## 4 Results and Discussion
### Localization Results Using Random Forest  
For the random forest model in this paper, the base model is classification and regression trees (CART). The split criteria are mean square error MSE. The number of random features to consider at each split is set as 5. Prior to employing the random forest model for predicting impact locations, it is crucial to optimize the number of decision trees involved in the model. In this study, an exploratory trial-and-error experiment was conducted to \begin{table}
\begin{tabular}{l l l l l l l l} \hline
**Coefficients of** & \multirow{2}{*}{**Delete None**} & \multirow{2}{*}{**Delete 1**} & \multirow{2}{*}{**Delete 2**} & \multirow{2}{*}{**Delete 3**} & \multirow{2}{*}{**Delete 4**} & \multirow{2}{*}{**Delete 5**} & \multirow{2}{*}{**Delete 6**} \\
**Variables** & & & & & & & & \\ \hline Amplitude & \(-0.38874\) & \(-0.40864\) & \(-0.40198\) & \(-0.43819\) & \(-0.4686\) & \(-0.47675\) & \(-0.47685\) \\ ASL & \(-0.14194\) & \(-0.18554\) & \(-0.1897\) & \(-0.19827\) & \(-0.10552\) & \(-0.1097\) & \(-0.11016\) \\ Average & \(0.054975\) & \(-0.28685\) & \(-0.30435\) & \(-0.02979\) & \(-0.02353\) & \(-0.02833\) & \(-0.02848\) \\ Reverberation & \(-0.0445\) & \(0.28347\) & \(0.296833\) & \(0.035397\) & \(0.033767\) & \(0.042611\) & \(0.042782\) \\ Truquency & \(1.56\times 10^{-5}\) & \(-6.00\times 10^{-6}\) & \(-2.00\times 10^{-5}\) & \(1.37\times 10^{-5}\) & \(1.48\times 10^{-5}\) & \(2.34\times 10^{-5}\) & \(2.31\times 10^{-5}\) \\ Count & \(-0.00236\) & \(-0.00195\) & \(-0.00168\) & \(-0.00228\) & \(-0.00215\) & \(-0.00231\) & \(-0.00232\) \\ Signal Strength & \(-6.30\times 10^{-6}\) & \(-6.40\times 10^{-6}\) & \(-7.50\times 10^{-6}\) & \(-2.00\times 10^{-6}\) & \(-4.70\times 10^{-6}\) & \(-1.50\times 10^{-6}\) & \(-1.50\times 10^{-6}\) \\ Energy & \(-0.66253\) & \(0.054989\) & \(0.060861\) & \(0.02966\) & \(0.043758\) & \(0.024108\) & \(0.024254\) \\ Frequency & \(-0.02227\) & \(-0.03006\) & \(-0.01738\) & \(-0.03135\) & \(-0.03521\) & \(-0.03764\) & \(-0.03763\) \\ Absolute & \(-2.30\times 10^{-6}\) & \(-9.00\times 10^{-7}\) & \(-3.50\times 10^{-7}\) & \(-1.10\times 10^{-6}\) & \(8.92\times 10^{-8}\) & \(5.72\times 10^{-8}\) & / \\ Energy & \(0.000384\) & \(-0.00117\) & \(-0.0014\) & \(-0.00319\) & \(-0.00323\) & / & / \\ FROS & \(33.16985\) & \(65.97887\) & \(66.95417\) & \(50.09611\) & / & / & / \\ Rise Time & \(0.00504\) & \(0.001808\) & \(0.001882\) & / & / & / & / \\ PCNTS & \(0.010839\) & \(0.014069\) & / & / & / & / & / \\ Peak & \(-0.05168\) & / & / & / & / & / & / \\ Intercept & \(36.09853\) & \(39.63695\) & \(39.70405\) & \(43.43703\) & \(43.1448\) & \(43.42157\) & \(43.43426\) \\ \hline R\({}^{2}\) & \(0.9361\) & \(0.9281\) & \(0.9255\) & \(0.9197\) & \(0.9187\) & \(0.9176\) & \(0.9176\) \\ RMSE & \(1.4614\) & \(1.5507\) & \(1.5784\) & \(1.6390\) & \(1.6485\) & \(1.6599\) & \(1.6599\) \\ \hline \end{tabular}
\end{table} 
Table 2: Coefficients of features used in the linear regression equation, and R\({}^{2}\) and RMSE for backward elimination. \begin{table}
\begin{tabular}{l l l l l l l l} \hline
**Coefficients of** & \multirow{2}{*}{**Delete 7**} & \multirow{2}{*}{**Delete 8**} & \multirow{2}{*}{**Delete 9**} & \multirow{2}{*}{**Delete 10**} & \multirow{2}{*}{**Delete 11**} & \multirow{2}{*}{**Delete 12**} & \multirow{2}{*}{**Delete 13**} \\
**Variables** & & & & & & & \\ \hline Amplitude & \(-0.53962\) & \(-0.53972\) & \(-0.54393\) & \(-0.58384\) & \(-0.60369\) & \(-0.60258\) & \(-0.59833\) \\ ASL & \(-0.04556\) & \(-0.04548\) & \(0.201282\) & \(0.235985\) & \(0.230852\) & \(0.2291 optimize the random forest model by incrementally increasing the number of decision trees, ranging from 1 to 200, while examining the out-of-bag (OOB) error. The OOB error serves as a valuable metric for evaluating the random forest model during the training phase. For each decision tree within the random forest, a random subset of the training data is selected and employed to construct the tree, while the remaining data points are utilized for calculating the OOB error.