21 An Improved Real-Time Particle Filter for Robot Localization Dario Lodi Rizzini and Stefano Caselli Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Parma, Parma, Italy 1. Introduction Robot localization is the problem of estimating robot coordinates with respect to an external reference frame. In the common formulation of the localization problem, the robot is given a map of its environment, and to localize itself relative to this map it needs to consult its sensor data. The effectiveness of a solution to the localization problem in an unstructured environment strongly depends on how it copes with the uncertainty affecting robot perception. The probabilistic robotics paradigm provides statistical techniques for representing information and making decision, along with a unifying mathematical framework for probabilistic algorithms based on Bayes rule (Thrun et al., 2005). For this reason, bayesian filtering has become the prevailing approach in recent works on localization (Elinas & Little, 2005; Sridharan et al., 2005; Hester & Stone, 2008). Bayesian filtering is a general probabilistic paradigm to arrange motion and sensor data in order to achieve a solution in the form of distribution of state random variables. Bayesian filters differ in the representation of the probability density function (PDF) of state. For example, the resulting estimation of Gaussian filters (Kalman Filter, Extended Kalman Filter) (Leonard & Durrant-Whyte, 1991; Arras et al., 2002) is expressed in the form of a continuous parametric function, while the state posterior is decomposed in discrete elements for nonparametric filters. The main nonparametric algorithm is called Particle Filter (PF) (Fox et al., 1999) and relies on importance sampling (Doucet et al., 2001). With importance sampling, the probability density of the robot pose is approximated by a set of samples drawn from a proposal distribution, and an importance weight measures the distance of each sample from the correct estimation. The nonparametric approach has the advantage of providing a better approximation of the posterior when a parametric model does not exist or changes during iteration, e.g. in initialization or when environment symmetries determine a multi-modal PDF. Even if techniques like Multi-Hypothesis Tracking (Arras et al., 2002) attempt to manage multi- modal distributions, particle filters are more efficient and can represent all kinds of PDFs, including uniform distributions. Moreover, particle filters limit errors due to the linearization of model equations that can lead to poor performance and divergence of the