# A Doppler Frequency-Offset Estimation Method Based on the Beam Pointing of LEO Satellites
## 4 Simulation Analysis  
To analyze the frequency-offset estimation accuracy of the DFS-BP algorithm, this paper uses STK's SGP4 model and the DFS-BP algorithm to perform Doppler frequency-shift simulations for satellites in different scenarios, and it compares the frequency-offset estimation errors of the two methods. This section mainly conducts simulation work in three aspects:  
* Case 1: The DFS-BP algorithm is used to simulate the Doppler frequency offset with a minimum elevation angle of 0\({}^{\circ}\) and a terminal geographic latitude of 0\({}^{\circ}\). The simulation results are compared against those obtained from the SGP4 model in STK. Under the condition of the same orbital altitude and orbital inclination, the influence of different latitude values on the satellite's beam-pointing frequency-offset estimation model is analyzed. * Case 2: The DFS-BP algorithm is used to simulate the Doppler frequency offset with a minimum elevation angle of 0\({}^{\circ}\) and varying terminal geographic latitudes. The simulation results are compared with those from the SGP4 model in STK. The accuracy of the Doppler frequency-offset estimation by the DFS-BP algorithm is then analyzed. To analyze the accuracy of the Doppler frequency-offset estimation of the DFS-BP algorithm, the Root Mean Square Errors (RMSEs) of the Doppler frequency-offset estimation errors under different orbital altitudes and orbital inclinations are compared. The \(\pm\)95% confidence intervals (CIs) are also analyzed. * Case 3: The DFS-BP algorithm is employed to simulate the Doppler frequency offsets of various satellite minimum elevation angles. The simulation results are compared with those obtained from the SGP4 model in STK. The accuracy of the Doppler frequency-offset estimation by the DFS-BP algorithm is subsequently analyzed. Simulation of Doppler Frequency Shift When the Minimum Elevation Angle Is 0\({}^{\circ}\) and the Geographical Location of the Terminal Is 0\({}^{\circ}\)  
The Doppler frequency-shift simulation parameters for a minimum elevation angle of 0\({}^{\circ}\) are listed in Table 1. \begin{table}
\begin{tabular}{c c} \hline
**Parameter Name** & **Parameter Value** \\ \hline Orbital altitude, h & 480 km \\ Earth radius, R & 6378 km \\ Eccentricity, e & 0.0 \\ Orbital inclination, i & 50\({}^{\circ}\) \\ Satellite geocentric latitude, \(\beta\) & 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\), 30\({}^{\circ}\), 40\({}^{\circ}\), 50\({}^{\circ}\) \\ Earth’s rotation period, T & 86,164 s \\ Signal propagation speed, c & 2.998 \(\times\) 10\({}^{8}\) m/s \\ Signal carrier frequency, Fc & 2.0 GHz \\ \hline \end{tabular}
\end{table} 
Table 1: Doppler frequency-shift simulation parameter table for a minimum elevation angle of 0\({}^{\circ}\). The simulation process of Doppler frequency-offset estimations under this condition is as follows:  
* According to the simulation parameters, the STK tool is utilized to simulate the Doppler frequency-offset variation of the LEO satellite during visible time, with a minimum elevation angle of 0\({}^{\circ}\) and a terminal geographic latitude of 0\({}^{\circ}\). The simulation outputs include the Doppler frequency-offset variation over the visible period, as well as the satellite's azimuth and elevation angles. * Using the satellite beam-pointing method, the Doppler frequency-offset variation is calculated according to the azimuth and elevation angles of LEO satellites. * When the satellite geocentric latitudes are set to 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\), 30\({}^{\circ}\), 40\({}^{\circ}\), and 50\({}^{\circ}\), compare the frequency-offset estimation error between the Doppler frequency-offset estimation based on STK simulations and the Doppler frequency-offset estimation based on the DFS-BP method. The differences among the three sub-equations in Equation (30) are analyzed through the RMSE of the frequency-offset estimation errors.