  Indoor localization is a supporting technology for a broadening range of
pervasive wireless applications. One promis- ing 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 a priori 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 tensor and use tensor
algebraic methods for an adaptive tubal-sampling of this fingerprint space. In
particular using a recently proposed tensor algebraic framework in [1] 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 71% for the high SNR case
and 55% for the low SNR case.
