Measuring the Uncertainty of Probabilistic Maps Representing Human Motion for Indoor Navigation

Abstract

Indoor navigation and mapping has recently become an important field of interest for researchers because global navigation satellite systems (GNSS) are very often unavailable inside buildings. FootSLAM - a SLAM (Simultaneous Localization and Mapping) algorithm for pedestrians based on noisy step measurements - addresses the indoor mapping and positioning problem and can provide accurate positioning in many structured indoor environments. FootSLAM estimates the posterior distributions of both human motion and the map of the environment which is a probabilistic representation of possible human motion at any location in an environment. These maps however, are themselves {\it uncertain} because they are estimated from noisy sensor observations. We believe that the uncertainty of a map and that of human motion can be represented based on information theory. In this paper, we investigate how to compare FootSLAM maps via two entropy metrics. Since collaborative FootSLAM requires the alignment and combination of several individual FootSLAM maps, we also investigate measures that help to align maps that partially overlap. We distinguish between the map entropy conditioned on the history of pedestrian's poses, which is a measure of the uncertainty of the estimated map, and the entropy rate of the pedestrian's steps conditioned on the history of poses and conditioned on the estimated map. Because FootSLAM maps are built on a hexagon grid, the entropy and relative entropy metrics are derived for the special case of hexagonal transition maps. The entropy gives us a new insight on the performance of probabilistic maps.