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Extended Kalman filter (EKF) is one of the most widely used Bayesian estimation methods in the optimal control area. Recent works on mobile robot control and transportation systems have applied various EKF methods, especially for localization. However, it is difficult to obtain adequate and reliable process-noise and measurement-noise models due to the complex and dynamic surrounding environments and sensor uncertainty. Generally, the default noise values of the sensors are provided by the manufacturer, but the values may frequently change depending on the environment. Thus, this paper mainly focuses on designing a highly accurate trainable EKF-based localization framework using inertial measurement units (IMUs) for the autonomous ground vehicle (AGV) with dead reckoning, with the goal of fusing it with a laser imaging, detection, and ranging (LiDAR) sensor-based simultaneous localization and mapping (SLAM) estimation for enhancing the performance. Convolution neural networks (CNNs), backward propagation algorithms, and gradient descent methods are implemented in the system to optimize the parameters in our framework. Furthermore, we develop a unique cost function for training the models to improve EKF accuracy. The proposed work is general and applicable to diverse IMU-aided robot localization models.