EqNIO: Subequivariant Neural Inertial Odometry

Abstract

Neural networks that regress the displacement and associated covariance of an inertial measurement unit (IMU) purely from its accelerometer and gyroscope measurements have become key enablers to low-drift inertial odometry, but still ignore the physical roto- reflective symmetries inherent in IMU data, thus hindering generalization. In this work, we show that IMU data, displacements and covariances transform equivariantly, when rotated around and reflected across planes parallel to gravity. We design a neural network that equivariantly estimates a gravity-aligned frame from IMU data, leveraging tailored linear and non-linear layers, and uses it to canonicalize the data. We train an off-the-shelf inertial odometry network on this data and map its outputs back into the original frame, thus obtaining equivariant covariances and displacements. To highlight its generality, we apply the framework to both filter-based and end-to-end approaches and show better performance on the TLIO, Aria, RIDI and OxIOD datasets than existing methods.