Quadtree-based ancestry tree maps for 2D scattered data SLAM

Abstract In a typical Rao-Blackwellized particle filter Simultaneous localization and mapping (SLAM), each particle carries its own map. Ancestry tree maps are proposed in the literature to handle occupancy grid maps with a large memory footprint, allowing very large particle counts. This paper describes how quadtrees can be used to implement ancestry tree maps in scattered data SLAM. We introduce a logarithmic-time query method to provide a natural neighborhood-like local polygonal neighborhood. Further, we propose an efficient and simple-to-implement local interpolant utilizing the polygonal neighborhood, and show that the interpolant RMSE is comparable to Sibson interpolant. We combine the query method with an ancestry tree consisting of quadtrees to obtain an effective map representation for scattered data SLAM. With map size of n and number of particles P, we obtain an average case time complexity of per time step. The introduced approach is experimentally validated on magnetic field SLAM with real-world data, showing that the performance is in line with the derived time complexity. The literature suggests that with ancestry trees the memory consumption drops from O(nP) to in practice. Empirical data confirm that this seems to be the case also with scattered data SLAM.