Krekovic, MirandaDokmanic, IvanVetterli, Martin2020-05-232020-05-232020-05-232020-01-0110.1109/TSP.2020.2982780https://infoscience.epfl.ch/handle/20.500.14299/168898WOS:000531386900001We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the & x201C;structure from sound & x201D; approach to microphone localization with unknown sources. In our earlier work we proposed computational methods for localization from point-to-plane distances and noted that such localization suffers from various ambiguities beyond the usual rigid body motions; in this paper we provide a complete characterization of uniqueness. We enumerate all cases of configurations which lead to the same distance measurements as a function of the number of planes and points, and algebraically characterize the related transformations in both 2D and 3D.Engineering, Electrical & ElectronicEngineeringpoint-to-plane distance matrixinverse problem in the euclidean spaceuniqueness of the reconstructioncollocated source and receiverindoor localization and mappingorientation estimationpositiontext::journal::journal article::research article