This paper presents an optimal sampling approach to plan the optimum paths for a glider fleet. Optimal sampling has recently received considerable attention in the research community and consists in planning the paths to minimize some sampling metrics related to the phenomenon under study. Different criteria (e.g. A, G, or E optimality) used in the geosciences to obtain an optimum design lead to different sampling strategies. In particular, the A criterion produces paths for the gliders that minimize the overall level of uncertainty over the area of interest. However, there are commonly operative situations in which the marine scientists may prefer not to minimize the overall uncertainty of a certain area, but instead they may be interested in achieving an acceptable uncertainty sufficient for the scientific or operational needs of the mission. We propose and discuss here an approach named sampling on-demand that explicitly addresses this need. In our approach the user provides an objective map, setting both the amount and the geographic distribution of the uncertainty to be achieved after assimilating the information gathered by the fleet. A new optimality criterion, A_η, is introduced. The resulting optimization problem is solved by an algorithm based on Simulated Annealing producing optimum paths for the vehicles. The algorithm takes into account the constraints imposed by the glider navigation features, the desired geometric features of the paths and the problems of reachability caused by ocean currents. Ocean currents and temperature data resulted from an ocean mathematical model are used to validate the method in different scenarios in a area covering the Western Mediterranean Sea.
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