Trackside-measurement-based railway track irregularity estimation using a vehicle-track model and extended Kalman filtering strategy

Track vertical irregularity is a key indicator of railway track condition, but conventional inspection methods cannot provide frequent measurements at critical sections. Fixed rail and sleeper sensors offer repeated trackside responses during train passage, yet continuous mileage-domain estimation from trackside measurements remains insufficiently studied. Therefore, this study proposes an extended Kalman filter (EKF) framework for estimating vertical irregularity from fixed trackside responses. To illustrate its applicability, the framework is evaluated using three common types of trackside measurements: sleeper acceleration, rail displacement, and rail acceleration. Numerical tests are conducted to evaluate the proposed algorithm. The effects of sensor spacing, random sensor failure, measurement noise, and vehicle–track parameter mismatch are considered. The results show that the framework achieved root-mean-square errors (RMSEs) of 0.238, 0.147, and 0.208 mm for sleeper acceleration, rail displacement, and rail acceleration, respectively, at 0.6 m spacing without added noise. Increasing the spacing to 2.4 m raised the RMSEs to 0.457, 0.962, and 0.805 mm, with most of the additional error occurring at longer wavelengths. Random sensor loss caused observation-dependent degradation, with rail displacement showing the greatest sensitivity to failure layout. Under noise conditions, the rail-displacement RMSE remained stable but the acceleration-based estimates deteriorated more markedly. Parameter mismatch also produced observation-dependent errors. These results demonstrate the numerical feasibility of continuous irregularity estimation from fixed trackside responses. With further field validation and adaptive calibration, the framework could support frequent track-geometry monitoring at critical sections using permanently installed rail or sleeper sensors.