Analytic Combined IMU Integration (ACI²) For Visual Inertial Navigation

Abstract

Batch optimization based inertial measurement unit (IMU) and visual sensor fusion enables high rate localization for many robotic tasks. However, it remains a challenge to ensure that the batch optimization is computationally efficient while being consistent for high rate IMU measurements without marginalization. In this paper, we derive inspiration from maximum likelihood estimation with partial-fixed estimates to provide a unified approach for handing both IMU preintegration and time-offset calibration. We present a modularized analytic combined IMU integrator (ACI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) with elegant derivations for IMU integrations, bias Jabcobians and related covariances. To simplify our derivation, we also prove that the right Jacobians for Hamilton quaterions and SO(3) are equivalent. Finally, we present a time offset calibrator that operates by fixing the linearization point for a given time offset. This reduces re-integration of the IMU measurements and thus improve efficiency. The proposed ACI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and time-offset calibration is verified by intensive Monte-Carlo simulations generated from real world datasets. A proof-of-concept real world experiment is also conducted to verify the proposed ACI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> estimator.