Statistical Inference for Change-of-Aperture Problems in Command and Control: Executive Summary of ONR Grant, 1999-2001

Project Description

Almost every aspect of Command and Control (C2) deals with making decisions in the presence of uncertainty. The uncertainty may come from noisy data or, indeed, regions of the battlespace where there are no data at all. It is this latter aspect, namely, lack of knowledge, that requires the most care. Statistical models that account for noisy data are well accepted by the science and engineering community, but the full quantification of uncertainty due to lack of knowledge (caused either by hidden processes or missing data) falls under the purview of statistical modeling.

It is typically the case that the battle commander has a different "aperture" than a platoon commander. The battle commander needs more global, aggregated information, whereas the platoon commander is often making decisions based on local, more focused information. Our emphasis is on making maps that are accurate and easily interpretable at different resolutions/apertures. The intent is not to decide which apertures belong to which level of command, but rather to develop a methodology that makes change-of-aperture possible.

Objectives

Using Bayesian statistical methodology, the more-or-less precise uncertainty in key C2 parameters can be made more precise through computation of the posterior distribution of the parameters given the data. All decisions are then based on the posterior distribution. Our objective is to develop statistical methodology that allows rapid decisions to be made based on accurate maps at different resolutions/apertures.

Approach

Combining the two aspects of noisy (or missing) data and change-of-aperture, we construct statistical models that deal with computation of the posterior distributions directly. Because of the hierarchical nature of C2 problems with change-of-aperture, models can often be built using an acyclic directed graph (ADG). In an ADG, each 'node' can have 'parents' that it depends on, and the node can have 'children' that depend on it. If each node in an ADG has only one parent, then the ADG is a tree.

Spatial dependence can be incorporated through the ADG's parent-child relationship, which is a type of multi-resolution model. In addition, very fast statistical algorithms can be developed for removing noise and filling in missing data at all apertures, in the case of a tree-structured model. One of the research topics is to develop fast algorithms for the more general and flexible ADGs. Regardless, this involves spatial mapping for which the capabilities of a Geographic Information System (GIS) are being investigated. The resulting posterior distributions are summarized in different ways, depending on the command queries; under investigation is a statistical methodology to produce an (approximately) optimal map for all queries. Finally, the temporal component will be incorporated to allow fast updating of spatial maps based on newly acquired C2 data.

This research was supported by the Probability and Statistics Program of the Office of Naval Research.

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Last modified: Monday, December 10, 2007 11:55 AM.