Global robot localization with random finite set statistics

We re-examine the problem of global localization of a robot using a rigorous Bayesian framework based on the idea of random finite sets. Random sets allow us to naturally develop a complete model of the underlying problem accounting for the statistics of missed detections and of spurious/erroneously detected (potentially unmodeled) features along with the statistical models of robot hypothesis disappearance and appearance. In addition, no explicit data association is required which alleviates one of the more difficult sub-problems. Following the derivation of the Bayesian solution, we outline its first-order statistical moment approximation, the so called probability hypothesis density filter. We present a statistical estimation algorithm for the number of potential robot hypotheses consistent with the accumulated evidence and we show how such an estimate can be used to aid in re-localization of kidnapped robots. We discuss the advantages of the random set approach and examine a number of illustrative simulations.