期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 68, 期 -, 页码 2480-2498出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2020.2982780
关键词
Point-to-plane distance matrix; inverse problem in the Euclidean space; uniqueness of the reconstruction; collocated source and receiver; indoor localization and mapping
资金
- Swiss National Science Foundation [20FP-1 151073]
- Google Faculty Research Award
We 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 structure from sound 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.
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