Skip to Main Content
The problem of global positioning using a rigorous Bayesian framework based on the theory of random finite sets and their corresponding density functions is covered in this condensed tutorial. The positioning scenario considered involves a number of anonymous beacons with known position relative to which the agent can measure its position. Since the beacons are anonymous, determining the agents position relative to a single (and even multiple in some cases) beacon is ambiguous. However, by exploiting the mobility of the agent through the environment, it is shown that it is possible to converge to an unambiguous position estimate. Random sets allow one to naturally develop a complete model of the underlying problem which accounts for the statistics of missed detections (due to signal weakness/blocking etc) and of spurious/erroneously detected beacons (due to potentially unmodeled beacons and/or reflected/multi-path signals). Following the derivation of a complete Bayesian solution, we outline a first-order statistical moment approximation, the so called probability hypothesis density filter.