  In this paper we propose a new analytical preintegration theory for
graph-based sensor fusion with an inertial measurement unit (IMU) and a camera
(or other aiding sensors).Rather than using discrete sampling of the
measurement dynamics as in current methods,we derive the closed-form solutions
to the preintegration equations, yielding improved accuracy in state
estimation.We advocate two new different inertial models for preintegration:
(i) the model that assumes piecewise constant measurements, and (ii) the model
that assumes piecewise constant local true acceleration.We show through
extensive Monte-Carlo simulations the effect that the choice of preintegration
model has on estimation performance.To validate the proposed preintegration
theory, we develop both direct and indirect visual-inertial navigation systems
(VINS) that leverage our preintegration.In the first, within a tightly-coupled,
sliding-window optimization framework, we jointly estimate the features in the
window and the IMU states while performing marginalization to bound the
computational cost.In the second, we loosely-couple the IMU preintegration with
a direct image alignment that estimates relative camera motion by minimizing
the photometric errors (i.e., image intensity difference), allowing for
efficient and informative loop closures. Both systems are extensively validated
in real-world experiments and are shown to offer competitive performance to
state-of-the-art methods.
