Abstract: 

In this talk, we introduce a new class of problems related to integrating inertial measurements obtained from an IMU that play a significant role in navigation combined with visual data. While there have been tremendous technological advances in the precision of instrumentation, integrating acceleration and angular velocity still suffers from drift in the displacement estimates. Neural networks have come to the rescue in estimating displacement and the associated uncertainty covariance. However, such networks do not consider the physical roto-reflective symmetries inherent in IMU data, leading to the need to memorize the same priors for every possible motion direction, which hinders generalization. In this work, we characterize these symmetries and show that the IMU data and the resulting displacement and covariance transform equivariantly when rotated around the gravity vector and reflected with respect to arbitrary
planes parallel to gravity. We propose a network for predicting an equivariant gravity-aligned frame from equivariant vectors and invariant scalars derived from IMU data, leveraging expressive linear and non-linear layers tailored to commute with the underlying symmetry transformation. Such a canonical frame can precede existing architectures that are end-to-end or filter-based. We will include an introduction to the inertial filtering problem and we will present
results in real-world datasets.

Zoom link: https://caltech.zoom.us/j/88141815847?pwd=ayPBbwoDE91IWysv1P4Oxp6zbamrSQ.1