Automatic detection of falls is important for enabling people who are older to safely live independently longer within their homes. Current automated fall detection systems are typically designed using inertial sensors positioned on the body that generate an alert if there is an abrupt change in motion. These inertial sensors provide no information about the context of the person being monitored and are prone to false positives that can limit their ongoing usage. We describe a fall-detection system consisting of a wearable inertial measurement unit (IMU) and an RF time-of-flight (ToF) transceiver that ranges with other ToF beacons positioned throughout a home. The ToF ranging enables the system to track the position of the person as they move around a home. We describe and show results from three machine learning algorithms that integrate context-related position information with IMU based fall detection to enable a deeper understanding of where falls are occurring and also to improve the specificity of fall detection. The beacons used to localize the falls were able to accurately track to within 0.39 meters of specific waypoints in a simulated home environment. Each of the three algorithms was evaluated with and without the context-based false alarm detection on simulated falls done by 3 volunteer subjects in a simulated home. False positive rates were reduced by 50% when including context.