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This paper introduces novel schemes for indoor localization, outlierdetection, and radio map interpolation using Wireless Local Area Networks(WLANs). The localization method consists of a novel multicomponentoptimization technique that minimizes the squared $\ell_{2}$-norm of theresiduals 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 groupedusing a new criterion based on the similarity between the so-called AccessPoint (AP) coverage vectors. In addition, since AP readings are prone tocontaining inordinate readings, called outliers, an augmented optimizationproblem is proposed to detect the outliers and localize the user with cleanedonline measurements. Moreover, a novel scheme to record fingerprints from asmaller number of RPs and estimate the radio map at RPs without recordedfingerprints is developed using sparse recovery techniques. All localizationschemes are tested on RSS fingerprints collected from a real environment. Theoverall scheme has comparable complexity with competing approaches, while itperforms with high accuracy under a small number of APs and finer granularityof RPs.

Structured Group Sparsity: A Novel Indoor WLAN Localization, Outlier Detection, and Radio Map Interpolation Scheme