Multiscale Graphical Modeling in Space: Applications to Command and Control

Recently, a class of multiscale tree-structured models was introduced in terms of scale-recursive dynamics defined on trees. The main advantage of these models is their association with a fast, recursive, Kalmanfilter prediction algorithm. In this article, we propose a more general class of multiscale graphical models over acyclic directed graphs, for use in command and control problems. Moreover, we derive the generalized-Kalmanfilter algorithm for graphical Markov models, which can be used to obtain the optimal predictors and prediction variances for multiscale graphical models. 1 Introduction Almost every aspect of command and control (C2) involves dealing with information in the presence of uncertainty. Since information in a battlefield is never precise, its status is rarely known exactly. In the face of this uncertainty, commanders must make decisions, issue orders, and monitor the consequences. The uncertainty may come from noisy data or, indeed, regions of the battle space whe..