Complexity-reduced FootSLAM for indoor pedestrian navigation using a geographic tree-based data structure

FootSLAM or simultaneous localisation and mapping (SLAM) for pedestrians is a technique that addresses the indoor positioning and mapping problem based on human odometry (aka pedestrian dead reckoning), for example with a foot-mounted inertial sensor. FootSLAM follows the FastSLAM factorisation, using a Rao-Blackwellised particle filter to simultaneously estimate the building layout and the pedestrian's pose – his position and orientation. To that end, FootSLAM divides the 2D space into a grid of uniform and adjacent hexagons and counts the number of times that each particle crosses the edges of the hexagons it visits. As we shall show, the complexity of FootSLAM grows quadratically with time, preventing the mapping of large areas. In this paper, we present a new geographic tree-based data structure, called H-tree, to reduce the quadratic-in-time computational growth rate of naïve FootSLAM to t times log t. In addition, we introduce a compact representation (alphabet) for the set of six counters that are used to map the transitions of the particles across the edges of each hexagon. This alphabet is particularly effective during the exploration phases of FootSLAM that requires much particle diversity. In this contribution, the computational savings of the H-tree are presented both theoretically and with real-world data. In practice, we believe that FootSLAM can be applied in quasi real-time applications that require rapid mapping of unknown areas. Additionally, the mass market offline mapping process can be undertaken much more efficiently.