Continuous motion planning for information forecast

This paper addresses planning of continuous paths for mobile sensors to improve long-term forecast performance. With the information gain defined by the mutual information between the continuous measurement path and the future verification variables, two expressions for computing the information gain for a linear time-varying system are derived: the filter form and the smoother form. The smoother form, inspired by the conditional independence structure, is shown to be preferable, since it does not require integration of differential equations for long time intervals, it simplifies the process of calculating the accumulated information on the fly, and its time derivative extracts out the pure impact of sensing regardless of the process noise. Utilizing the spatial interpolation technique to relate the sensor movement to the evolution of the observation matrix, the optimal path planning formulation and the real-time steering law are presented. A numerical example of a simplified weather forecast validates the proposed methodology.