## 1 Introduction  
Railway track irregularities are caused by vehicle dynamics and natural degradation. Changes in track geometric parameters directly affect the operational safety of trains and are the main factors affecting determining the speed and smoothness of the train [1, 2]. The geometric parameters of a track comprise seven internal track parameters--track gauge, track direction, and high and low, horizontal (ultra-high), versein, warp, and track gauge change rate--and two external track geometry parameters--lateral and vertical deviations from the track midline to the left and right of the track relative to the design line position [3]. The Chinese railway department implements a comprehensive integrated inspection and monitoring program for railroad infrastructure according to the principle of \"dynamic inspection as the main, static inspection as a supplement\" [4]. The dynamic inspection vehicle carries out high-accuracy and high-efficiency dynamic inspection of internal geometric parameters of tracks for all lines [5], but its mileage positioning accuracy is low. In addition, the maintenance department use a track geometry state detector to carry out precise mileage positioning and detection of the external parameters of the track for problematic sections, which is used to guideline repair and maintenance. Furthermore, the railway maintenance department applies the track geometry state detector to periodically measure the condition of the static geometry of lines in its jurisdiction, for which the detection task is demanding. The operating length of high-speed railway in China has reached 40,000 km. The trunk line length of a single railway engineering department may be up to hundreds of kilometers, and the maintenance time used for detection of track geometric parameters is about 4 h [6, 7]. Thus, the detection period is short, and the task is challenging [8, 9]. Consequently, there is an urgent need for efficient and high-accuracy equipment for the measurement of track geometric parameters. Based on the different types of track geometric parameters measured, track geometry testing equipment can be divided into absolute and relative measuring types. Absolute measurement equipment consists of track geometry condition measuring instruments, which are used to measure the track geometry parameters of lines dedicated to passengers. This equipment is composed of two parts--a total station and a detector--and has a measurement efficiency of about 160 m/h [10; 11]. Various absolute measurement track detectors have passed the measurement certification of the China Railway Group Corporation and are widely used [12]. The testing parameters of this equipment are complete, yielding high testing accuracy. However, such detectors rely on the track control point (CPIII) to operate, and their testing efficiency is low. Amberg (Switzerland), Trimble (USA), and the Railway Engineering Consulting Group Co., Ltd. developed the \"two rolleys system\", which improves measurement efficiency to 1.5 km/h. However, the measurement accuracy of this system is low, and can only be used for the measurement of geometric parameters of ballast track [13]. The GRP1000 IMS of Amberg (Switzerland), which combines the total station and inertial measurement unit with the track inspection instrument in a single vehicle system, performs a CPIII resection measurement every 60 m, thus resulting in a measurement efficiency of 1.5 km/h. However, due to frequent station changes by the total station and lapping of the measured section, the working efficiency is reduced, and \"lap error\" can occur [14]. Harnessing the rapid development of precise positioning techniques, such as global navigation satellite systems (GNSS), and using the GNSS real-time kinematic (RTK) technique, HTA Burgdorf developed a track surveying platform in cooperation with terra vermessungen AG, Switzerland to improve the measurement efficiency for external parameters of tracks [15].