Passive mobile robot localization within a fixed beacon field

Abstract

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 approach 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. Geometric 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 refine 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 contain 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. Numerous simulations are presented, as well as results from an underwater experiment conducted at the U.C. Berkeley R.B. Gump Biological Research Station on the island of Moorea, French Polynesia.