The invention provides a method of estimating the position of a user device carried by a user, the method comprising: providing an initial position of the user device; measuring a vertical acceleration of the user device, thereby generating vertical acceleration data; measuring an orientation of the user device, thereby generating principal direction data; processing the vertical acceleration data to detect one or more steps taken by the user, and subsequently validating the detection of one or more of said one or more steps; generating one or more motion vectors in respect of the validated steps taken by the user using the principal direction data; and estimating an updated position of the user device by combining the motion vector(s) with the initial position. The method may be used by, for example, a smartphone to estimate its position, particularly where other positioning systems are unavailable.