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We study the problem of simultaneously reconstructing a polygonal room and atrajectory of a device equipped with a (nearly) collocated omnidirectionalsource and receiver. The device measures arrival times of echoes of pulsesemitted by the source and picked up by the receiver. No prior knowledge aboutthe device's trajectory is required. Most existing approaches addressing thisproblem assume multiple sources or receivers, or they assume that some of theseare static, serving as beacons. Unlike earlier approaches, we take into accountthe measurement noise and various constraints on the geometry by formulatingthe solution as a minimizer of a cost function similar to \emph{stress} inmultidimensional scaling. We study uniqueness of the reconstruction fromfirst-order echoes, and we show that in addition to the usual invariance torigid motions, new ambiguities arise for important classes of rooms andtrajectories. We support our theoretical developments with a number ofnumerical experiments.

Look, no Beacons! Optimal All-in-One EchoSLAM