  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.
