# A Particle PHD Filter for Dynamic Grid Map Building towards Indoor Environment
## 4 Simulation
### Accuracy Comparison of Speed Estimation
#### 4.2.2 The Robot Is in Motion  
We select four target points on the navigation map and use the ROS navigation package to navigate the Mir Robot. The robot reaches the four points in sequence and moves in a loop. The Simulation environment in Gazebo is shown in Figure 11a and the yellow cylinder is the dynamic object to be estimated (a square box object can replace the cylindrical object, and it is not shown in Figure 11a). The robot trajectory is shown as the green line in Figure 11b. The movement of dynamic objects is the same as in Section 4.2.1, and the trajectory is shown by the red arrow. The comparison result of the speed estimation using the filter with the CV motion model is shown in Figure 12, and combining the CV and CS motion model proposed in this paper is shown in Figure 13 when the Mir Robot is in motion. In the x-direction, the velocity estimation error using the filter with the CV motion model is larger than the estimation error when the robot is stationary, regardless of whether the target is maneuvering or moving at a constant speed. While the filter with the proposed motion model can still achieve a relatively good performance in all motion stages of the dynamic object, although the fluctuation of the estimation speed error has also increased. In the y-direction, the \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Object**} & \multicolumn{3}{c}{**CV Model(m/s)**} & \multicolumn{3}{c}{**The System(m/s)**} & \multicolumn{3}{c}{**Improvement**} \\ \cline{3-11} \multicolumn{2}{c}{} & **RMSE** & **MAE** & **S.D.** & **RMSE** & **MAE** & **S.D.** & **RMSE** & **MAE** & **S.D.** \\ \hline cylinder & x & 0.7098 & 0.5012 & 0.7069 & 0.2148 & 0.1518 & 0.2052 & 69.73\% & 69.71\% & 70.97\% \\  & y & 0.0207 & 0.0170 & 0.0205 & 0.0262 & 0.0208 & 0.0263 & \(-\)26.57\% & \(-\)22.35\% & \(-\)28.29\% \\ box & x & 0.7029 & 0.4983 & 0.7016 & 0.2036 & 0.1424 & 0.2029 & 71.03\% & 71.42\% & 71.08\% \\  & y & 0.0142 & 0.0114 & 0.0138 & 0.0179 & 0.0120 & 0.0159 & \(-\)26.05\% & \(-\)5.26\% & \(-\)15.27\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The result of the metric absolute speed error when the robot is stationary. Figure 10: Comparison of filter speed estimation using the proposed motion model and true value speed when the robot is stationary. (**a**) Velocity comparison in the x-direction of the box; (**b**) Velocity comparison in the x-direction of the cylinder; (**c**) Velocity comparison in the y-direction of the box; (**d**) Velocity comparison in the y-direction of the cylinder. filter's speed estimation error with the CV motion model or the motion model proposed in this paper both increase significantly and even reach 0.15-0.2 m/s. That is mainly because when the robot and the dynamic object are moving, the area that is not scanned by the laser at the current time may be scanned the next time, and the scanned area may be blocked the next time. As the measurement area of the same object changes, a corresponding speed estimate will be generated, which will eventually be superimposed on the speed estimate of a whole dynamic object, causing the estimation to be biased and the accuracy to decrease. Figure 11: (**a**) Simulation environment in Gazebo; (**b**) Control interface in Rviz. Figure 12: Comparison of filter speed estimation using CV motion model and true value speed when the robot is in motion. (**a**) Velocity comparison in the x-direction of the box; (**b**) Velocity comparison in the x-direction of the cylinder; (**c**) Velocity comparison in the y-direction of the box; (**d**) Velocity comparison in the y-direction of the cylinder. The comparison of RMSE, Mean Error, and Standard Deviation (S.D.) of the metric absolute speed error when the robot is in motion are shown in Table 3. Compared with the CV motion model, the proposed method that combines the CS and CV motion model can improve the speed estimation accuracy by more than 65% in the x-direction.