## 4 Experiment Results
### The Performance of Object Localization and Tracking
As shown in the left figure of Figure 15, it can be observed that when the outliers are detected and eliminated, the variance of the \(x\)-coordinate is relatively small, and the estimated target trajectory can follow the desired path more smoothly and more consistently than that in the right figure of Figure 14. It is noted that since there are no obvious outliers in the measurement by the EKF method in Case 3-1 and Case 3-2, the results of the tracking will be similar before and after outlier rejection. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} Target \\ Coordinate \\ \end{tabular} & \begin{tabular}{c} **Axis** \\ \end{tabular} & \
\begin{tabular}{c} **NRLM** \\ \end{tabular} &
\begin{tabular}{c} **EKF** \\ \end{tabular} \\ \hline \multirow{2}{*}{(14, 37)} & x & 0.56 & 0.52 & 0.51 \\ \cline{2-5}  & y & 0.44 & 1.51 & 0.45 \\ \hline \multirow{2}{*}{(18, 37)} & x & 0.26 & 0.20 & 0.21 \\ \cline{2-5}  & y & 1.16 & 1.58 & 1.12 \\ \hline \multirow{2}{*}{(14, 41)} & x & 0.09 & 0.07 & 0.10 \\ \cline{2-5}  & y & 0.72 & 0.56 & 0.28 \\ \hline \multirow{2}{*}{(18, 41)} & x & 0.24 & 0.23 & 0.22 \\ \cline{2-5}  & y & 0.05 & 0.60 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case 1—RMSE of target coordinates (\(X\), \(Y\)) for the marker pen (unit: cm). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} Target \\ Coordinate \\ \end{tabular} & \begin{tabular}{c} **Axis** \\ \end{tabular} & \
\begin{tabular}{c} **NRLM** \\ \end{tabular} &
\begin{tabular}{c} **EKF** \\ \end{tabular} \\ \hline \multirow{2}{*}{(14, 37)} & x & 0.28 & 0.36 & 0.28 \\ \cline{2-5}  & y & 1.31 & 0.97 & 0.89 \\ \hline \multirow{2}{*}{(18, 37)} & x & 0.30 & 0.30 & 0.27 \\ \cline{2-5}  & y & 0.35 & 0.94 & 0.45 \\ \hline \multirow{2}{*}{(14, 41)} & x & 0.58 & 0.59 & 0.44 \\ \cline{2-5}  & y & 1.11 & 0.60 & 0.23 \\ \hline \multirow{2}{*}{(18, 41)} & x & 0.13 & 0.17 & 0.14 \\ \cline{2-5}  & y & 0.28 & 0.39 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Case 2—RMSE of target coordinates (\(X\), \(Y\)) for human index finger (unit: cm). Another test trajectory is shown in the right figure of Figure 15. The estimated target coordinates are around the reference trajectory. However, there is a delay in the \(x\)-direction near the end point. This is caused by the constant occurrence of outliers as the target moves. Because the Kalman gain is smaller in the presence of outliers, the estimated coordinates are closer to the predicted trajectory. In Figure 15, it can be observed that there are differences between the real trajectories and the estimated trajectories, but the estimated tracking trajectories are quite stable, which means that the proposed algorithm can be fairly stable to localize the detected object. In this work, the key issue for object localization is not only to directly estimate the accurate position but also to estimate the stable position. In reality, position estimation is prone to deviation due to the influences of various factors, such as the size of the sensors and the geometry of sensor positions. It is not practical to consider these factors because it makes the system complicated and not easy to solve. However, in a fixed system, these influences are also fixed and always result in a fixed offset in position estimation with a fixed position. Thus, even if there is an error between the position estimation and the real position, the error can be directly compensated by an offset calibration to achieve the correct object localization and tracking. In Figure 15 and Tables 3 and 4, it can be observed that the