Nonparametric Density Estimation for Learning Noise Distributions in Mobile Robotics

By admitting an explicit representation of the uncertainty associated with sensing and actuation in the real world, the probabilistic robotics paradigm has led to remarkable improvements in the robustness and performance of autonomous systems. However, this approach generally requires that the sensing and actuation noise acting upon an autonomous system be specified in the form of probability density functions, thus necessitating that these densities themselves be estimated. To that end, in this paper we present a general framework for directly estimating the probability density function of a noise distribution given only a set of observations sampled from that distribution. Our approach is based upon Dirichlet process mixture models (DPMMs), a class of infinite mixture models commonly used in Bayesian nonparametric statistics. These models are very expressive and enjoy good posterior consistency properties when used in density estimation, but the density estimates that they produce are often too computationally complex to be used in mobile robotics applications, where computational resources are limited and speed is crucial. We derive a straightforward yet principled approximation method for simplifying the densities learned by DPMMs in order to produce computationally tractable density estimates. When implemented using the infinite Gaussian mixture model (a specific class of DPMMs that is particularly well-suited for mobile robotics applications), our approach is capable of approximating any continuous distribution on R arbitrarily well in total variation distance, and produces C∞, bounded, everywhere positive, and efficiently computable density estimates suitable for use in real-time inference algorithms on mobile robotic platforms.