Error theory of chord-based measurement system regarding track geometry and improvement by high frequency sampling

摘要

The chord-based measurement system has been used for a long time in the measurement of track irregularity, however, the error theory is seldom studied. As a typical case, the mid-chord offset system (MCO-system) is selected in this paper to study the error propagation of chord-based systems. The measurement model and restoration model are established to describe the measurement and restoration process of the MCO-system. To evaluate the accumulation of error, the Error Amplification Factor (EAF) is defined. The regularities of error accumulation are analyzed in the distance domain and the wavelength domain. Furthermore, an error propagation formula of different wavelengths is proposed. High frequency sampling is introduced to improve the performance of the MCO-system, where a least square model is established to handle the redundant measured data, and it can be theoretically proven that the influence of measuring errors can be reduced to zero if the sampling frequency approaches infinity. The error theory given in this paper is useful for designing devices based on the MCO-system and the error of different wavelengths can be accurately controlled. As an application, field measurement is carried out to verify the feasibility and correctness of the models by comparison with the restoration method using a digital inverse filter.