# An Obstacle-Tolerant Path Planning Algorithm for Mobile-Anchor-Node-Assisted Localization
## 5 Performance Evaluation
### Simulation Results  
#### 5.3.1 Impact of Blocking Rate  
In an obstacle-free environment, OTPP performs as the Z-curve. The MAN travels the entire basic square with five beacon points. However, in the obstacle-present environment, the number of beacon points varies with the shapes of obstacles. Without loss of generality, shapes of obstacles are categorized into three types which are described in Section 3.2. Table 5 displays the experimental results which show the average number of beacon points needed by OTPP and Z-curve for different types of obstacles. The average number of beacon points needed by OTPP is observed to be less than that needed by the Z-curve in all obstacle-present environments.  
Figure 11(a) is the result of comparing the Z-curve and OTPP, with respect to the impact of blocking rate on localization error. Both the localization errors of OTPP and Z-curve increase with an increase in blocking rate. The higher the blocking rate, the higher the difference between the localization errors of the Z-curve and OTPP schemes. The difference is more obvious when the blocking rate is higher than 10%. When the blocking rate is 30%, the difference between the localization errors reaches a value of 0.072 CR.  
Figure 11(b) is the result of comparing the Z-curve and OTPP, with respect to the impact of blocking rate on localization coverage. The coverage of the Z-curve decreases with an increase in the blocking rate while OTPP maintain almost full coverage. When the ratio is 30%, the difference in localization coverage between the Z-curve and OTPP reaches 15%.  
We then analyzed the OTPP in terms of the localization accuracy and coverage with a different communication range by fixing \(d\) as 16 m and changing the resolutions (\(CR/d\)). Figure 12(a),b illustrate the localization accuracy and coverage with different resolution values (\(CR/d=1.25d\), \(1.5d\), \(1.75d\), and \(2d\), respectively), in OTPP.  
In an obstacle-free environment which is blocking rate = 0, the localization accuracy and coverage ratio with resolution = \(1.25d\) is lower than the others because its communication range is less than \(1.6d\) which violates lemma 1, resulting in insufficient location messages received by unknown nodes. When the resolution is higher than \(1.6\ d\), the localization error then decreases to \(0.2\ CR\) and the  
Figure 12: Impact of blocking rate on (**a**) localization error and (**b**) coverage ratio.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Types of Obstacle** & **OTPP** & **Z-Curve** \\ \hline Obstacle-free & 5 & 5 \\ Type I & 6 & 8 \\ Type II & 10 & 16 \\ Type III & 10 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average number of beacon points.  
coverage ratio is 100%. As the blocking rate of obstacles increases, the beacon points are added in OTPP according to the obstacle types and therefore shorten the distance between unknown nodes and beacon points so the localization error with resolution \(1.25d\) and blocking rate decreases and the coverage ratio increases when blocking rate is under 5%. As the blocking rate increases to more than 5%, the localization accuracy and coverage both increase. However, for those whose resolution > \(1.6d\), their localization error and coverage are almost not affected by blocking rates.  
In summary, compared to Z-curve, OTPP has less number of beacon points, lower localization errors and higher localization coverage. OTPP therefore performs better in obstacle-present environments. When the communication range \(CR\geq\sqrt{(5/2)}d\), 100% localization coverage ratio is achieved.