Gradient-ascent schemes for the guidance of mobile sensors used in the estimation of spatially distributed systems

The problem of mobile sensors for effective state reconstruction of spatially varying processes is considered. The optimal approach for integrated state estimation and mobile sensor guidance suffers from heavy computational requirements of differential Riccati equations. While the filter covariance in such a case is propagated forward in time, the sensor guidance scheme must be integrated backwards in time resulting in an open-loop policy. As a consequence, a closed-loop approach that is at the same time computationally tractable is favored. Two schemes for the concurrent computation of filter gains and mobile sensor guidance are proposed and are based on significantly reduced computational requirements, favorably leading to real-time implementable estimation schemes. Using gradient-ascent schemes, the combined estimator-plus-guidance schemes reposition the sensor to spatial regions of more useful information; these comprise regions with larger estimation errors. Numerical implementation of both proposed designs are applied to a one-dimensional diffusion equation with a single mobile sensor.