  In recent years, Neural Radiance Fields (NeRF) have emerged as a powerful
tool for 3D reconstruction and novel view synthesis. However, the computational
cost of NeRF rendering and degradation in quality due to the presence of
artifacts pose significant challenges for its application in real-time and
robust robotic tasks, especially on embedded systems. This paper introduces a
novel framework that integrates NeRF-derived localization information with
Visual-Inertial Odometry(VIO) to provide a robust solution for robotic
navigation in a real-time. By training an absolute pose regression network with
augmented image data rendered from a NeRF and quantifying its uncertainty, our
approach effectively counters positional drift and enhances system reliability.
We also establish a mathematically sound foundation for combining visual
inertial navigation with camera localization neural networks, considering
uncertainty under a Bayesian framework. Experimental validation in the
photorealistic simulation environment demonstrates significant improvements in
accuracy compared to a conventional VIO approach.
