  This paper presents expression of mutual information that defines the
information gain in planning of sensing resources, when the goal is to reduce
the forecast uncertainty of some quantities of interest and the system dynamics
is described as a continuous-time linear system. The method extends the
smoother approach in [5] to handle more general notion of verification entity -
continuous sequence of variables over some finite time window in the future.
The expression of mutual information for this windowed forecasting case is
derived and quantified, taking advantage of underlying conditional independence
structure and utilizing the fixed-interval smoothing formula with correlated
noises. Two numerical examples on (a) simplified weather forecasting with
moving verification paths, and (b) sensor network scheduling for tracking of
multiple moving targets are considered for validation of the proposed approach.
