This paper presents a methodology for predicting remaining train arrival times along a predefined railway path using sectionally sampled GPS-based observations collected between consecutive stations. Station-level remaining arrival times are derived from multiple train trips and analyzed using a linear regression model, enabling assessment of both prediction accuracy and temporal consistency. The approach provides continuous predictions of remaining arrival times at each station along the path rather than focusing solely on the final destination. Results demonstrate that median remaining arrival time errors decrease with increasing sampling density, an effect attributed to greater sample availability that captures a larger proportion of the underlying train dynamics and timetable adherence. Under these conditions, the proposed methodology achieves a station-based average median remaining arrival time error of less than 91 seconds. Across 100 repeated out-of-sample evaluations, the results indicate reproducible performance and acceptable coarseness even when the sampling density is substantially reduced. This continuous, station-level prediction capability enables early detection of delays and potential timetable conflicts, providing minute-level predictive accuracy suitable for decision support for train dispatchers