Detection of Linear Translations Using Inertial Sensors

The generalized likelihood-ratio framework for zero-velocity detection has had a significant impact on the indoor navigation community, accelerating the wides-pread adoption and popularization of foot-mounted inertial navigation. Recently, a detector of rotations around a fixed axis was proposed, thereby marking the first extension of the generalized likelihood-ratio test to motions other than zero-velocity events. This letter presents an additional advancement in this domain by introducing the first detector of linear translations. A signal model that assumes a constant acceleration direction and zero angular velocity is considered. The test statistic associated with the acceleration model is derived as the minimized smallest eigenvalue of a matrix dependent on the unknown gravity direction, where the minimization is performed over all possible gravity directions. Further, it is demonstrated how to incorporate zero velocity and constant rotation direction hypotheses, thereby constructing a motion classifier that can decide between four hypotheses. The performance of the classifier is demonstrated using data from resistance training, reaching an accuracy of 95%.