Toward Near-Optimal and Scalable Placement and Orientation of Directional Sensors for Stochastic Directional Trajectory Detection

Directional sensors are widely used to monitor moving targets, yet conventional placement methods often represent targets as spatial points or overlook the coupling among sensor location, orientation, and target travel direction. This paper develops a theoretically grounded and scalable framework for joint placement and orientation of directional sensors for stochastic directional-trajectory detection. Directed trajectories are represented by heading and signed perpendicular offset, preserving opposite travel directions along the same geometric path, and their stochastic occurrence is formulated through an intensity model that can be represented using a log-Gaussian Cox process. Sensor performance is evaluated at the trajectory level by incorporating directional field-of-view geometry, distance-dependent detection probability, sensing frequency, dwell time, and repeated sensing opportunities. Network performance is quantified through missed-trajectory intensity and a corresponding void-probability objective. To improve computational efficiency, we introduce a dwell-time-aware binary sensing surrogate with deployment-aware radius calibration and an omni-greedy algorithm that ranks locations using an omnidirectional surrogate before orientation refinement. Theoretical analysis provides bounds on sensing approximation error, greedy decision preservation, location–orientation approximation, and end-to-end deployment performance. Experiments using real maritime AIS and wildlife GPS trajectories show that omni-greedy reduces selection-stage candidate evaluations by roughly 18–21× while maintaining detection performance close to full directional greedy optimization; when candidate responses are cached, total planning time is dominated by shared precomputation and radius calibration.