Detection of Rotations Around a Fixed Axis Using Gyroscopes

The generalized likelihood-ratio test for zero-velocity detection provides a statistical motivation for commonly used zero-velocity detectors within inertial sensing. However, thus far, no equivalent statistical tests for other types of motions have been presented. Therefore, current activity and movement classifiers for inertial sensors typically rely on data-driven algorithms with features based on standard statistical measures. This letter studies the detection of rotations around a fixed axis using generalized likelihood-ratio tests. Two signal models are considered to describe such rotations. The first assumes a constant angular velocity and the second assumes a constant rotation direction. The resulting detection statistics are derived as the sample variance of the gyroscope measurements and the smallest eigenvalue of a positive semidefinite matrix that is proportional to the square of the gyroscope measurements over the detection interval. Experimental results support the use of the constant rotation direction model, thereby highlighting the need for a signal model that is more general than the constant angular velocity model.