Loop Robots develops and operates the next generation of fully autonomous disinfection robots in hospitals and healthcare settings. Accurate localization is essential in order to navigate reliably and effectively disinfect the tight hallways and corners of a patient room, operating room, or intensive care unit in a hospital. Odometry, or dead-reckoning, is the process of estimating the robots pose with respect to a known initial pose. It forms the backbone of the robots localization strategy, as well as being critical to many other processes that run on the robot, such as control and mapping. The current strategy of generating odometry using the wheel encoders is prone to drift due to the integration of errors into the estimate. Moreover, the estimation takes place on the horizontal plane due to the nature of the wheel encoders. To improve the odometry and extend it to the full 3D space, a solution that makes use of all of the onboard sensors in a tightly-coupled manner is required. In this Thesis, we make the first steps towards this larger goal. The contributions of this thesis include: (1) an Extended Kalman Filter (EKF) algorithm to fuse data from the Inertial Measurement Unit (IMU) and wheel encoders to estimate position and orientation of the robot in 6-DoF; (2) a line feature extraction and tracking methodology to extract primitives from LIDAR data and (3) A Moving Horizon Estimation (MHE) scheme based on a factor-graph formulation to perform pose estimation on the horizontal plane using LIDAR data and wheel encoders. We test the three modules individually using a combination of simulations and real-world data wherever possible. We found that the MHE scheme was able to reduce drift over the long term, but is sensitive to the effects of outliers in feature matching, motion distortion of LIDAR scans, and wheel slip. The EKF scheme is able to reduce the overall drift and correct for wheel slips. Based on these results, promising avenues for the improvement of all the proposed modules are given, along with recommendations on how to combine them all in a tightly-coupled fashion.