Train Speed Estimation Based on Weights Incorporating Systematic and Random Error Components

Train on-board systems estimate speed using data from multiple sensors, each of which may fail under specific operating conditions. Accurate speed estimation is critical for railway safety. This study considers a hypothetical 60-second braking scenario. Speed is measured by five sensors with different characteristics and measurement models. Sensor data are fused using three methods: mean, median, and weighted. The weights are proportional to the inverse square of the measurement uncertainty. These uncertainties include both random and systematic components. Unlike many existing studies, the proposed approach incorporates systematic effects instead of relying solely on variances. The results show that the mean and median methods are simple to implement but do not provide the most accurate estimates. The mean is highly sensitive to outliers and performs poorly when a sensor malfunctions, for example, during wheel slide. The weighted method accounts for both random and systematic effects and provides the closest agreement with the reference value, although it requires analysis of the underlying measurement models.