## 4 Experiment Results
### The Performance of TOF Estimation  
In this section, the fixed threshold method [12; 13], the two-maximums algorithm [15], the energy genetic-ant colony optimization-three-cycle (EGACO) algorithm with the GN model [21], the proposed NRLM algorithm with the GN model (23), and the proposed NRLM algorithm with the DE model (24) are tested to compare the standard deviations of the TOF estimation in Case 1 and Case 2, where the targets are all stationary. All approaches tested here are applied to the same fitting window. The standard deviations of the testing results of five receiver channels are shown in Figures 9 and 10. It is noted that the vertical axis presents the standard deviations of distances with the corresponding TOFs in Figures 9 and 10 for intuitive observation.  
It is observed that the threshold method has a larger variation in TOF estimation when it is the target in both cases. Since the threshold method uses a fixed threshold value to detect TOF, it can not handle most situations. Regardless of whether the target is a pen or a human finger, the amplitude of the interference wave, which is greater than the threshold value, seriously affects the estimation results and produces some outliers. The results of TOF estimation of the two-maximums algorithm are relatively stable and more accurate than those of the threshold method because it applies linear interpolation based on the envelope model on the rising edge to estimate the TOF, and the rising edge is also located in the ideal echo region from the method in Section 2.3.3. However, the linear interpolation used in the two-maximums algorithm is very sensitive to changes in the slope of the rising edge, resulting in corresponding interference to TOF estimation.  
In Figures 9 and 10, it is observed that the proposed NRLM algorithm with the DE model has better performance than the other methods in most cases, including the EGACO algorithm with the GN model and the proposed NRLM algorithm with the GN model. The EGACO uses the GN model and estimates the TOF by judging the maximum energy position of the signal. The result of EGACO is similar to that of the threshold method in many cases because it estimates the TOF by signal energy, which is easily affected by the shape of the signal, especially when the object is in the non-stationary state. The curve-fitting results of the NRLM algorithm with the GN model and the DE model are shown in Figure 11. The GN model characterizes the actual envelope better than the DE model, such that the residual error of curve-fitting using (7) is smaller than that of (8). However, the GN model is more sensitive to the variation of the measured echo signal because it fits the onset of the echo well and interferes with the TOF. On the other hand, although the TOF estimation of the DE model has a certain deviation, the rising edge of the model is less sensitive to the variation of the echo, which is consistent with the simulation result in Section 3. Therefore, it can be concluded that the NRLM algorithm with the DE model provides a more stable TOF estimation than other methods, and the TOF data estimated by  
Figure 8: (**Left**): The architecture of the experimental system; (**Right**): The photo of the real experiment environment of the ultrasonic platform with the target as a human finger.  
the NRLM algorithm with the DE model is used in all cases in the object localization and tracking in Section 4.2.