B34 Measurement of an athlete's back angle using magnetic north, accelerometer and a mechanical gyroscope

Abstract

We desire to know the true three-dimensional absolute angle of an athlete's upper back while in vigorous motion. Much of the angle information can be obtained from a high-quality geomagnetic compass, provided the athlete is moving in an area with a straight magnetic field. Unfortunately the angle of rotation around the geomagnetic North direction cannot be detected by magnetic field sensors, and accelerometers cannot distinguish gravitation from acceleration, so at least one additional piece of angular displacement information is needed. In this paper we present a combined measuring method for the angle of a backpack worn by an athlete. With the athlete standing still, a triad of accelerometers measures the gravitational field and thus the true downward direction in the backpack reference frame. This is used to set the zero angle on two axes of a mechanical "vertical" gyroscope. During subsequent motion, rotation of the gyroscope axes is used to develop an incomplete quaternion, that is, one that does not account for rotation about the gyroscope rotor axis. A geomagnetic compass is used to develop another incomplete quaternion but this time with unknown rotation about the local Earth North vector. The unknown rotation axes could in principle align, but in practice this is easily avoided, so the two incomplete rotations can be resolved into a single quaternion representing the true absolute angle of the backpack. To illustrate the method, the design of the geomagnetic and gyroscope systems will be presented, along with details of the mathematics and an example of the measurement of a ski motion on a real ski slope.