Precision Dilution in Triangulation Based Mobile Robot Position Estimation

When navigating from landmarks, the numerical computation of the differential behavior of the mapping from measurements to states is well understood. This paper seeks to develop tools to foster an intuitive grasp of the spatial variation in the differential behavior of this mapping. Graphical methods are adapted from marine navigation in order to introduce the issues in low dimensional cases. The implicit function theorem and the pseudoinverse are then used in the general case to derive a quantity analogous to the geometric dilution of precision (GDOP) as it is used in satellite based guidance. An explicit expression is obtained for the conditioning of the triangulation computation as a function of position. This expression also directly provides the conditions under which the computation becomes singular. The application to a few common cases is illustrated.