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Humans are capable of manipulating objects based solely on the sense of touch. For robots to achieve the same feat in unstructured environments, global localization of objects via touch is required. Bayesian approaches provide the means to cope with uncertainties of the real world, but the estimation of the Bayesian posterior for the full six degrees of freedom (6-DOF) global localization problem is computationally prohibitive. We propose an efficient Bayesian approach termed Scaling Series. It is capable of solving the full problem reliably in real time. This is a Monte Carlo approach that performs a series of successive refinements coupled with annealing. We also propose an analytical measurement model, which can be computed efficiently at run time for any object represented as a polygonal mesh. Extensive empirical evaluation shows that Scaling Series drastically outperforms prior approaches. We demonstrate general applicability of the approach on five common solid objects, which are rigidly fixed during the experiments. We also consider 6-DOF localization and tracking of free-standing objects that can move during tactile exploration.