This paper addresses the coupled tasks of constructing a spatial
  representation of the environment with a mobile robot using noisy
  sensors (sonar) and using such a map to determine the robot's
  position without a prior estimate.  The map is not meant to
  represent the actual spatial structure of the environment so much as
  it is meant to represent the major structural components of what the
  robot ``sees''.  This can, in turn, be used to construct a model of
  the physical objects in the environment.  One problem with such an
  approach is that maintaining an absolute coordinate system for the
  map is difficult without periodically calibrating the robot's
  position.

  We demonstrate that in a suitable environment it is possible to use
  sonar data to recalibrate position and orientation estimates on an
  ongoing basis.  This is accomplished by incrementally constructing
  and updating a model-based description of the acquired data.  Given
  coarse position estimates of the robot's location and orientation,
  these can be refined to high accuracy using the stored map and a set
  of sonar readings from a single position.  This approach is then
  generalized to allow global position estimation, where position and
  orientation estimates are not available.

  We consider the accuracy of the method based on a single sonar reading
  illustrate its region of convergence using empirical data.