An investigation of the concepts of purposeful searches
Norman Thomas Saunders, Harald Ziehms · 1972
A discrete-time discrete-space search model is considered in which an observer employing an idealized detection device is searching for a uniformly distributed stationary target. The model is formulated as a discretetime counting process, called the search process, which under weak additional conditions is uniquely determined by a sequence of probabilities. Formulas for the timeto-detection and the detection rate of a search are derived in terms of the parameters of the search process, and are applied to two special types of searches, the systematic search and the random search. Using these search types as boundary cases a purposeful search is defined, and sufficient conditions on the sequence of probabilities are established for the purposeful search. Possible extensions of the search process to less restricted models are indicated.