Abstract
Maritime accidents cause thousands of disappearances every year, with migrant crossings being particularly dangerous and under-reported. Current coastal and NGO search and rescue services are unable to provide a timely response, so new technologies such as autonomous UAVs are needed. We present a thorough formalization of the maritime search and rescue problem considering its time-critical and probabilistic nature. Further, we introduce a method for determining the optimal search altitude for any aerial thermal-based detection system, so as to maximize overall mission success.