With the expansion of railway operation scale and the increase in service time, the demand for the efficiency of track condition inspection and maintenance has risen remarkably. The traditional manual track inspection or hand-pushed equipment can hardly meet the requirements of modern railways for inspection efficiency and accuracy. Non-contact methods based on on-board dynamic inspection, such as the combination of optical and inertial sensors, can efficiently complete the measurement of track geometric parameters, profiles, and other key indicators. However, the measurement of single sensors (for example, line-structured optical sensors) under dynamic conditions has problems like trajectory distortion, especially the limited accuracy in the direction of rail extension, which becomes a key factor restricting the accuracy of track 3D point cloud construction. Compensating the platform vibration in a high dynamic environment with the position and attitude changes measured by inertia and constructing a real 3D point cloud can enhance the dimension of detection information and have a wide application prospect. Currently, there are no related mature methods and applications for high-precision line structured light 3D point cloud construction. In our study, an inertial trajectory measurement method with the fusion of odometry and IMU is proposed, which has a high short-term accuracy retention ability and improves the accuracy of the 3D point cloud. The point cloud data is applied to the field of track geometric parameter measurement. Based on the point cloud data, the vertical and horizontal 10 m chord measurements, and the level are calculated to realize the application value of the data.

To address the above issues, we propose a real-time construction method of track 3D point clouds based on multi-sensor fusion. The multi-sensor fusion point cloud calculation method is shown in Fig. 3. Firstly, we improve the short-term holding accuracy of inertial navigation by optimizing the initial alignment algorithm of the inertial measurement system and the inertial attitude solving algorithm within the framework of extended Kalman filtering. Then, we design the coordinate conversion method of point cloud construction, which converts the point cloud data measured by the line-structured optical sensors to the geographic coordinate system. Finally, the geometric parameters of the track are projected according to the 3D point cloud to achieve the application of the point cloud data. The train cannot start and stop randomly in the actual detection task, so it is necessary to achieve the dynamic and rapid alignment of the attitude. We construct and solve the Wahba equation and optimize the alignment algorithm based on the inertial system. In terms of inertial trajectory solution, the measurement equation is derived based on the specific force equation, which directly observes the misalignment angle and the zero deviation of the plus meter. The measurement equation is derived based on the trajectory recursive equation, which directly observes the misalignment angle, the position error, and the scale coefficient of the odometer. Based on the extended Kalman filter framework, the fusion filtering of the odometer and IMU data is realized. In the point cloud coordinate conversion algorithm, the trajectory and attitude are interpolated, and the coordinates are converted according to the joint calibration parameters. In terms of 3D point cloud data application, a typical application scheme of the track point cloud is introduced, which is the non-contact rapid measurement of track geometric parameters.

The feasibility and accuracy advantages of the method are verified through the special train experiments of the Beijing Circular Railway Test. 1) The heading angle error varies greatly in the initial 500 s, and then gradually stabilizes within 1°. The horizontal attitude angle error is rapidly reduced to below 0.1° within 20 s. The alignment angle error is close to the theoretical one, and the alignment accuracy is close to the theoretical value and can be applied to the actual working conditions of train detection. 2) As shown in Fig. 7, based on the method proposed in our study, the measurement error of the roll angle is within -0.025°?0.010°, and the measurement error of pitch angle is within ±0.01°, which shows high accuracy. As shown in Fig. 8, after accurate calibration, the mounting declination in the pitch direction is -0.05°. After considering the installation deviation angle, the accuracy of elevation measurement is obviously improved, and the elevation drift is only 3.92 m when the train travels for 50 km. The elevation error increases the fastest in the section from 439860 to 439944 s in the figure, the cumulative mileage is about 1.6 km, and the elevation error has increased by 1.3 m, which shows that the elevation error is within 0.81‰ of the cumulative mileage. As shown in Fig. 9, the train travels about 91.7 km cumulatively, the maximum deviation of plane is 290.84 m, and the plane deviation is about 3.17‰ of the mileage. Based on the comprehensive above data, the accuracy maintenance ability of the inertial measurement method proposed in our study can be illustrated. 3) The measurement repeatability of the vertical 10 m chord measurements is used as an evaluation index, and the repeatability of the method in our study is 0.71 mm. The measured and reference values for vertical and horizontal 10 m chord and level are compared in Fig. 12, and the trend of the waveforms of the two detections is more consistent. The peak values of the measured values and reference values at 11 preset working conditions are shown in Table 1. The maximum error value of the horizontal 10 m chord and level is 0.41 mm, and the maximum error value of the vertical 10 m chord is 1.07 mm. The rail direction and horizontal value better represent the measurement accuracy of the system, and the measurement deviation in the actual unevenness parameter accounts for a maximum of 4.8%, which can satisfy the accuracy requirement of practical application.

The method proposed in our study does not require static initial alignment and can dynamically complete the attitude initialization and detection tasks with the start and stop of the train, which solves the influence of train scheduling constraints on the detection accuracy. The multi-sensor fusion significantly improves the short-time accuracy retention ability and ensures the stability of local accuracy by reducing the correction frequency. This method has a wide application prospect in the field of railway condition monitoring, which can provide strong technical support for track disease identification and real-time maintenance and provide a guarantee for improving the safety and efficiency of railway operation.