Performance of Stochastically Intermittent Sensors in Detecting a Target Traveling between Two Areas

Abstract

We study the problem of detecting a target that moves between a hiding area and an operating area over multiple fixed routes. The research is carried out with one or more cookie-cutter sensors with stochastic intermission, which turn on and off stochastically governed by an on-rate and an off-rate. A cookie-cutter sensor, when it is on, can detect the target instantly once the target comes within the detection radius of the sensor. In the hiding area, the target is shielded from being detected. The residence times of the target, respectively, in the hiding area and in the operating area, are exponentially distributed and are governed by rates of transitions between the two areas. On each travel between the two areas and in each travel direction, the target selects a route randomly according to a probability distribution. Previously, we analyzed the simple case where the sensors have no intermission (i.e., they stay on all the time). In the current study, the sensors are stochastically intermittent and are synchronized (i.e., they turn on or off simultaneously). This happens when all sensors are affected by the same environmental factors. We derive asymptotic expansions for the mean time to detection when the on-rate and off-rate of the sensors are large in comparison with the rates of the target traveling between the two areas. Based on the mean time to detection, we evaluate the performance of placing the sensor(s) to monitor various travel route(s) or to scan the operating area.

Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

“…Wang and Zhou conducted numerical studies to calculate the non-detection probability of a randomly moving target by a stationary or moving searcher in a square search region [21]. They also considered the search problem where a target moves between a hiding area and an operating area via multiple pathways where the searchers are equipped with either cookie-cutter sensors [22] or stochastically intermittent sensors [23]. In contrast, the two-sided search problem is traditionally addressed by formulating the problem as a game-theory problem [24] [25].…”