Autonomous mobile robots operating in novel environments depend critically on accurate state estimation, often utilizing visual and inertial measurements. Recent work has shown that an invariant formulation of the extended Kalman filter improves the convergence and robustness of visual-inertial odometry by utilizing the Lie group structure of a robot's position, velocity, and orientation states. However, inertial sensors also require measurement bias estimation, yet introducing the bias in the filter state breaks the Lie group symmetry. In this paper, we design a neural network to predict the bias of an inertial measurement unit (IMU) from a sequence of previous IMU measurements. This allows us to use an invariant filter for visual inertial odometry, relying on the learned bias prediction rather than introducing the bias in the filter state. We demonstrate that an invariant multi-state constraint Kalman filter (MSCKF) with learned bias predictions achieves robust visual-inertial odometry in real experiments, even when visual information is unavailable for extended periods and the system needs to rely solely on IMU measurements.

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