LAUSR

Abstract This paper proposes a novel approach to measure track irregularity by using a multipoint chord reference (MCR) system. This paper is the first part presenting the theoretical proofs and methodology for analyzing the system performance in a spatial domain. Part II will study the performance in wavelength domain through numerical approaches. In this paper, a unified framework of the MCR system is introduced with a series of definitions. Mathematical models are established based on sensor fusion and least square optimization techniques. The error theory of the MCR system is discussed and the error amplification factor (EAF) is defined to quantify the error accumulation characteristics of the MCR system in the spatial domain. The stability of the MCR system was analyzed and propositions are put forward to reveal the basic relationship between the minimum measurable wavelength and different configurations. In particular, the MCR(n, 1) system was studied, for which propositions were put forward to describe the relationship between the EAF and stability of the MCR system. The MCR system has significant advantages over some current techniques for track irregularity measurement, such as single point chord method as well as gyroscope- and accelerometer-based techniques. The MCR system enables us to use low-cost sensors to achieve the same or even higher precision as the currently used techniques by increasing the number of sensors and sampling frequency. This system can be especially useful to measure track irregularities with short wavelengths, such as rail corrugation. Although the MCR system is mostly used in the railway engineering field, it can be applied to any field in which an irregular surface or curve is required to be measured.