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 real-time robotic navigation. 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 a photorealistic simulation environment demonstrates significant improvements in accuracy compared to a conventional VIO approach.