Indoor location estimation is a significant task for many ubiquitous and pervasive computing applications, with numerous solutions based on IEEE802.11, bluetooth, ultrasound and infrared technologies. Most of these techniques use the fingerprint-based approach, which needs exhaustive collection of the received signal strengths in various positions of the physical space. In the present work, we exploit the spatial correlation structure of the fingerprints and use the framework of Matrix Completion to build complete training maps from a small number of random sample fingerprints. The experimental evaluation with real data presents the localization accuracy based on complete reconstructed training maps, without making an exhaustive collection of fingerprints.