A stochastic map for uncertain spatial relationships

In this paper we will describe a representation for spatial relationships which makes explicit their inherent uncertainty. We will show ways to manipulate them to obtain estimates of relationships and associated uncertainties not explicitly given, and show how decisions to sense or act can be made a priori based on those estimates. We will show how new constraint information, usually obtained by measurement, can be used to update the world model of relationships consistently, and in some situations, optimally. The framework we describe relies only on well-known state estimation methods.