  In this paper, we introduce two indoor Wireless Local Area Network (WLAN)
positioning methods using augmented sparse recovery algorithms. These schemes
render a sparse user's position vector, and in parallel, minimize the distance
between the online measurement and radio map. The overall localization scheme
for both methods consists of three steps: 1) coarse localization, obtained from
comparing the online measurements with clustered radio map. A novel graph-based
method is proposed to cluster the offline fingerprints. In the online phase, a
Region Of Interest (ROI) is selected within which we search for the user's
location; 2) Access Point (AP) selection; and 3) fine localization through the
novel sparse recovery algorithms. Since the online measurements are subject to
inordinate measurement readings, called outliers, the sparse recovery methods
are modified in order to jointly estimate the outliers and user's position
vector. The outlier detection procedure identifies the APs whose readings are
either not available or erroneous. The proposed localization methods have been
tested with Received Signal Strength (RSS) measurements in a typical office
environment and the results show that they can localize the user with
significantly high accuracy and resolution which is superior to the results
from competing WLAN fingerprinting localization methods.
