Location-based applications attract more and more attention in recent years. Examples of such applications include commercial advertisements, social networking software and patient monitoring. The received signal strength (RSS) based location fingerprinting is one of the most popular solutions for indoor localization. However, there is a big challenge in collecting and maintaining a relatively large RSS fingerprint database. In this work, we propose and compare two algorithms namely, the Gaussian process (GP) and Gaussian process with variogram, to estimate and construct the RSS fingerprints with incomplete data. The fingerprint of unknown reference points is estimated based on measurements at a limited number of surrounding locations. To validate the effectiveness of both algorithms, experiments using Bluetooth-low-energy (BLE) infrastructure have been conducted. The constructed RSS fingerprints are compared to the true measurements, and the result is analyzed. Finally, using the constructed fingerprints, the localization performance of a probabilistic fingerprinting method is evaluated.