  In this paper, we study state estimation of multi-visual-inertial systems
(MVIS) and develop sensor fusion algorithms to optimally fuse an arbitrary
number of asynchronous inertial measurement units (IMUs) or gyroscopes and
global and(or) rolling shutter cameras. We are especially interested in the
full calibration of the associated visual-inertial sensors, including the IMU
or camera intrinsics and the IMU-IMU(or camera) spatiotemporal extrinsics as
well as the image readout time of rolling-shutter cameras (if used). To this
end, we develop a new analytic combined IMU integration with intrinsics-termed
ACI3-to preintegrate IMU measurements, which is leveraged to fuse auxiliary
IMUs and(or) gyroscopes alongside a base IMU. We model the multi-inertial
measurements to include all the necessary inertial intrinsic and IMU-IMU
spatiotemporal extrinsic parameters, while leveraging IMU-IMU rigid-body
constraints to eliminate the necessity of auxiliary inertial poses and thus
reducing computational complexity. By performing observability analysis of
MVIS, we prove that the standard four unobservable directions remain - no
matter how many inertial sensors are used, and also identify, for the first
time, degenerate motions for IMU-IMU spatiotemporal extrinsics and auxiliary
inertial intrinsics. In addition to the extensive simulations that validate our
analysis and algorithms, we have built our own MVIS sensor rig and collected
over 25 real-world datasets to experimentally verify the proposed calibration
against the state-of-the-art calibration method such as Kalibr. We show that
the proposed MVIS calibration is able to achieve competing accuracy with
improved convergence and repeatability, which is open sourced to better benefit
the community.
