Towards Optimal Sensor Trajectory for Flow Reconstruction

Decades of research have optimized the placement of a sparse set of sensors in a flow for reconstruction, yet very little research exists on how to move those sensors if they could be actively steered. Such mobile sensors can track evolving structures that static (Eulerian) or passively advected (Lagrangian) sensors miss, resulting in sharper low‑order reconstructions. We generalize Proper Orthogonal Decomposition with QR pivoting (POD‑QR) from a static placement rule into a real‑time trajectory planner: each time window selects the most informative measurement points, and a particle‑tracking‑velocimetry algorithm steers the sensors toward them. Tests on Lamb–Oseen vortex, double‑gyre advection, Kolmogorov turbulence, and cylinder vortex shedding show that these "moving POD‑QR" sensors consistently outperform both Eulerian and Lagrangian strategies at practical sensor counts. By repurposing classical sensor placement theory, this framework provides a clear benchmark for real-time flow reconstruction and lays the groundwork for future feedback-based flow control using mobile sensors.