If the construction and maintenance of Wi-Fi radio maps (WRMs) were fully automated, the implementation of a global-scale Wi-Fi indoor positioning system would be possible. This paper proposes a WRMs calibration system that automates the initial construction and maintenance of radio maps using crowdsourced fingerprints collected from numerous smartphones without location information. The system incorporates an unsupervised learning algorithm into an incremental and adaptive calibration process. The unsupervised learning algorithm constructs an initial radio map, using fingerprints collected from unknown locations, by finding a hidden structure among them. Once a positioning service is available based on the initial radio map, the radio map continues to adapt to signal changes in the environment through the incremental and adaptive calibration process using the fingerprints that are continuously collected from the service users. Experiments carried out in an office building have shown that the proposed system could successfully construct and maintain a precise radio map without requiring any location information. In a long-term experiment that lasted for five months, the proposed system was able to not just maintain but also improve the quality of the radio map. These results indicate that Wi-Fi indoor positioning systems can be automatically constructed and maintained in continuously changing Wi-Fi environments without manual calibration efforts.