Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T01:46:05.509Z Has data issue: false hasContentIssue false
  • English
  • Français

Search for a moving target under minimax estimation

Published online by Cambridge University Press:  14 July 2016

Thomas L. Corwin
Thomas L. Corwin*
Affiliation:
Daniel H. Wagner, Associates
*
∗Postal address: Daniel H. Wagner, Associates, Station Square One, Paoli, PA 19301, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A target is assumed to choose its starting position in a search at an unknown position in a finite search space. No prior probability distribution for the target's initial location is assumed. During the search the target is assumed to move from position to position in the search space according to a Markov process. A search is defined to be the observation of a sequence of random variables. Representations for the minimax estimator for target location at any stage of the search, the least favorable prior distribution for the target, and the value of the estimation game are presented. An example is computed in which Bayes estimators are compared with minimax estimators for target location.

Keywords

SEARCHMOVING TARGETMINIMAX ESTIMATORBAYES ESTIMATOR
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 167 - 180
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research carried out under ONR Contract N00014–77–C–0511.

References

[1] Alpern, S. (1974) The search game with mobile hider on the circle. In Differential Games and Control Theory, Dekker, New York, 181–200.Google Scholar
[2] Brown, S. S. (1981) Optimal search for a moving target in discrete space and time. Operat. Res. To appear.Google Scholar
[3] Gal, S. (1972) A general search game. Israel J. Math. 12, 32–45.Google Scholar
[4] Hellman, O. B. (1970) On the effect of search upon the probability distribution of a target whose motion is a diffusion process. Ann. Math. Statist. 41, 1717–1724.Google Scholar
[5] Isaacs, R. (1965) Differential Games. Wiley, New York.Google Scholar
[6] Lukka, M. (1977) On the optimal searching tracks for a moving target, SIAM J. Appl. Math. 32, 126–132.Google Scholar
[7] Pursiheimo, U. (1977) On the optimal search for a target whose motion is conditionally deterministic with stochastic initial conditions on location and parameters. SIAM J. Appl. Math. 32, 126–132.Google Scholar
[8] Saretsalo, L. (1973) On the optimal search for a target whose motion is a Markov process. J. Appl. Prob. 10, 847–856.Google Scholar
[9] Stone, L. D. (1977) Search for targets with generalized conditionally deterministic motion. SIAM J. Appl. Math. 33, 456–468.CrossRefGoogle Scholar
[10] Stone, L. D. (1979) Necessary and sufficient conditions for optimal search for moving targets. Math. Operat. Res. 4, 431–440.Google Scholar
[11] Stone, L. D., Brown, S. S., Buemi, R. P. and Hopkins, C. R. (1978) Numerical optimization of search for a moving target. Daniel H. Wagner, Associates Report to the Office of Naval Research.CrossRefGoogle Scholar
[12] Von Neumann, J. and Morgenstern, O. (1953) Theory of Games and Economic Behaviour. Princeton University Press.Google Scholar