Spatial Cognition and Computation 1: 291–321, 1999.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Geometric reasoning under uncertainty for map-based
WILLIAM B. THOMPSON
, CAROLYN M. VALIQUETTE
, BONNIE H.
and KAREN T. SUTHERLAND
Department of Computer Science, University of Utah, U.S.A.;
Graduate Programs in
Software, University of St. Thomas, St. Paul, MN, U.S.A.;
Department of Computer Science,
Augsburg College, Minneapolis, MN, U.S.A.
Abstract. Map-based navigation in outdoor terrain lacking man-made structures or other
highly distinctive landmarks can produce severe localization problems. This paper presents
an approach to navigation which implements high level geometric reasoning and matching
strategies based on those used by skilled human navigators. This approach, which is demon-
strated on a real example involving imagery of mountainous terrain obtained with a video
camera and USGS map data, is designed to avoid many of the pitfalls occurring when an
attempt is made to navigate by modeling the environment mathematically. It exploits feature
attributes which cannot be easily expressed quantitatively but are central to the successful
human navigation process.
Key words: localization, maps, navigation
An essential aspect of map-based navigation is the determination of an agent’s
current location based on sensed data from the environment. Formally, this
amounts to specifying the current viewpoint in some world model coordinate
system. This localization process has two distinct components: one involving
the establishment of correspondences between aspects of the sensed data and
the map or model, and the other involving derivation of constraints on the
viewpoint based on the correspondences that have been determined.
Correspondences can be established at the signal or feature level. Signal-
level matching correlates sensed data with predictions of how the sensed data
should appear. It works best when the uncertainty in the viewpoint is small
and when it is relatively easy to accurately generate expected sensor data.
For example, in the TERCOM and SITAN cruise missile guidance systems, a
digital elevation model is matched against a downward looking, radar sensed
elevation proﬁle (Andreas et al. 1978; Baird and Abramson 1984).