Pedestrian dead reckoning using differential geometric properties of human gait

In some embodiments, a method comprises: receiving acceleration data from a motion sensor of a mobile device carried by a user, the acceleration data represented by a space curve in a three-dimensional (3D) acceleration space, the space curve indicative of a cyclical vertical displacement of the user's center of mass accompanied by a lateral left and right sway of the center of mass when the user is stepping; computing a tangent-normal-binormal (TNB) reference frame from the acceleration data, the TNB reference frame describing instantaneous geometric and kinematic properties of the space curve over time; and computing a direction of travel of the user based on an orientation of a unit binormal (B) vector of the TNB reference frame in the 3D acceleration space, and computing a speed of the user based on a linear regression model applied to the kinematic properties of the TNB reference frame.