## 5 Results and Discussion  
This section shows the performance of the proposed system in terms of location estimation error. Within the simulations, a total of 100 repetitions for three different scenarios to be estimated were randomly generated following a uniform distribution. The localization estimation error is calculated based on the averaged euclidean distance between the estimated and real location as:\[e=\sqrt{\left(x_{t}-x_{e}\right)^{2}+\left(y_{t}-y_{e}\right)^{2}+\left(z_{t}-z_{e }\right)^{2}}, \tag{22}\]  
where \(\left(x_{t},y_{t},z_{t}\right)\) is the real location of the photodetector (miner) and \(\left(x_{e},y_{e},z_{e}\right)\) is the estimated location. Simulation param are summarized in Table 1. The dimensions of the tunnel and the positions of the transmitters were chosen to generate a coherent simulation space. The tunnel dimension is selected as (5, 5, 5) m. Also, the transmitted power for all three LEDs and the filter gain are determined as 70 W and 1, respectively. The characteristics of the LEDs, as well as the photodetector were obtained from the different technical data-sheets [10; 44; 45]. The simulations were done in three different scenarios (photodetector and LEDs locations). The position of the LEDs and photodetector are also shown in Table 1 for the three scenarios. The transmitters (LEDs) are located on the ceiling, whereas the receiver (photodetector) is located within the tunnel. The LOS channel model is considered for the VLC system between the transmitter and receiver. The Lambertian model with mode number equal to 1 is used for simulations in this paper. The semi angle for half power is selected as 65\({}^{\circ}\) for the LEDs and photodetector. Further details of the param used in the simulation are found in Table 1.  
Based on the proposed method, the channel impulse responses are calculated between LEDs and the photodetector. Then, a convolution between these impulse responses and the signals to be transmitted by the LED is done. The received signal by the photodetector is the superposition of three LED signals with their respective channel impulse responses. The frequencies of the three carrier tones for the LEDs are selected as (3.5 MHz), (8.5 MHz) and (13.5 MHz), respectively. The FIR band pass filters (BPFs) are designed in the photodetector side with bandwidths of (2.5-4.5 MHz), (7.5-9.5 MHz), and (12.5-14.5 MHz), respectively to separate the carrier tone of each LED. Then, the received powers are calculated for each filtered signal based on the proposed algorithm to estimate the \(d\) param as the diam of spheres with powers \(P_{r}(t)\) and \(P_{t}(t)\). Three spheres are plotted based on the estimated \(d\) param and by centering the LEDs locations based on the proposed method. Then, the \(x\), \(y\), and \(z\) param are calculated based on Equations (17), (20) and (21), respectively. Sometimes there are two estimated values for the \(z\) parameter, and the value that corresponds to the dimensions of the tunnel is selected. Generally the other value does not correspond to the dimensions of the tunnel. If both \(z\) values are with the dimensions of the tunnel, the algorithm considers the next time frame to eliminate this error.