The accuracy of the satellite-based positioning system is severely affected in the presence of local phenomenons like multipath, NLOS and interferences. These local effects are difficult to model due to spatial and (or) temporal dependencies. This study aims to model the position error on the track and later use it for the track classification. The characterization of the track errors can be beneficial as it can help to increase the capacity of the railway track by providing adaptable protection level and also for sending warning alerts to the other trains if any of them is in degraded mode to avoid any sort of accidents. We present a very simple machine learning approach to model the position error. For this purpose, we investigate the Expectation-Maximization (EM) algorithm to estimate the parameters of the Gaussian Mixture Model (GMM). We intuitively selected 3 classes to represent different error shape features to avoid complexity and to keep some diversity. In the learning phase, 5 different runs are used to capture as much as the error variations on the track throughout the day. The models estimated in the learning process is applied to the test samples for the track characterization. The results show that class representation varies due to the error variation within the day. For some particular obstacles, the track is always represented by the class that shows deteriorated conditions. It also shows that the class representation is very similar to the learning samples when the error models are applied to the test sample collected on a different day with a nearly similar satellite configuration.