# Fingerprinting Acoustic Localization Indoor Based on Cluster Analysis and Iterative Interpolation
## 4 Experimental Validation
### Analysis of the Iterative Interpolation Method  
In this work, four adjacent RPs selected by the global linear matching method are used for target location estimation. In the process of virtual RPs generation, the maximum number of iterations is set as \(T_{max}=10\). In addition, when the difference between the results of two adjacent iterations interpolation positioning process is less than \(\varepsilon=0.0001\) m, the iteration process will end.  
The global positioning results by examining the average error and maximum error of the positioning results of 13 test points has been evaluated. As shown in Figure 7, the iterative interpolation method can reduce the average error from 0.0945 m to 0.0406 m, and the maximum error from 0.2290 m to 0.0818 m. In the process of iterative interpolation, the effect of location accuracy improvement is obvious in the first six iterations. However, along with the iterative process and the improvement of positioning accuracy, the effect is gradually weakened. The same phenomenon also occurred at the maximum error.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cases** & **A-Amount** & **A-Time (s)** & **A-Error (m)** \\ \hline No partition & 72 & 0.0271 & 0.0945 \\ Coordinate partition & 22.3 & 0.0084 & 0.1214 \\ Cluster analysis partition & 21.7 & 0.0081 & 0.0813 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the influence on positioning effect between database partition methods. A-amount, average matching amount; A-time, average matching time; A-error, average positioning error.  
Figure 7: The changes of mean error and maximum error of location estimation according with the iterate interpolation process.  
As Table 2 shows, 6 cases were considered to compare the positioning effect of different interpolation methods. The maximum errors and average errors were selected as the evaluation indicators. For iterative interpolation methods, the V-RPs is defined as the average value of the virtual RPs generated during the localization process of the test points.  
According to Table 2, in the fingerprinting acoustic localization process without interpolation, 72 RPs can provide apparently higher accuracy than the one with 20 RPs. The results confirmed the viewpoint that improving RPs density can directly improve the positioning accuracy.  
In the cases of global interpolation method, the interpolation method can make further improvement for the positioning accuracy. On the other side, the initial RPs ratio can also affect the location results. That is, when the total RPs of the acoustic localization process based on global interpolation method are the same, more initial RPs means better positioning accuracy, but the influence of initial RPs ratio is weaker than the number of the total RPs.  
In the case of iterative interpolation method, it is easy to see that iterative interpolation method needs only 12.3% virtual RPs of the global interpolation method for similar precise location results when the number of initial RPs is 20. When the number of initial RPs is 72, iterative interpolation method needs only 10.5% virtual RPs of the global interpolation method for a slightly less precise positioning results.