylor, and investigated families of bounded linear transformations in Banach spaces.
Also known as Swerling Case V (5), is no fluctuation.
Swerling Case 1 (or i)
Represent constant gain within the hit in the scan but varies from scan to scan with no correlation
Swerling Case 2 (or ii)
Represent fluctuation from pulse to pulse as well as scan to scan
The PDF for Case 1 and 2 is
PDF{…} = ( 1 / RCS ) * exp( -{0…..} / RCS)
Where:
RCS = mean(Sigma values)
Swerling Case 3 (or iii)
Swerling Case 3 is the same as Swerling Case 1 but has "a" dominating reflective surface
Swerling Case 4 (or iv)
Swerling Case 4 is the same as Swerling Case 2 but has "a" dominating reflective surface
The PDF for Case 3 and 4 is
PDF{…} = ( (4 * {0…..} ) / RCS^2 ) * exp( (-2 * {0…..}) / RCS)
Where:
RCS = mean(Sigma values)
Swerling Case 5 (or v)
See Swerling case 0
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
theoreticians in the second half of the 20th century. He is best known for the class of statistically "fluctuating target" scattering models he developed at the RAND Corporation in the early 1950s to characterize the performance of pulsed radar systems, referred to as Swerling Target I, II, III, and IV in the literature of radar. He also made significant contributions to the optimal estimation orbits and trajectories of satellites and missiles, later refined by Rudolph Kalman as the Kalman filter
Kalman filter
In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...
.
Education
Peter Swerling received a B.S.Bachelor of Science
A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...
in Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from the California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
in 1947 and a B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in Economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
from Cornell in 1949. He then attended the University of California, Los Angeles
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
, where he received an M.A.
Master of Arts (postgraduate)
A Master of Arts from the Latin Magister Artium, is a type of Master's degree awarded by universities in many countries. The M.A. is usually contrasted with the M.S. or M.Sc. degrees...
in Mathematics in 1951 and a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in Mathematics in 1955. His thesis Families of Transformations in the Function Spaces H^p was advised by Angus Taylor, and investigated families of bounded linear transformations in Banach spaces.
Entrepreneurship
In 1966, Peter Swerling founded Technology Service Corporation (TSC). TSC currently has nationwide operations with 2010 sales of over $83M. In 1983, he co-founded Swerling Manassee and Smith, Inc., of Canoga Park, California, and served as its president and CEO from 1986 until his retirement in 1998.Swerling Targets
Swerling Case 0Also known as Swerling Case V (5), is no fluctuation.
Swerling Case 1 (or i)
Represent constant gain within the hit in the scan but varies from scan to scan with no correlation
Swerling Case 2 (or ii)
Represent fluctuation from pulse to pulse as well as scan to scan
The PDF for Case 1 and 2 is
PDF{…} = ( 1 / RCS ) * exp( -{0…..} / RCS)
Where:
RCS = mean(Sigma values)
Swerling Case 3 (or iii)
Swerling Case 3 is the same as Swerling Case 1 but has "a" dominating reflective surface
Swerling Case 4 (or iv)
Swerling Case 4 is the same as Swerling Case 2 but has "a" dominating reflective surface
The PDF for Case 3 and 4 is
PDF{…} = ( (4 * {0…..} ) / RCS^2 ) * exp( (-2 * {0…..}) / RCS)
Where:
RCS = mean(Sigma values)
Swerling Case 5 (or v)
See Swerling case 0
External links
- Rand reports authored by Peter Swerling, Rand Corporation
- Papers authored by Peter Swerling, Scientific Commons
- Peter Swerling obituary and biography, SIAM
- Peter Swerling obituary and biography, American Institute of Physics (via Archive.org)
- Mathematics Genealogy Project profile