Optimal Configuration of Alarm Sensors for Monitoring Mobile Ergodic Markov Phenomena on Arbitrary Graphs

Motivated by persistent monitoring tasks, this paper considers the placement of alarm sensors incapable of long-distance communication on arbitrary graphs and the selection of the rates of their revisits (by an external agent) to monitor a mobile phenomenon whose movements occur on a graph and are modeled as an ergodic Markov chain. The alarm sensors can be placed on nodes and edges in the graph and act as both sensors and classifiers (i.e., they make a classification decision about the presence of the phenomenon based on a measurement of their surroundings). An approach to design the classifier for each alarm sensor is provided and methods to fuse the measurements of colocated alarm sensors are given. Sensor placement problems to optimize Fisher information, probability of misclassification, or the penalty incurred by poor detections, missed detections, and false alarms are formulated. Approaches to solve the formulated problems for the different optimization criteria are provided. Characteristics of these approaches are described and their merits are discussed. The sensors' revisit rates are selected by matching the recurrence times of the phenomenon at the sensor locations. The different approaches are illustrated through simulations.