Optimal Sampling of Nonstationary Spatiotemporal Fields Using a Mobile Sensor Network*

This paper provides a decentralized control algorithm for multiple autonomous vehicles to sample environmental quantities on closed paths. We present a multi-vehicle control algorithm that samples a nonstationary spatiotemporal field using optimal interpolation to evaluate the sampling performance. The control algorithm leverages a coordinate transformation under which uniform sampling is optimal, because the unknown field is stationary in the new coordinates. The algorithm regulates the spacing between vehicles in order to limit the local maximum mapping error of the field reconstruction and preserves the steady-state vehicle sampling speed, which is a nondimensional measure of vehicle speed scaled by the spatial and temporal decorrelation lengths of the field at the vehicles location. The sampling performance is illustrated using a numerical simulation in a hypothetical environmental field.