A location system for locating and determining the motion and velocity of a wireless device. The methods include direct inferences about whether a device is in motion versus static based on a statistical analysis of the variation of radio signal strengths over time. The system is trained according to a sparse set of identified locations from which signal strengths are measured. The system uses the signal properties of the identified locations to interpolate for a new location of the wireless device. The system uses a probabilistic graph where the identified locations of the floor plan, expected walking speeds of pedestrians, and independent inference of whether or not the device is in motion are used to determine the new location of the device.