Closed-loop guidance of mobile sensors for the estimation of spatially distributed processes

The paper provides a computationally efficient scheme tier the spatial repositioning of mobile sensors used in the real-time estimation of spatially distributed processes. Instead of considering the computationally expensive option of propagating the covariance operator forward in time with the guidance propagated backward in time, the proposed closed loop guidance scheme repositions the mobile sensors according to the positive direction of the spatial gradient of the resulting state estimation error. The proposed coupled state estimation and sensor guidance is applied to advection-diffusion PDEs in one and two spatial dimensions and compared to the case of a Kalman filter with fixed-in-space sensors.