Informative windowed forecasting of continuous-time linear systems for mutual information-based sensor planning

This paper presents an 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 Choi and How (2010b) to handle a more general notion of the 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 an underlying conditional independence structure and utilizing a two-filter formula for fixed-interval smoothing with correlated noises. Two numerical examples on (a) a two-state linear system with time-varying one-way coupling dynamics, and (b) idealized weather forecasting with moving verification paths demonstrate the validity of the proposed quantification methodology.