# A Particle PHD Filter for Dynamic Grid Map Building towards Indoor Environment
## 5 Discussion  
The above three simulation experiments can prove the superiority of the algorithm proposed in this paper. First, set the two dynamic objects, the box and cylinder, to move only within the robot's perception area, and estimate their speeds when the robot is stationary and in motion. The results prove the effectiveness of the method proposed in this paper to establish the dynamic grid map in the robot coordinate system. At the same time, the method of combining the CS and CV motion model makes the algorithm estimate the speed of dynamic objects faster and with higher accuracy compared with CV motion  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Dynamic Object**} & \multirow{2}{*}{
\begin{tabular}{c} **Velocity** \\ **Direction** \\ \end{tabular} } & \multicolumn{2}{c}{**Mean of Peak Error (m/s)**} & \multicolumn{2}{c}{**Convergence Time(s)**} \\ \cline{3-6}  & & **Nuss’s Method** & **The Proposed Method** & **Nuss’s Method** & **The Proposed Method** \\ \hline \multirow{3}{*}{box} & x-direction & 1.1899 & 0.4654 & 2.9625 & 0.312 \\  & y-direction & 0.7971 & 1.0833 & 3.1125 & 0.825 \\ \cline{1-1}  & x-direction & 1.7644 & 1.5356 & 2.925 & 0.751 \\ \cline{1-1}  & y-direction & 0.2788 & 0.6005 & 2.55 & 1.275 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Algorithm performance comparison.  
Figure 17: Number of particles and time cost (**a**) using the Nuss’s method; (**b**) using the method proposed in this paper.  
model. Secondly, when dynamic objects enter and leave the robot's sensing range, the algorithm proposed in this paper can converge to the true value in a relatively short time. Then, during the execution of the algorithm, the number of particles will be dynamically adjusted as the number of grids occupied by dynamic objects changes, so that the algorithm can be applied to different scenes more efficiently.  
Meanwhile, we notice two shortcomings of the proposed method. First, a grid map of appropriate resolution can fully characterize the shape of the object. An object usually contains multiple grid cells, and different parts of the object may be observed at different times, which will lead to estimation errors. Secondly, the dynamic object segmentation in this paper is based on whether the distance and angle information measured by the laser is continuous, but the recognition of dynamic objects is not involved here. Therefore, if a dynamic object is completely occluded and then enters the robot's sensing range or an object enters the robot's sensing range, the algorithm cannot judge whether it is related to the previous dynamic object. However, usually in the process of indoor navigation, we do not need such recognition correspondence; we only need to know the position and speed information of dynamic objects.  
In the future research, we will combine the extended object tracking method based on the original method to eliminate the estimation error caused by the changes from the measurement part of the same object. In addition to the navigation algorithm, we will introduce the speed information of dynamic objects to improve the robot's dynamic obstacle avoidance ability.