While GPS long has been an industry standard for localization of an entity or person anywhere in the world, it loses much of its accuracy and value when used indoors. To enable services such as indoor navigation, other methods must be used. A new standard of the Wi-Fi protocol, IEEE 802.11mc (Wi-Fi RTT), enables distance estimation between the transmitter and the receiver based on the Round-Trip Time (RTT) delay of the signal. Using these distance estimations and the known locations of the transmitting Access Points (APs), an estimation of the receiver’s location can be determined. In this thesis, a smartphone Wi-Fi RTT based Indoor Positioning System (IPS) is presented using an Unscented Kalman Filter (UKF). The UKF using only RTT based distance estimations as input, is established as a baseline implementation. Two extensions are then presented to improve the positioning performance; 1) a dead reckoning algorithm using smartphone sensors part of the Inertial Measurement Unit (IMU) as an additional input to the UKF, and 2) a method to detect and adjust distance measurements that have been made in Non-Line-of-Sight (NLoS) conditions. The implemented IPS is evaluated in an office environment in both favorable situations (plenty of Line-of-Sight conditions) and sub-optimal situations (dominant NLoS conditions). Using both extensions, meter level accuracy is achieved in both cases as well as a 90^th percentile error of less than 2 meters.