## 4 Results and Discussion
### Results of Experiment 1  
The first experiment is performed in the real indoor environment, which is presented in Figure 10, to demonstrate the performance of the proposed indoor positioning system under line-of-sight conditions. The position for each sample is estimated with the LSAV algorithm using the GPS satellite's signal, which is within the angle of view of each repeater. As mentioned previously, G19 is ignored because it is seen by more than one repeater. Under these conditions, the CNR of the received GPS signals, from the selected satellites for the indoor position estimation, is provided in Figure 13.  
The sum of the indoor distances (\(d_{1}\), \(d_{2}\), and \(d_{3}\)), including receiver clock bias (\(t^{receiver}_{bias}\)), are calculated in Equation (1) and subtracted from each to obtain the difference terms (\(d_{2}+\ t^{receiver}_{bias}\))\(-\)(\(d_{1}+t^{receiver}_{bias}\)) and (\(d_{3}+t^{receiver}_{bias}\))\(-\)(\(d_{1}+t^{receiver}_{bias}\)) for each sample. Figure 14a,b shows the indoor distance difference terms in which the receiver clock biases are removed due to the subtraction, while in Figure 14c, it demonstrates the individual distances with the receiver clock bias (\(d_{1}+t^{receiver}_{bias}\), \(d_{2}+t^{receiver}_{bias}\), \(d_{3}+t^{receiver}_{bias}\)). Figure 13: CNR of each GPS signal received by the repeaters. As seen in Figure 14c, the indoor distances with receiver clock bias (\(d_{1}+t_{bias}^{receiver}\), \(d_{2}\)\(+\)\(t_{bias}^{receiver}\), \(d_{3}+t_{bias}^{receiver}\)) can go up to thousands of meters. When the receiver clock bias is removed, with subtraction, the indoor differences can be found in the range of tens of meters. The calculated indoor distance difference terms (blue curve in Figure 14a,b) are averaged with a moving average filter of a five-sample window size. The resulting terms (red curve in Figure 14a,b) show a closer result to the measured indoor distance differences (black dashed line in Figure 14a,b), which can be calculated using the measured indoor distances \(d_{1}\), \(d_{2}\), and \(d_{3}\) in Figure 10.  
Figure 15a depicts the GPS repeater and outdoor GPS antenna positions according to their latitude and longitude in Experiment 1. These results show that the LSNAV algorithm has resulted in a solution for 74 out of 100 collected samples. The reason why the LSNAV does not result in a solution for every sample collected is addressed subsequently in the CNR provided in Figure 13. For some samples, due to environmental changes or multipath, the LSNAV algorithm has been applied to the GPS repeater. Figure 14: The indoor distance differences (**a,b**) and indoor distances with the receiver clock bias term (**c**). an abrupt change in CNR occurs. For these samples, that do not have good CNR from all three repeaters, LSNAV does not result in a solution. Moreover, a moving average filter with a five-sample window size has been applied over the 74 results from LSNAV, which then give 69 location estimations. The resulting 69 locations are depicted in Figure 15a,b with red dots. Figure 15a presents the results on a latitude-longitude graph, whereas Figure 15b presents the results on a local reference frame where the center is the real position of the receiver, which was previously determined  
Figure 15: The results of the Experiment 1: (**a**) repeater positions, outdoor GPS antenna positions, collected samples (red dots), real position of the receiver (black square), estimated position (blue square), and CEP (blue circle) on latitude-longitude graph; (**b**) collected samples (red dots), real position of the receiver (black square), estimated position (blue square) on local reference frame whose center is the real position of the receiver. by physical measurements in the experimental setup with respect to the building whose coordinates and plan are well known. We calculated the radius of 50% CEP as 3.3 m and plotted it in Figure 15a. Moreover, the indoor position is estimated as the mean of these 69 points obtained with moving average filtering.