On Minimal Trajectories for Mobile Sampling of Bandlimited Fields

摘要: We study the design of sampling trajectories for stable and reconstruction bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As performance metric we use path density set that defined as total distance traveled by moving sensors per unit volume region being monitored. Focusing first on parallel lines, identify lines with minimal contains known then show problem becomes ill posed when optimization performed over all demonstrating feasible trajectory arbitrarily low density. However, well-posed if explicitly specify stability margins. demonstrate this obtaining non-trivial lower bound an arbitrary contain specified bounds.