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