## 5 Conclusions  
Dynamic coordinate measurement in industrial manufacturing is a popular issue which needs to be solved urgently. wMPS is now recognized as a promising solution because of its great potential. Nevertheless, the dynamic error caused by measurement principle gains little research and limits its further development. In this article, we first analyzed the mechanism of dynamic error. Then error modeling and simulations experiments about the uncertainty were carried out. The characteristics of the dynamic error were expounded. To validate the mathematical model, practical experiments were done and the results matched well with simulations. It laid the foundation for error compensation and performance improvement. It is noteworthy that we have made an assumption that the receiver moves at a constant speed. As stated in Section 1, wMPS has a measurement frequency of 20 Hz. It is often used in industrial manufacturing such as aircraft assembly and leveling, digital shipbuilding, and tooling monitoring. There is often no jump in acceleration for moving targets on such occasions. In a measurement cycle, i.e., 50 ms, the speed of the target can be seen as constant. The assumption is acceptable in practice.  
In the future, we will focus our research on error compensation through hardware and software enhancement. The inertial measurement unit (IMU) can sense its own acceleration at a frequency of 400 Hz (such as STIM 300) and it will be embedded in the receiver. At each measurement cycle, the IMU will provide the real-time speed of the receiver. The model may be further optimized. Besides, the rotation speed of the transmitter has a great influence on the dynamic error. We will try more advanced shaft system and improve the rotation speed, which can also ensure a longer working life. As for software, a model-based compensation algorithm may be a good choice for dynamic error restriction. The development of machine learning provides novel ideas for our future work.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Straightness Error/mm**} \\ \cline{2-6}  & **Simulation Experiments** & \multicolumn{2}{c}{**Practical Experiments**} & \multicolumn{2}{c}{**Deviation**} \\ \cline{2-6}  & **5 m** & **7 m** & **5 m** & **7 m** & \\ \hline v = 30 mm/s & 0.635 & 0.829 & 0.647 & 0.906 & 0.012 & 0.077 \\ v = 60 mm/s & 1.082 & 1.627 & 1.130 & 1.693 & 0.048 & 0.066 \\ v = 120 mm/s & 2.352 & 3.070 & 2.434 & 3.161 & 0.082 & 0.091 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Deviation between simulation and practical experiments.  
Figure 13: Straightness error of practical trajectory at 7-m at different speeds.  
**Author Contributions:** Conceptualization, methodology, experiment design, and original draft, S.S. and L.Y.; experiment and analysis, R.D. and Z.Z.; software, J.L.; supervision and funding acquisition, J.Z. and C.L.; review and editing, S.S.  
**Funding:** This research was funded by the National Key Research and Development Program of China, Grant No. 2017 YFF0204802; National Natural Science Foundation of China, Grant Nos. 51721003, 51775380, 51705023 and Natural Science Foundation of Tianjin, Grant No. 16 JCZDJC38100.  
**Conflicts of Interest:** The authors declare no conflict of interest.