Passive mobile robot localization within a fixed beacon field

This thesis describes a geometric algorithm for the localization of mobile nodes in networks of sensors and robots using bounded regions, in particular we explore the range-only and angle-only measurement cases. The algorithm is a minimalistic ap-proach to localization and tracking when dead reckoning is too inaccurate to be useful. The only knowledge required about the mobile node is its maximum speed. Geomet-ric regions are formed and grown to account for the motion of the mobile node. New measurements introduce new constraints which are propagated back in time to re-fine previous localization regions. The mobile robots are passive listeners while the sensor nodes actively broadcast making the algorithm scalable to many mobile nodes while maintaining the privacy of individual nodes. We prove that the localization regions found are optimal–that is, they are the smallest regions which must con-tain the mobile node at that time. We prove that each new measurement requires quadratic time in the number of measurements to update the system, however, we demonstrate experimentally that this can be reduced to constant time. Numerou