In the military science of ballistics, circular error probable (CEP)
(also circular error probability or circle of equal probability[1]) is
a measure of a weapon system's precision. It is defined as the radius
of a circle, centered on the mean, whose boundary is expected to
include the landing points of 50% of the rounds.[2][3] That is, if a
given bomb design has a CEP of 100 metres (330 ft), when 100 are
targeted at the same point, 50 will fall within a 100 m circle
around their average impact point. (The distance between the target
point and the average impact point is referred to as bias.)
Contents 1 Concept 2 Conversion between CEP, DRMS, 2DRMS, and R95 3 Use in popular culture 4 See also 5 References 6 Further reading 7 External links Concept[edit] 20 hits distribution example The original concept of CEP was based on a circular bivariate normal
distribution (CBN) with CEP as a parameter of the CBN just as μ and
σ are parameters of the normal distribution. Munitions with this
distribution behavior tend to cluster around the mean impact point,
with most reasonably close, progressively fewer and fewer further
away, and very few at long distance. That is, if CEP is n metres, 50%
of rounds land within n metres of the mean impact, 43.7% between n and
2n, and 6.1% between 2n and 3n metres, and the proportion of rounds
that land farther than three times the CEP from the mean is only 0.2%.
CEP is not a good measure of accuracy when this distribution behavior
is not met. Precision-guided munitions generally have more "close
misses" and so are not normally distributed. Munitions may also have
larger standard deviation of range errors than the standard deviation
of azimuth (deflection) errors, resulting in an elliptical confidence
region.
Measure Probability (%) Distance root mean square (DRMS) 63 to 68 Circular error probability (CEP) 50 Twice the distance root mean square (2DRMS) 95 to 98 95% radius (R95) 95 From/to CEP DRMS R95 2DRMS CEP – 1.2 2.1 2.4 DRMS 0.83 – 1.7 2.0 R95 0.48 0.59 – 1.2 2DRMS 0.42 0.5 0.83 – Use in popular culture[edit] The term is used in the movie Clear and Present Danger when the ground team reports "Circlar error probability Zero. Impact with high order detonation. Have a nice day." Here CEP is meant to convey that the bomb landed exactly on target.[citation needed] See also[edit] Hoyt distribution Probable error References[edit] ^ Nelson, William (1988). "Use of Circular Error Probability in Target Detection" (PDF). Bedford, MA: The MITRE Corporation; United States Air Force. Ehrlich, Robert (1985). Waging Nuclear Peace: The Technology and Politics of Nuclear Weapons. Albany, NY: State University of New York Press. p. 63. ^ Circular Error Probable (CEP), Air Force Operational Test and Evaluation Center Technical Paper 6, Ver 2, July 1987, p. 1 ^ Payne, Craig, ed. (2006). Principles of Naval Weapon Systems. Annapolis, MD: Naval Institute Press. p. 342. ^ a b Frank van Diggelen, "GNSS Accuracy – Lies, Damn Lies and Statistics", GPS World, Vol 18 No. 1, January 2007. Sequel to previous article with similar title [1] [2] ^ Frank van Diggelen, "GPS Accuracy: Lies, Damn Lies, and Statistics", GPS World, Vol 9 No. 1, January 1998 Further reading[edit] Blischke, W. R. and Halpin, A. H. (1966). "Asymptotic properties of some estimators of quantiles of circular error." Journal of the American Statistical Association, vol. 61 (315), pp. 618–32. JSTOR MacKenzie, Donald A. (1990). Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance. Cambridge, MA: MIT Press. ISBN 978-0-262-13258-9. Grubbs, F. E. (1964). "Statistical measures of accuracy for riflemen and missile engineers". Ann Arbor, ML: Edwards Brothers. Ballistipedia pdf Spall, J. C. and Maryak, J. L. (1992). "A feasible Bayesian estimator of quantiles for projectile accuracy from non-iid data." Journal of the American Statistical Association, vol. 87 (419), pp. 676–81. JSTOR pdf Daniel Wollschläger (2014), "Analyzing shape, accuracy, and precision of shooting results with shotGroups". Reference manual for shotGroups Winkler, V. and Bickert, B. (2012). "Estimation of the circular error probability for a Doppler-Beam-Sharpening-Radar-Mode," in EUSAR. 9th European Conference on Synthetic Aperture Radar, pp. 368–71, 23/26 April 2012. ieeexplore.ieee.org External links[edit] Circular Error Probable in B |