Analysis of mutual information for informative forecasting using mobile sensors

This paper presents several analysis of mutual information that is often used to define the objective function for trajectory planning (and scheduling) of sensor networks, when the goal is to improve the forecast accuracy of some quantities of interest. The approach extends the present author´s prior work in order to consider more general notion of verification entities and to enable more robust decision with potential uncertainty in the mission specifications. The expression of mutual information for windowed forecasting, in which the verification entities are defined by a finite time window instead of a single time instance, is derived and quantified without adding significant computational cost. It is also demonstrated that the sensitivity of mutual information to the variation of verification time can be calculated in the same process of computing the mutual information. Simple numerical examples are presented for preliminary validation of the applicability of the proposed analysis.