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In this paper, we perform a rigorous analysis of EKF-based visual-inertial odometry (VIO) and present a method for improving its performance. Specifically, we examine the properties of EKF-based VIO, and show that the standard way of computing Jacobians in the filter inevitably causes inconsistency and loss of accuracy. This result is derived based on an observability analysis of the EKF's linearized system model, which proves that the yaw erroneously appears to be observable. In order to address this problem, we propose modifications to the multi-state constraint Kalman filter (MSCKF) algorithm, which ensure the correct observability properties without incurring additional computational cost. Extensive simulation tests and real-world experiments demonstrate that the modified MSCKF algorithm outperforms competing methods, both in terms of consistency and accuracy.
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