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.

本文研究了用于轨道几何测量的非对称弦参考系统(ACR-system)的误差理论。与中弦偏移系统（MCO 系统）相比，ACR 系统即使在非常短的波长下也显示出更好的带通响应。由于其非线性相位响应，ACR 系统的实施具有挑战性。基于 z 变换，通过设计无限脉冲响应 (IIR) 滤波器来实现 ACR 系统的逆系统。此外，根据IIR滤波器的稳定性来解释ACR系统的稳定性。为了量化 ACR 系统的误差累积，在空间域中定义了误差放大因子 (EAF)，在波长域中定义了临界波长 (CW)。为了演示 ACR 系统的性能，使用高精度大理石平台开发和校准了测量小车。现场测量是在 500 米长的轨道段上进行的。最后，对逆系统的滤波和非滤波实现的比较表明，滤波方法优于非滤波方法。