## 4 A New Weight Model Based on SNR
The developed model is expressed by Equation (5) and is referred to as the HK model. In the equation, \(\sigma_{SNR}\) is the standard deviation of ten consecutive SNR values and \(SNR_{min}\) is the minimum SNR value. The parameter \(SNR_{min}\) should be fixed in each data processing step but can be modified when the equipment or environment changes. Other parameters--\(A\), \(B\), \(\alpha\), and \(\beta\)--were empirically determined in this study. The model equation is a form  
Figure 4: SNR measurements from all GPS satellites observed for 24 h at TEHE and comparison of LOS and NLOS signals. Figure 5: Time series of SNR and \(\sigma_{SNR}\) of PRN 16 at TEHE and comparison of LOS and NLOS signals. of an exponential function of the standard deviation \(\sigma_{SNR}\), and the weight will be chosen depending on the magnitude of \(\sigma_{SNR}\) with the dividing criterion value of 1.0. \[\left\{ \begin{aligned} \sigma_{SNR}>1.0&:& \sigma_{i}^{2}=A\cdot e^{\alpha(SNR_{\text{min}}-SNR_{i})}\\ \sigma_{SNR}\leq 1.0&:&\sigma_{i}^{2}=B \cdot e^{\beta(SNR_{\text{min}}-SNR_{i})}\end{aligned} \right. \tag{5}\]  
Here, NLOS and LOS signals were distinguished from the threshold value of 1.0, which was determined based on \(\sigma_{SNR}\) analysis results for LOS/NLOS signals from all satellites observed at TEHE. Caution must be exercised because NLOS signals can be falsely identified as LOS signals if the threshold value is excessively high. By contrast, LOS signals can be misinterpreted as NLOS signals if the threshold value is too low. The mean \(\sigma_{SNR}\) of NLOS signals from all satellites observed at TEHE was calculated as \(0.8\pm 0.3\). The threshold value was optimized by trying out values within the standard deviation. Specifically, seven threshold values were tested from 0.5 to 1.1, equally spaced at intervals of 0.1. A threshold value of 1.0 was the most effective choice for separating LOS from NLOS signals. Because this threshold is determined empirically, it can be changed. The same holds for the other model parameters, \(A\), \(B\), \(\alpha\), and \(\beta\). Figure 7 shows \(\sigma_{SNR}\) computations of the LOS and NLOS signals for PRN 16, with the threshold value of 1.0 denoted as the straight horizontal line in cyan. The horizontal axis corresponds to the sequential numbering assigned separately to LOS and NLOS signals and does not reflect the time sequence of the entire measurement set. Values of \(\sigma_{SNR}\) for LOS signals shown in the upper panel of Figure 7 were 0.5 or lower, except at the switching boundary between the LOS and NLOS signals. Most of the standard deviation values for the NLOS signals, depicted in the lower panel of Figure 7, remained above 0.5. However, LOS and NLOS signals cannot be clearly distinguished with one threshold for all satellites, and one should come up with different thresholds for each satellite. The difference in the threshold values may be due to errors in the building coordinates used for visibility analysis or unknown factors. The simulated measurement noise of the HK model, as defined by Equation (5), is depicted in Figure 8 as a function of SNR values ranging from 25 to 55. The horizontal axis represents the SNR values, and the solid blue circles and red crosses correspond to NLOS and LOS signals, respectively. This clear differentiation between NLOS and LOS signals indicates that the HK model equation assigns much less weight or greater measurement  
Figure 6: SNR observables of the PRN 16 depicted in a skylpot. The arrow indicates the direction of movement of PRN 16.  
noise values to NLOS signals than to LOS signals. By making this adjustment in the EKF, we can minimize the influence of NLOS signals. The variations in the measurement noise due to the three different SNR-based model equations are presented in Figure 9. For this analysis, PRN 17 is considered instead of PRN 16, which was examined in the preceding discussion. Furthermore, PRN 18 serves as an additional example that demonstrates a well-balanced integration of LOS and NLOS signal measurements.