This article describes an algorithm that provides visual odometry estimates from sequential pairs of RGBD images. The key contribution of this article on RGBD odometry is that it provides both an odometry estimate and a covariance for the odometry parameters in real-time via a representative covariance matrix. Accurate, real-time parameter covariance is essential to effectively fuse odometry measurements into most navigation systems. To date, this topic has seen little treatment in research which limits the impact existing RGBD odometry approaches have for localization in these systems. Covariance estimates are obtained via a statistical perturbation approach motivated by real-world models of RGBD sensor measurement noise. Results discuss the accuracy of our RGBD odometry approach with respect to ground truth obtained from a motion capture system and characterizes the suitability of this approach for estimating the true RGBD odometry parameter uncertainty.