# Indoor Carrier Phase Positioning Technology Based on OFDM System
## 4 Numerical Results
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline Channel model & 5G New Radio (NR) channel model (Indoor-Mixed office[36]). \\ \hline Carrier frequency & 3.5 GHz \\ \hline Carrier wavelength & 0.085 m \\ \hline Inter-site distance & 20 m \\ \hline Room size & 40 m \(\times\) 20 m \\ \hline Subcarrier spacing & 15 KHz \\ \hline Reference signal & New Radio PRS Structure from [37]. \\ \hline Reference Signal Transmission Bandwidth & 50 MHz \\ \hline Number of BSs & 6 \\ \hline UE-antennas & 4 \\ \hline Number of subcarriers & 3240 \\ \hline FFT Length & 4096 for 50 MHz \\ \hline Sampling rate & 61.44 MHz for 50 MHz \\ \hline Number of occasions used per positioning estimate & 1 \\ \hline Interference modelling & Perfect muting \\ \hline Clock error between BSs & Gaussian distribution with a mean of 25 ns and a variance of 10 ns. \\ \hline Clock error of the terminal & Gaussian distribution with a mean of 50 ns and a variance of 15 ns. \\ \hline Delay spread & Exponential distribution with a mean of 22 ns. \\ \hline Total transmission power & 24 dBm \\ \hline Maximum directional gain & 5 dBi \\ of an antenna element & \\ \hline UE speed & 1 m/s \\ \hline Position solution interval & 0.1 s \\ \hline NLOS error identification threshold & \(\Lambda=3\) \\ \hline Ratio test threshold & \(\epsilon=0.5\) \\ \hline LOS generation probability & Table 7.4.2-1 in the literature [36]. \\ \hline Fading model & Large scale fading: Table 7.4.1-1 in the literature [36]; Fast fading: Section 7.5 of [36]. \\ \hline Channel independence & The channel model of the reference device and the channel model of the user terminal are independent of each other. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System Parameters. Figure 5 shows the ratio test was used to check whether the DD integer ambiguities output by the EKF are reliable at the current epoch. The dashed line represents the preset threshold \(\epsilon=0.5\). After the 113 th epoch, the reliability rates are all below the threshold. Therefore the algorithm determines that the obtained integer ambiguities are reliable after the \(113 th\) epoch. Combined with Figure 4, it can be seen that it is valid to use the ratio test to determine whether the DD integer ambiguities converge to the actual value. We evaluate the performance of the TOA+CP EKF' based differential positioning method as in Figure 6. In addition, we also list two other cases for comparison, wherein GMM EKF' [31] is a method to perform positioning solution by TDOA measurement, which eliminates the NLOS error by model NLOS propagation as Gaussian mixture model; EKF' [32] represents a commonly used EKF location algorithm based on TDOA measurement. To eliminate the effect of clock errors, all three algorithms mentioned above use TDOA obtained from Equation (25) instead of TOA for positioning, and the algorithm proposed in this paper also requires SD carrier phase measurements. Figure 4: Schematic diagram of DD integer ambiguity convergence. Figure 5: Test of the reliability of DD integer ambiguities. Figures 6 and 7 show the performance of the three algorithms during mobile localization. Since all three algorithms use differential measurements for position solving, it can be seen from the results that the time-varying synchronization errors do not affect the positioning accuracy. At the initial epoch, the accurate integer ambiguity has not been solved, so the carrier phase measurement is difficult to determine the initial position. Therefore, initial positions of all three algorithms are calculated from the Chan algorithm [33] using TDOA measurements. It can be seen from Figures 6 and 7 that in the first few epochs, the positioning error of 'TOA+CP EKF' is significant, which is caused by the inaccurate integer ambiguity. In subsequent periods, as the algorithm correctly fix the integer ambiguity, the positioning error gradually decreases.