On the roles of smoothing in planning of informative paths
ACC'09 Proceedings of the 2009 conference on American Control Conference
Continuous trajectory planning of mobile sensors for informative forecasting
Automatica (Journal of IFAC)
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This paper investigates partially observed linear Gaussian systems in continuous time from an information-theoretic viewpoint. It identifies information supply, storage, and dissipation processes that quantify various dependencies between the unobservable and observable components of the state variables of such systems, which we call the signal and observation processes. The storage is that information in the past of the observation useful for estimating the present and future of the signal. It is so called because it is the information "stored" in the state variable of the Kalman--Bucy filter. The optimal properties of the Kalman--Bucy filter bring about a particular symmetry in its joint dynamics with the signal. This enables a dual system, with the same structure as the original, to be derived by time reversal. The information supply and dissipation processes of this dual problem are those of the original, with roles interchanged. The same symmetry enables us to define an entropic measure of the local time-asymmetry of the interaction between the signals and filters, which we call the rate of interactive entropy production. This is shown to be directly connected with the rates of information supply and dissipation. It is also intimately connected with the entropy production of an abstract statistical mechanical system at or near a stationary nonequilibrium state.