Experimental and numerical investigations of asymmetric chord-reference system regarding track geometry measurement

•Two implementations of the inverse system of ACR-system are introduced.•Error amplification factor (EAF) is defined to quantify the error accumulation of the ACR-system.•Numerical experiment is carried out to study the error accumulation of the ACR-system in wavelength domain.•A measurement trolley is developed and calibrated based on a high precision marble benchmark.•A field test is carried out to demonstrate the performance of ACR-system. This paper studies the error theory of the asymmetric chord-reference system (ACR-system) for track geometry measurement. In contrast to mid-chord offset system (MCO-system), ACR-system shows a much better band-pass response even in very short wavelengths. The implementation of the ACR-system is challenging due to its nonlinear phase response. Based on z-transform, the inverse system of the ACR-system is realized by designing an infinite impulse response (IIR) filter. Moreover, the stability of ACR-system is explained according to the stability of the IIR filter. To quantify the error accumulation of the ACR-system, error amplification factor (EAF) is defined in spatial domain, and critical wavelength (CW) is defined in wavelength domain. To demonstrate the performance of ACR-system, a measurement trolley is developed and calibrated using a high precision marble platform. A field measurement is carried out on a 500-meter-long rail section. Finally, a comparison between the filtering and non-filtering implementations of the inverse system shows that the filtering method outperforms the non-filtering one.