Multi-vehicle control and optimization for spatiotemporal sampling

In this paper we analyze the mapping accuracy of a sensor network using a quantitative measure of the mapping error as performance metric. We use optimal interpolation to calculate the estimation error of a map of a spatiotemporal field produced by assimilating observations collected by a group of vehicles. The vehicles travel in a closed trajectory in a steady, uniform flowfield. The mapping error is analyzed for statistically homogeneous fields and for inhomogeneous fields in which the correlation coefficient depends on position. For the homogeneous field, we design a closed-loop speed controller to minimize the average mapping error and, for the inhomogeneous field, we introduce an artificial flowfield to minimize a convex combination of the average error and maximum error.