Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 151598, 8 pages
http://dx.doi.org/10.1155/2013/151598
Research Article

Parabolic Spiral Search Plan for a Randomly Located Target in the Plane

Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Received 14 May 2013; Accepted 12 September 2013

Academic Editors: D. Bahuguna and A. M. Peralta

Copyright © 2013 Mohamed Beltagy and Mohamed Abd Allah El-Hadidy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper addresses the problem of searching for a located target in the plane by using one searcher starting its motion from the point . The searcher moves along parabolic spiral curve. The position of the target has a known distribution. We show that the distance between the target position and the searcher starting point depends on the number of revolutions, where the complete revolution is done when . Furthermore, we study this technique in the one-dimensional case (i.e., when the searcher moves with linear search technique). It is desired to get the expected value of the time for detecting the target. Illustrative examples are given to demonstrate the applicability of this technique assuming circular normal distributed estimates of the target position.