arXiv:2610.41768v1 Announce Type: new Abstract: Recent years have seen multiple impressive results in visual-inertial odometry (VIO) techniques, by which accurate state estimation can be achieved via the extended Kalman filter (EKF) or nonlinear optimization. However, these approaches are rarely open source, and they tend to fail in real experiments due to the temporary lack of feature points and fast motion. Therefore, in this study, we used encoders to overcome the temporary failure of purely vision-based simultaneous localization and mapping (SLAM). Here, we propose a generative measurement model for encoders and derive an expression for the maximum a posteriori (MAP) estimate and necessary Jacobians for optimization. We use our theory to present a novel tightly coupled visual-inertial encoder RGB-Depth (RGB-D) SLAM system. Tests on our system on an in-house dataset confirmed that our modeling effort led to accurate (with a root mean squared error (RMSE) of approximately 2-7 cm) and robust state estimation in real time. The source code and our dataset containing the encoder information have been published for verification.