## 2 Experimental Setup and Problem Statement  
The problem to be solved was 3-D target localization in an infinitely large media. The experiment was carried out in water, where it is easier to set up targets and make measurements than in solids. Additionally, conducting the experiment in water did not affect the study of localization methods.  
Figure 1 is the experimental setup used for 3-D target localization. The experiment was carried out in a water tank with dimensions of 300 mm \(\times\) 400 mm \(\times\) 500 mm. A solid sphere (29 mm in diameter) was immersed in water as the target. An actuator and a sensor were used to transmit ultrasonic signals and receive scattered signals, respectively. The sensor was moved \(N\) (in our case \(N=12\)) times to receive \(N\) scattered signals that traveled from the actuator to the sensor along \(N\) different paths. A signal generator was used for excitation. The scattered signals were recorded by a Data Acquisition (DAQ) system. A PC was used for signal processing, such as extracting ToFs from the scattered signals and performing localization algorithms (the traditional ToF-based method, the probability-based ToF method, and IMWLE).  
The experimental setup consisted of the following:  
A solid sphere with a diameter of 29 mm;An immersion transducer (1 MHz center frequency, 7 mm diameter);  
A distributed feedback fiber laser (DFB-FL) ultrasonic sensing system (self-developed);  
A water tank with dimensions of 300 mm \(\times\) 400 mm \(\times\) 500 mm;  
A three-axis mobile platform (self-developed) driven by stepper motor. It was used to move the sensor from one receiving position to another;  
A signal generator (Tektronix AFG1022).  
The experiment consisted of four steps:  
The actuator was excited by a signal generator to transmit ultrasonic signals at a fixed position;  
The sensor was used to receive scattered signals from the target. Then, the scattered signals were recorded by a DAQ system;  
The sensor was moved to different receiving positions. The scattered waves were also recorded at these positions by the DAQ system;  
All recorded signals were processed in PC for target localization.  
The localization algorithm was conducted within a virtual calculation domain of \(120\;\mathrm{mm}\times 120\;\mathrm{mm}\times 170\;\mathrm{mm}\) in the central part of the tank in order to decrease the influence of reflected signals. The coordinate system was established as shown in Figure 1 and the point \(O\) was the origin. The coordinates of the actuator, the 12 receiving positions, and the target are listed in Table 1.  
This paper focuses on the 3-D target localization method. We make the following statements considering the equipment available in our laboratory.  
An immersion transducer (1 MHz center frequency, 7 mm diameter) was chosen to be the actuator. The positions of the target and the actuator were fixed. In the experimental setup, the actuator and the target center were nearly aligned, as shown in Table 1. This was done to increase the energy of the received signals from the target. This knowledge was not utilized in the localization method to ensure that the location of the target remained unknown. In practical applications, an actuator with uniform directivity would be a better choice.  
The DFB-FL ultrasonic sensing system we developed [18] was used to receive and record scattered signals due to its high sensitivity [19]. The sensing system includes a sensor, a DAQ, and a PC. The sensor was clamped and moved by a stepping motor. In practical applications, other types of sensors can also be used as long as the scattered signals can be received. It is not necessary for sensors to move from one receiving position to another. A sensor array composed of multiple sensors is also a good choice.  
Figure 1: Experimental setup illustration. The target, actuator, and sensor are immersed in water.