HMM-Based Dynamic Mapping with Gaussian Random Fields

Abstract

This paper focuses on the mapping problem for mobile robots in dynamic environments where the state of every point in space may change, over time, between free or occupied. The dynamical behaviour of a single point is modelled by a Markov chain, which has to be learned from the data collected by the robot. Spatial correlation is based on Gaussian random fields (GRFs), which correlate the Markov chain parameters according to their physical distance. Using this strategy, one point can be learned from its surroundings, and unobserved space can also be learned from nearby observed space. The map is a field of Markov matrices that describe not only the occupancy probabilities (the stationary distribution) as well as the dynamics in every point. The estimation of transition probabilities of the whole space is factorised into two steps: The parameter estimation for training points and the parameter prediction for test points. The parameter estimation in the first step is solved by the expectation maximisation (EM) algorithm. Based on the estimated parameters of training points, the parameters of test points are obtained by the predictive equation in Gaussian processes with noise-free observations. Finally, this method is validated in experimental environments.