In recent years, positioning and navigation become an important topic in research. The most popular positioning system is an outdoor positioning called Global Positioning System (GPS). However, due to the influence of weak signal strength, weather conditions, diverse geographical and living environments, GPS sometimes cannot support indoor positioning and, if it can, the 5-10 meters error range does not meet the indoor positioning requirement. In order to provide a better solution with higher accuracy for indoor localization, we can benefit from the proliferation of indoor communication devices. Different technologies such as WiFi, Radio Frequency Identification (RFID) and Ultra-wideband (UWB) have been commonly used in indoor positioning systems. However, WiFi has a high energy consumption for indoor localization, as it consumes 3 to 10 watts per hour in the case of using 3 routers to do the job. In addition, due to its dependency on reference tags, the overall cost of the RFID-based approaches may usually cost more than $300 which is economically prohibitive. In terms of UWB, its low area coverage brings great challenges to popularizing its acceptance as a device for indoor positioning. The Bluetooth Low Energy (BLE) based iBeacon solution primarily focuses on the proximity based detection, and its low power consumption and low price bring great potential for its popularity. In this report, assuming that the resident owns a smartphone which is powered on, we present an iBeacon based indoor positioning system and provide some strategies and algorithms to overcome the indoor noise of possibly weak indoor Bluetooth signals. In our system, the Received Signal Strength Index (RSSI) is pre-processed to eliminate noise. Then, the distance between a mobile device and a BLE signal source can be calculated by combination use of pre-processed RSSI, Kalman Filter, and machine learning. In the end, the current mobile device position can be determined by using a triangulation algorithm. Our experimental results, acquired through running experiments in a real-world scenario, show that the localization error can be as low as 0.985m in the 2D environment. We also compared our results against other works with the same research objectives.