Optimal linear tracking for a hidden target on one of K-intervals

In this paper, we consider one of the most important missing target search problems, in which the bounded linear search interval has been divided into a number of small sub-intervals. The probability of the target was calculated in each sub-interval through the distribution function of the target position; after truncation, the sub-intervals with a low probability of the target being present were removed. After that, the problem was transformed into a discrete search problem where the target resides in one of a set of sub-intervals. This problem has been solved to obtain the minimum effort required for target detection, where this effort is limited by a normal distribution. In addition, we obtain the maximum value of the target detection probability and also study the stability of the minimum search effort. Finally, we present an example to show the effectiveness and applicability of our model.