This paper presents a localization system for an autonomous wheelchair that includes several sensors, such as odometers, LIDARs, and an IMU. It focuses on improving the odometric localization accuracy using an LSTM neural network. Improved odometry will improve the result of the localization algorithm, obtaining a more accurate pose. The localization system is composed by a neural network designed to estimate the current pose using the odometric encoder information as input. The training is carried out by analyzing multiple random paths and defining the velodyne sensor data as training ground truth. During wheelchair navigation, the localization system retrains the network in real time to adjust any change or systematic error that occurs with respect to the initial conditions. Furthermore, another network manages to avoid certain random errors by using the relationship between the power consumed by the motors and the actual wheel speeds. The experimental results show several examples that demonstrate the ability to self-correct against variations over time, and to detect non-systematic errors in different situations using this relation. The final robot localization is improved with the designed odometric model compared to the classic robot localization based on sensor fusion using a static covariance.