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The visibility of stationary and moving targets in the plane subject to a Poisson field of shadowing elements

  • M. Yadin (a1) and S. Zacks (a2)

Abstract

A methodology for an analytical derivation of visibility probabilities of n stationary target points in the plane is developed for the case when shadows are cast by a Poisson random field of obscuring elements. In addition, formulae for the moments of a measure of the total proportional visibility along a star-shaped curve are given.

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Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Technion City, Haifa 32000, Israel.
∗∗ Postal address: Center for Statistics, Quality Control and Design, State University of New York at Binghamton, Binghamton, NY 13901, USA.

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Research partially supported by Contract DAAGZ983K0176 with the U.S. Army Research Office.

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References

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[1] Ailam, G. (1966) Moments of coverage and coverage space. J. Appl. Prob. 3, 550555.
[2] Chernoff, H. and Daly, J. F. (1957) The distribution of shadows. J. Math. Mech. 6, 567584.
[3] Eckler, A. R. (1969) A survey of coverage problems associated with point and area targets. Technometrics 11, 561589.
[4] Feller, W. (1966) An Introduction to Probability Theory and Its Applications , Vol. II, 2nd edn. Wiley, New York.
[5] Greenberg, I. (1980) The moments of coverage of a linear set. J. Appl. Prob. 17, 865868.
[6] Likhterov, Ya. ?. and Gurin, L. S. (1966) The probability of interval overlap by a system of random intervals (in Russian). Engineering Cybernetics 4, 4555.
[7] Robbins, H. E. (1944) On the measure of random sets. Ann. Math. Statist. 15, 7074.
[8] Robbins, H. E. (1945) On the measure of random sets, II. Ann. Math. Statist. 16, 342347.
[9] Siegel, A. F. (1978) Random space filling and moments of coverage in geometric probability. J. Appl. Prob. 15, 340355.
[10] Siegel, A. F. (1978) Random arcs on the circle. J. Appl. Prob. 15, 774789.
[11] Solomon, H. (1978) Geometric Probability. SIAM, Philadelphia.
[12] Yadin, M. and Zacks, S. (1982) Random coverage of a circle with applications to a shadowing problem. J. Appl. Prob. 19, 562577.
[13] Yadin, M. and Zacks, S. (1984) The distribution of measures of visibility on line segments in three dimensional spaces under Poisson shadowing processes.
[14] Zacks, S. and Yadin, M. (1984) The distribution of the random lighted portion of a curve in a plane shadowed by a Poisson random field of obstacles. In Statistical Signal Processing , ed. Wegman, E. J. and Smith, J. G., Marcel Dekker, New York, 273286.

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