Data fusion and optimal placement of fixed and mobile sensors

Modern technology can equip small devices (like mobile phones) with sensing-capabilities for various threats, offering a mobile, 'opportunistic' pool of secondary sensors that can be polled to augment the information provided by a pre-deployed set of primary sensors, to reduce uncertainty in threat-detection. We derive an optimal decision-rule for fusing the information from fixed and mobile, accounting for the costs of erroneous decisions. We also formulate a model for an 'equitable' solution to the problem of the optimal positioning of sensors.