Vertical center of mass movement measuring apparatus comprising an inertial sensing device, for producing outputs relating to rotation and acceleration in its local frame of reference and configured for fastening to the back of an animal, preferably a person, a memory and a processor, wherein the processor is programmed to provide a quaternion corresponding to the rotation of the inertial sensing device and a first acceleration, both based on an output of the rotation sensing device, and the processor is programmed to combine the quaternion and the first acceleration and based on the result of the combination to provide, when the device is fastened close enough to the center of mass of a moving object such as a person, an estimate of vertical displacement, or a derivative of vertical displacement, of the center of mass in a global reference frame.