Look, no Beacons! Optimal All-in-One EchoSLAM
This work addresses the challenge of simultaneous localization and mapping (SLAM) in acoustics without relying on static beacons, which could benefit applications in robotics and indoor navigation, though it appears incremental by building on existing echo-based methods.
The paper tackles the problem of reconstructing a polygonal room and device trajectory using only a single moving source-receiver pair, without beacons, by formulating a cost function that accounts for measurement noise and geometric constraints. They demonstrate uniqueness conditions for reconstruction from first-order echoes and identify new ambiguities for certain room and trajectory classes, supported by numerical experiments.
We study the problem of simultaneously reconstructing a polygonal room and a trajectory of a device equipped with a (nearly) collocated omnidirectional source and receiver. The device measures arrival times of echoes of pulses emitted by the source and picked up by the receiver. No prior knowledge about the device's trajectory is required. Most existing approaches addressing this problem assume multiple sources or receivers, or they assume that some of these are static, serving as beacons. Unlike earlier approaches, we take into account the measurement noise and various constraints on the geometry by formulating the solution as a minimizer of a cost function similar to \emph{stress} in multidimensional scaling. We study uniqueness of the reconstruction from first-order echoes, and we show that in addition to the usual invariance to rigid motions, new ambiguities arise for important classes of rooms and trajectories. We support our theoretical developments with a number of numerical experiments.