# Comprehensive Evaluations of NLOS and Linearization Errors on UWB Positioning
## 4 Conclusions  
Aiming at evaluating the impacts of linearization errors and NLOS errors on UWB positioning accuracy, a robust particle filter UWB positioning algorithm based on IGGIII was presented in this paper. Meanwhile, traditional UWB positioning methods such as Bancroft, LS, EKF, UKF, CKF, and PF were used to aid separating the independent influences of such two kinds of errors on the UWB positioning performance. The results based on TOF-UWB data in the simulation test and field test demonstrated that (1) the linearization errors exist in UWB positioning significantly while using linearization adjustments (i.e., LS and EKF). However, it can be eliminated by using the nonlinearized filter (i.e., UKF, CKF, and  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Bancroft** & **LS** & **EKF** & **UKF** & **CKF** & **PF** & **RPF** \\ \hline Time (s) & 2.8 & 5.8 & 6.3 & 21.9 & 13.6 & 45.4 & 51.6 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Algorithm running times in field experiment.  
Figure 12: Positioning error statistics of different algorithms in the field experiment: (**a**) 3D positioning error statistics of different algorithms; (**b**) horizontal positioning error statistics of different algorithms; (**c**) vertical positioning error statistics of different algorithms.  
PF). Such elimination would be weakened by the coupled errors in UWB measurements. When there was only white noise (as shown in the simulation test), the nonlinearized filters provided visible accuracy improvements. Otherwise, the improvements will be invisible while coupling with a strong NLOS signal. (2) The IGGIII robust algorithm can constrain the impact of NLOS errors on UWB positioning accuracy obviously. In general, compared to the solutions from the Bancroft, LS, EKF, UKF, CKF, and PF, the RPF produced 64.9%, 63.5%, 42.5%, 39.9%, 15.1%, and 13.1% 3D position improvements on average, respectively. The truncation errors and NLOS errors can, respectively, lead to 36.6% and 23.7% accuracy degradations in UWB 3D positioning. However, the presented method cost more running time than the other methods, with about 17.4 times, 14.7 times, 7.3 times, 2.3 times, 3.7 times, and 1.2 times compared to the times needed in Bancroft, LS, EKF, UKF, CKF, and PF. In addition, the horizontal accuracy of UWB (centimeter level) was much higher than those in the vertical direction (meter level) own to the geometry structure between the tag and base stations. Based on the conclusions in this paper, the goal in our future work is to upgrade the UWB positioning accuracy in the vertical component.  
Data curation, Y.L. and Q.X.; funding acquisition, Z.G.; investigation, Q.X.; methodology, Y.L. and Z.G.; software, Y.L.; supervision, C.Y.; validation, Y.L.; visualization, Y.L.; writing--original draft, Y.L.; writing--review and editing, Z.G. and C.Y. All authors have read and agreed to the published version of the manuscript.  
This work was partially funded by the National Key Research and Development Program of China (Grant No. 2021 YFB3901301), the National Natural Science Foundation of China (NSFC) (Grants No. 42274022).