Omnidirectional bats, point-to-plane distances, and the price of uniqueness

Miranda Krekovic, Ivan Dokmanic, Martin Vetterli
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We 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
more » ... D 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. Index Terms-Collocated source and receiver, first-order echoes, indoor localization, room geometry reconstruction, point-to-plane distance matrix (PPDM), SLAM.
doi:10.1109/icassp.2017.7952759 dblp:conf/icassp/KrekovicDV17 fatcat:rg7zzzeff5hdnir5ddchgvu6sy