Autonomous vehicles have gained significant attention due to technological advancements and their potential to transform transportation. A critical challenge in this domain is precise localization, particularly in LiDAR-based map matching, which is prone to errors due to degeneracy in the data. Most sensor fusion techniques, such as the Kalman filter, rely on accurate error covariance estimates for each sensor to improve localization accuracy. However, obtaining reliable covariance values for map matching remains a complex task. To address this challenge, we propose a neural network-based framework for predicting localization error covariance in LiDAR map matching. To achieve this, we introduce a novel dataset generation method specifically designed for error covariance estimation. In our evaluation using a Kalman filter, we achieved a 2 cm improvement in localization accuracy, a significant enhancement in this domain.