## 4 Data Smoothing Algorithm
### Detection Accuracy Results and Analysis of Inertial Track Geometry State Detector
#### 5.3.2 Measurement Accuracy Repeatability Test  
The line test was repeated and accurately measured three times under the same environmental conditions using the inertial track geometry detector at a speed of 3 km/h. Based on the data processing software of the inertial detector system developed in this study, the data for the test line were processed, and the track geometry parameters of the test line were obtained. For the detection accuracy analysis, we examined and compared the geometric parameters of track direction, high and low, and horizontal (ultra-high). It should be noted that track gauge, track gauge change rate, and mileage can be measured by a track gauge sensor and mileage sensor on the inertial detector, so they were not  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Model** & **Qualification** & **Parameter** \\ \hline Laser Gyroscope & HT-50 TM & \begin{tabular}{c} Zero Bias Stability \\ Zero Bias Repeatability \\ Monthly repeatability of deviation \\ Scale Factor Nonlinearity \\ \end{tabular} & \(\leq\)0.01 \({}^{\circ}\)/h (1\(\sigma\)) \\ \begin{tabular}{c} Accelerometer \\ I/F Conversion \\ Circuit \\ GPS \\ \end{tabular} & \begin{tabular}{c} JN-06M \\ GZH-06 \\ OEM/19 \\ EC50P-5000 \\ SDVH20 \\ \end{tabular} & \begin{tabular}{c} Monthly repeatability of deviation \\ Scale Factor Nonlinearity \\ \(\leq\)1 \(\times\) 10\({}^{-4}\) \\ \(\leq\)0.5 Hz \\ \end{tabular} \\ \
\begin{tabular}{c} GPS \\ Odemeter \\ Displacement \\ Transduce \\ \end{tabular} &
\begin{tabular}{c} EC50P-5000 \\ SDVH20 \\ \end{tabular} & Resolution & \(<\)0.002 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The main components and technical indicators of the inertial track detector.  
Figure 6: Design of data processing software for track inspector system.  
analyzed in this study. For the convenience of comparative analysis, this test only used the measurement results for the track geometric parameters of the double-wheel side reference track for comparison. The track geometric parameters of the single-wheel side track could be calculated using the geometric parameters of the double-wheel side track, and the accuracy level is consistent.  
The repeatability comparison of the three repeated detection datapoints of the track direction (high and low, and horizontal (ultra-high)) parameters of the test line are shown in Figure 7. Figure 7a-c show the real value of the track direction, high and low, and horizontal (ultra-high) parameters obtained from the three repeated detections of the test line. Figure 7b shows the difference between the second and third measurement results and the first measurement results in the track direction, high and low, and horizontal (ultra-high) parameter data obtained. It can be seen from Figure 7 that the repeatability error of the track direction, high and low, and horizontal (ultra-high) parameters detected by the inertial track geometry state detector based on inertial/GNSS/odometer integrated navigation was better than 0.2 mm, which shows an improved accuracy of the inertial track geometry state detector system.  
Figure 7: _Cont._