Estimating the Angular Velocity From Body-Fixed Accelerometers

This paper presents a novel way of determining the angular velocity of a rigid body from accelerometer measurements. This method finds application in crashworthiness and motion analysis in sports, for example, where impacts forbid the use of mechanical gyroscopes. Based on previous work, the time-integration (TI) and polynomial-roots (PR) estimates of the angular velocity are first computed. The TI and PR estimates are then linearly combined through a weighted sum whose weighting factor is chosen so as to minimize the `variance of the resulting estimate. The proposed method is illustrated in an experiment, where the twelve accelerometer array (OCTA) is moved manually. A comparison of the angular-velocity estimates obtained from the proposed method and those obtained from a magnetic displacement sensor shows that the resulting estimates are robust and do not suffer from the drift problems that hinder the TI method. Moreover, comparison with a previously reported method indicates that the method proposed here is less sensitive to measurement errors, especially at low angular velocities.