Data-Driven Planning Phase of Maritime SAR Using Satellite Observations

Maritime search and rescue operations rely on accurate drift predictions to define effective search areas for missing persons. Existing systems often depict uncertainty using statistical ellipses or ensemble-based probability maps, which may not effectively capture directional biases and underlying flow structures. In this study, we introduce a geometric framework that constructs possible object trajectories directly from the drift dynamics. Starting from the last known position, we integrate the translational and rotational drift components with arbitrary perturbations to model realistic scenarios. The resulting envelope of the trajectories defines a reachable set that adapts to the flow without relying on sampling or covariance estimations. Using satellite-derived wind and current data, we demonstrat that this approach produces envelopes that are physically consistent and operationally relevant. Our method offers a mathematically grounded alternative to ensemble techniques, enhancing interpretability and improving the SAR planning efficiency. We illustrate its effectiveness with examples that simulate real-world scenarios.