Indoor localization is a challenging task as the signal propagation in indoor environments does not adhere to the classical path loss or other simple models. Modern high-accuracy indoor localization algorithms rely on fingerprinting methods that entail an offline phase of data collection and mapping phase. This work puts forth a dictionary learning framework for fingerprinting indoor locations using GSM, WiFi, and other sensor measurements. Different from the existing works, the proposed methods are model-free, can handle missing measurements, and fingerprints can be flexibly updated in an online fashion. The dictionary learning algorithm itself is appropriately modified to ensure incoherence between fingerprints of nearby locations and appropriate weighing of the sparse coefficients. A hidden markov model based tracking algorithm is also provided that considers the recent history while estimating the user location. Detailed experiments are carried out over four different maps to demonstrate the efficacy and usefulness of the proposed algorithm, in comparison to the state-of-the-art classification-based and model-based indoor localization algorithms.