Indoor Positioning Systems (IPSs) are used to estimate the position of mobile devices in indoor environments. Fingerprinting is the most used technique because of its higher accuracy. However, this technique requires a labor-intensive training phase that measures the Received Signal Strength Indicator (RSSI) at all Reference Points (RPs) locations. On the other hand, model-based IPSs use signal propagation models to estimate distances from RSSI. Thus, they do not require expensive training but result in higher positioning errors. In this work, we propose SynTra-IPS (Synthetic Training Indoor Positioning System), a hybrid approach between a fingerprint and a model-based IPS that uses synthetic, simulated datasets combined with data fusion techniques to eliminate the fingerprint collection cost. In our solution, we use the map of the scenario, with known anchor nodes' positions and the log-distance signal propagation model, to generate several synthetic, model-based, fingerprint training datasets. In the online phase of our solution, the positions estimated by the several synthetic datasets using K-Nearest Neighbors (KNN) are combined using data fusion techniques into a single, more accurate position. We evaluated the performance of our SynTra solution in a real-world, large-scale environment using mobile devices with Bluetooth Low Energy (BLE) technology, and we compared our solution to classic approaches from the literature. Our results show that SynTra can locate mobile devices with an average error of only 2.36 m while requiring no real-world environment training.