Uncertainty-aware estimation, planning, and control for tracking multiple drifting patches in flow fields

In this study, we present a replay-based framework for uncertainty-aware persistent tracking of multiple advected surface patches using an autonomous marine vehicle operating in spatiotemporal-varying currents. The method combines three components: local flow estimation, covariance-aware patch-boundary propagation with intermittent boundary fusion, and mission-level scheduling over multiple patches. Each patch is represented by a polygonal boundary, whose vertices are propagated through the estimated flow field while carrying per-vertex covariance, thereby quantifying uncertainty growth during advection. A flow-aware gain-scheduled linear quadratic regulator (LQR) was designed to shape the desired surge speed to take advantage of favorable currents. When the vehicle services a patch, boundary detections are fused to reduce the active patch uncertainty, and optional local map-covariance refinement is used to reduce subsequent uncertainty regrowth in the surrounding flow field. A boundedness analysis shows that if each patch is revisited within a prescribed maximum interval, then the corresponding patch uncertainty remains uniformly bounded; a companion feasibility condition relates the allowable revisit interval to vehicle speed, service time, and tour length over the patch set. To validate the result, a data replay simulation using HF-radar currents from the San Francisco Bay region was used to demonstrate the expected bounded sawtooth uncertainty behavior under feasible revisit conditions. In addition, our proposed duration-weighted predictive scheduler outperforms nearest-patch and round-robin baselines and, in spatially separated patch configurations, achieves lower mean patch uncertainty and lower control-effort proxy than a highest-J baseline. These results indicate that combining uncertainty-aware propagation with cost-aware scheduling is a viable strategy for persistent monitoring of evolving marine surface phenomena.