Gaussian mixture models for probabilistic localization

Abstract

Abstract-One of the key tasks during the realization of probabilistic approaches to localization is the design of a proper sensor model, that calculates the likelihood of a measurement given the current pose of the vehicle and the map of the environment. In the past, range sensors have become popular for mobile robot localization since they directly measure distance. However, in situations in which the robot operates close to edges of obstacles or in highly cluttered environments, small changes in the pose of the robot can lead to large variations in the acquired range scans. If the sensor model used does not appropriately characterize the resulting fluctuations, the performance of probabilistic approaches may substantially degrade. A common solution is to artificially smooth the likelihood function or to only integrate a small fraction of the measurements. In this paper we present a more fundamental and robust approach which uses mixtures of Gaussians to model the likelihood function for single range measurements. In practical experiments we compare our approach to previous methods and demonstrate that it yields a substantially increase in robustness.

Efficiently learning high-dimensional observation models for Monte-Carlo localization using Gaussian mixtures

“…This set of experiments is designed to investigate the case that the robot is not able to localize itself at different locations with the same robustness. In our previous work [15], we demonstrated that whenever the robot traverses regions close to obstacles, doorways, or clutter, the likelihood of the true position decreases. In the case of global localization using a particle filter this leads to serious problems because the particles at these positions have a high risk of being depleted.…”

“…Due to that, in this paragraph we will describe typical likelihood models for range sensors and we shortly will introduce the likelihood models of our previous work [14], [15]. Afterwards, we will present our new high dimensional Gaussian mixture model that is able to represent multi-modalities in the likelihood function as well as dependencies between the individual laser beams.…”

“…Alternatively, our recently proposed method [15] is able to consider the multi-modality of the observation model but is unable to represent the dependency between the individual scans. In contrast to this, the novel method presented in this paper combines the advantages of these previous models: It considers the dependency between the beams of a range scan and it correctly handles the multi-modal nature of the likelihood function and at the same time can be computed efficiently.…”

“…Typically, such multi-modalities arise in the proximity of doorways, corners, and cluttered areas of the environment. One way to model the different modes in the distribution of the expected range observation for each laser beam is to explicitly consider the multi-model nature [15]. Whereas this technique yields appropriate, multi-model distributions for individual beams, it is unable to model the dependency between in individual beams.…”

“…In contrast to former approaches which modeled the likelihood functions as unimodal distributions for single beams [8], [13] or entire scans [14], [16], or as a multimodal distributions for single beams [15], we now consider high-dimensional, multi-modal mixture models. This allows us to take the dependency between the individual beams as well as the multi-modal nature of the distribution into account.…”