Description
Sensor Placement for Spatial Gaussian Processes with Integral Observations
Krista Longi (Univeristy of Helsinki)*; Chang Rajani (University of Helsinki); Tom Sillanpää (University of Helsinki); Joni Mäkinen (University of Helsinki); Timo Rauhala (Altum Technologies); Ari Salmi (University of Helsinki); Edward Haeggström (University of Helsinki); Arto Klami (University of Helsinki)
Gaussian processes (GP) are a natural tool for estimating unknown functions, typically based on a collection of point-wise observations. Interestingly, the GP formalism can be used also with observations that are integrals of the unknown function along some known trajectories, which makes GPs a promising technique for inverse problems in a wide range of physical sensing problems. However, in many real world applications collecting data is laborious and time consuming. We provide tools for optimizing sensor locations for GPs using integral observations, extending both model-based and geometric strategies for GP sensor placement. We demonstrate the techniques in ultrasonic detection of fouling in closed pipes.