Estimation of spatial fields using asymptotic embedding methods and Lagrangian sensing

This paper proposes a new method for estimating spatial fields using moving and fixed-in-space sensing devices. It is assumed that the spatial field can be generated as the state of an elliptic partial differential equation and an on-line state estimator is proposed that takes partial state estimates in order to reconstruct the spatial field. The proposed estimation scheme is based on asymptotic embedding methods which essentially embed the elliptic PDE into a parabolic PDE that describes the state estimate in each time instance. To further enhance the performance of the state estimator, a guidance scheme provides the spatial relocation of the sensing devices within the spatial domain.