Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilisticlocalization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), which approximate the posterior under a common Bayesian formulation of the localization problem. Building on the basic MCL algorithm, this article develops a more robust algorithm called Mixture-MCL, which integrates two complimentary ways of generating samples in the estimation. To apply this algorithm to mobile robots equipped with range finders, a kd-tree is learned that permits fast sampling. Systematic empirical results illustrate the robustness and computational efficiency of the approach. Key words: Mobile robots, localization, position estimation, particle filters, kernel density trees