Indoor Positioning Systems (IPS) using Bluetooth Low Energy (BLE) technology are currently becoming real and available, which has made them grow in popularity and use. However, there are still plenty of challenges related to this technology, especially in terms of Received Signal Strength Indicator (RSSI) fluctuations due to the behaviour of the channels and the multipath effect, that lead to poor precision. In order to mitigate these effects, in this paper we propose and implement a real Indoor Positioning System based on Bluetooth Low Energy, that improves accuracy while reducing power consumption and costs. The three main proposals are: frequency diversity, Kalman filtering and a trilateration method what we have denominated “weighted trilateration”. The analysis of the results proves that all the proposals improve the precision of the system, which goes up to 1.82 m 90% of the time for a device moving in a middle-size room and 0.7 m for static devices. Furthermore, we have proved that the system is scalable and efficient in terms of cost and power consumption. The implemented approach allows using a very simple device (like a SensorTag) on the items to locate. The system enables a very low density of anchor points or references and with a precision better than existing solutions.