Krekovic, MirandaDokmanic, IvanVetterli, Martin2016-09-192016-09-192016-09-19201710.1109/ICASSP.2017.7952759https://infoscience.epfl.ch/handle/20.500.14299/129447WOS:000414286203085We study simultaneous localization and mapping with a device that uses reflections to measure its distance from walls. Such a device can be realized acoustically with a synchronized collocated source and receiver; it behaves like a bat with no capacity for directional hearing or vocalizing. In this paper we generalize our previous work in 2D, and show that the 3D case is not just a simple extension, but rather a fundamentally different inverse problem. While generically the 2D problem has a unique solution, in 3D uniqueness is always absent in rooms with fewer than nine walls. In addition to the complete characterization of ambiguities which arise due to this non-uniqueness, we propose a robust solution for inexact measurements similar to analogous results for Euclidean Distance Matrices. Our theoretical results have important consequences for the design of collocated range-only SLAM systems, and we support them with an array of computer experiments.Collocated source and receiverfirst-order echoesindoor localizationroom geometry reconstructionpoint-to-plane distance matrix (PPDM)SLAMLCAV-SSPLCAV-APDAtext::conference output::conference proceedings::conference paper