Railway track vertical alignment is an important indicator of serviceability condition and thus plays a critical role for maintenance planning. Estimating the rail profile through the vertical acceleration readings provides an efficient alternative to the current practice of optical methods using special vehicles. This paper proposes an algorithm to estimate the rail vertical profile using the vertical acceleration of the vehicle resulting from the train-track dynamic interaction. The algorithm is designed to approximate the inverse of the transfer function from the rail vertical roughness to the train’s measured acceleration. The approximation problem is formulated into an H-infinity optimal control design problem, which can be further transferred into a problem of convex optimization. The proposed algorithm possesses several advantages including easy design, little tuning effort, and low computational cost. In addition, to take into account the model uncertainty, an optimization-based learning framework is proposed to further enhance the performance of the proposed algorithm. The numerical study has been conducted comprehensively to validate the observer’s properties and effectiveness in reconstructing of the rail vertical roughness.

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