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Indoor localization is a supporting technology for a broadening range of pervasive wireless applications. One promising approach is to locate users with radio frequency fingerprints. However, its wide adoption in real-world systems is challenged by the time- and manpower-consuming site survey process, which builds a fingerprint database <italic>a priori</italic> for localization. To address this problem, we visualize the 3-D RF fingerprint data as a function of locations (x-y) and indices of access points (fingerprint), as a <italic>tensor</italic> and use tensor algebraic methods for an <italic>adaptive</italic> tubal-sampling of this fingerprint space. In particular, using a recently proposed tensor algebraic framework in <xref ref-type="bibr" rid="ref1">[1]</xref> , we capture the complexity of the fingerprint space as a low-dimensional tensor-column space. In this formulation, the proposed scheme exploits adaptivity to identify reference points which are highly informative for learning this low-dimensional space. Further, under certain incoherency conditions, we prove that the proposed scheme achieves bounded recovery error and near-optimal sampling complexity. In contrast to several existing work that rely on random sampling, this paper shows that adaptivity in sampling can lead to significant improvements in localization accuracy. The approach is validated on both data generated by the ray-tracing indoor model which accounts for the floor plan and the impact of walls and the real world data. Simulation results show that, while maintaining the same localization accuracy of existing approaches, the amount of samples can be cut down by <inline-formula><tex-math notation="LaTeX"> $71$</tex-math><alternatives><inline-graphic xlink:type="simple" xlink:href="wang-ieq1-2505729.gif"/></alternatives></inline-formula> percent for the high SNR case and <inline-formula><tex-math notation="LaTeX">$55$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="wang-ieq2-2505729.gif"/></alternatives></inline-formula> percent for the low SNR case.

Adaptive Sampling of RF Fingerprints for Fine-Grained Indoor Localization