Domain decomposition methods in the distributed estimation of spatially distributed processes with mobile sensors

This paper considers the state estimation of spatially distributed processes via the employment of mobile sensors. In order to reduce the computational demands, a domain decomposition method is utilized and which decomposes the spatial domain into two subdomains. The estimator in the inner domain implements a hybrid Kalman filter with a mobile sensor, whereas the outer subdomain implements a naive observer. Coupling conditions at the inner/outer boundary serve as a means to exchange information between the two estimators and which constitute a consensus protocol. The motion of the mobile sensor is based on a spatial gradient scheme and serves as a further means of reducing the computational load associated with the solution to large scale differential Riccati equations. The proposed scheme is further extended to collaborative distributed estimation in which multiple mobile sensors are enforcing another level of consensus protocol in order to penalize the differences between their state estimates. Extensive numerical simulations of a one-dimensional parabolic partial differential equation are presented to further demonstrate the multi-level computational savings associated with the use of domain decomposition in state estimation of spatially distributed processes with mobile sensors.