  This paper introduces novel schemes for indoor localization, outlier
detection, and radio map interpolation using Wireless Local Area Networks
(WLANs). The localization method consists of a novel multicomponent
optimization technique that minimizes the squared $\ell_{2}$-norm of the
residuals between the radio map and the online Received Signal Strength (RSS)
measurements, the $\ell_{1}$-norm of the user's location vector, and weighted
$\ell_{2}$-norms of layered groups of Reference Points (RPs). RPs are grouped
using a new criterion based on the similarity between the so-called Access
Point (AP) coverage vectors. In addition, since AP readings are prone to
containing inordinate readings, called outliers, an augmented optimization
problem is proposed to detect the outliers and localize the user with cleaned
online measurements. Moreover, a novel scheme to record fingerprints from a
smaller number of RPs and estimate the radio map at RPs without recorded
fingerprints is developed using sparse recovery techniques. All localization
schemes are tested on RSS fingerprints collected from a real environment. The
overall scheme has comparable complexity with competing approaches, while it
performs with high accuracy under a small number of APs and finer granularity
of RPs.
