# Extended Particle-Aided Unscented Kalman Filter Based on Self-Driving Car Localization
## 5 Conclusions  
In this research, an extended version of particle-aided unscented Kalman filter was proposed for self-driving car localization. The extended PAUKF is based on more realistic assumptions. In this research, we processed the additional uncertainty by expanding the particle's dimensionality and by improving the weight calculation method of each particle. From the simulation results, we conclude that the previous basic PAUKF has significant limitations in a three-dimensional feature environment. The mean RMSE of estimation based on the previous basic PAUKF was 10.295 m. Compared to the previous basic PAUKF, the extended PAUKF handled the three-dimensional features appropriately. As a result, the mean RMSE of the extended PAUKF was 2.696 m, which represented a 73.81% improvement in precision compared to the previous basic PAUKF, because of the extended particle processing and improved weight selection scheme of the extended PAUKF. We also proposed the feasibility of sensor fusion methodology based on the PAUKF framework. Using our algorithm, a vehicle can receive more precise and robust location information on the basis of traffic lights, road markers, and other traffic elements. However, some limitations still need to be solved. The hyperparameters should be tuned for \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Position of Vehicle** & \multicolumn{3}{c}{**PF**} & \multicolumn{2}{c}{**PAUKF**} \\ \hline  & **Basic** & **Extended** & **Basic** & **Extended** & **Basic** & **Extended** \\ \hline
60 km/h & 30.426 & 29.465 & 11.057 & 6.317 & 10.199 & 2.478 \\
70 km/h & 30.176 & 29.351 & 10.973 & 6.238 & 10.314 & 1.767 \\
80 km/h & 29.883 & 28.319 & 10.989 & 6.265 & 10.458 & 2.303 \\
90 km/h & 29.025 & 29.919 & 11.052 & 5.861 & 10.627 & 2.169 \\
100 km/h & 29.349 & 29.981 & 11.094 & 6.324 & 10.893 & 2.833 \\
110 km/h & 28.365 & 29.144 & 10.851 & 6.303 & 9.751 & 3.441 \\
120 km/h & 29.932 & 30.072 & 10.999 & 6.098 & 9.826 & 3.881 \\ Mean & 29.571 & 29.465 & 11.002 & 6.201 & 10.295 & 2.696 \\ RMSE Change & \multicolumn{3}{c}{\(-\)0.36\%} & \multicolumn{3}{c}{\(-\)43.64\%} & \multicolumn{3}{c}{\(-\)73.81\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The root mean square error (RMSE) of the basic PAUKF and the extended PAUKF in different conditions (unit: m). optimal performance and the motion in vertical direction should be modeled not only by using noise, but also with consideration for the vertical dynamic. In future work, we plan to find the appropriate hyperparameters of the extended PAUKF and implement all the algorithms into a real ground vehicle with consideration for the vertical motion. Conceptualization, M.L. ; Software, M.L. ; Methodology, M.L. ; Validation, M.L. ; Writing--original draft preparation M.L. ; B.K. Writing--review & editing. All authors have read and agreed to the published version of the manuscript. This work was supported by Korea Hydro & Nuclear Power company through the project \"Nuclear Innovation Center for Haeoleum Alliance\" and Technology Innovation Program 2020 funded by the Ministry of Trade, Industry & Energy (MI, Korea). The authors declare no conflicts of interest. The standard deviation of vehicle noise in the vertical direction  
State at sample time k+1  
Timestamp  
Vehicles position in the x dimension at time k  
Yaw rate of the vehicle at time k  
Yaw angle of the vehicle at time k  
Sample time  
Vertical noise of the vehicle  
Distance between feature and vehicle  
The relative bearing angle between feature i and vehicle  
x, y, z position of the vehicle in map coordinate  
Relative distance at x, y, z direction between feature and vehicle.