Learning dictionary and compressive sensing for WLAN localization

Localization using the received signal strength (RSS) is a popular technique in the indoor location aware service because of the wide deployment of wireless local area networks (WLANs) and the spreading of mobile device with the measuring RSS function. In this paper, we investigate the RSS-based WLAN indoor positioning system using ℓ₀-norm recovery support of sparse representation. Based on the fingerprinting method, the radio map (RM) constructed in offline phase is decomposed into a dictionary and a corresponding sparse representation matrix, using the K-SVD learning overcomplete dictionary algorithm. The learned dictionary guarantees the condition of stable recovery sparse representation. The position of each reference point (RP) in the RM is characterized by an unique support in each vector of sparse representation. We use the orthogonal matching pursuit algorithm to find the support of sparse representation of the real-time measured RSS vector over the learned dictionary and thereby determine which RP is closest to the user. This is an ℓ₀-norm minimization problem. We also study the effect of the other RPs to the recovery solution of real-time measurement vector. We first derive the weighted vector that reflects the contribution of each RP in the localization formulation, then the user position is estimated by this vector and the positions of RPs.