## 4 Simulation Test  
In this experiment, the HWA-RNSS-7300 satellite navigation signal simulator of Beijing Huali Chuangtong Technology Co., Ltd. in Beijing, China. ), was used to generate the Beidou satellite navigation signal required for the experiment. The IF (intermediate frequency) data collector of Xingyuan Beidou Navigation Technology Co., Ltd. in Beijing, China, was used to down-convert the output signal of the simulator into an IF signal. The output IF signal is \(f_{\text{IF}}=4.092\) MHz, the sampling frequency is \(f_{\text{s}}=16.368\) MHz, and the number of sampling bits is 2 bits. The receiver uses a vector software receiver, the pre-detection integration time is 1 ms, and the tracking threshold is \(35\) dB/Hz. Because it is difficult to \begin{table}
\begin{tabular}{c c c c} \hline
**Position Error—Variance (m\({}^{2}\))** & **Velocity Error—Variance (m\({}^{2}\)/s\({}^{3}\))** & **Code Phase Error—Mean Square Error** & **Carrier Frequency Error—Mean Square Error** \\ \hline
10 & 2 & 12\({}^{\circ}\) & 0.02 Chip \\ \hline \end{tabular}
\end{table} 
Table 1: Initial settings of the relevant data of the vector loop. generate real jerk signals and large-value acceleration signals, the highly dynamic model of the Jet Propulsion Laboratory (JPL) in the United States was used to simulate the motion state of the receiver. The highly dynamic movement of the receiver relative to the satellite will follow Figure 2a,b. Figure 2a is the acceleration signal model of the receiver, Figure 2b is the jerk signal model [24], and the simulation time is 8 s. At first, the jerk of the receiver was zero, and the receiver made a uniform acceleration movement at an acceleration of \(-25\) g. However, the jerk suddenly increased to 100 g/s at 3 s and continued for 0.5 s. At this time, the acceleration of the receiver became 25 g and made a 2 s uniform acceleration motion with an acceleration of 25 g. At 5.5 s, the jerk suddenly changed to \(-100\) g/s and lasted for 0.5 s; at this time, the acceleration became \(-25\) g again, and uniform acceleration motion was made [25]. For the above-mentioned high dynamic model, this article uses the Discrete Wiener Process Acceleration (DWPA) [26; 27] to model it. The process equation and the observation equation are respectively (1) and (2), and the process noise covariance matrix  
\[Q^{2}=\left[ \begin{array}{ccc}\frac{1}{4}T^{4}I_{3}&\frac{1}{2}T^{3}I_{3}& \frac{1}{2}T^{2}I_{3}\\ \frac{1}{2}T^{3}I_{3}&\frac{1}{2}T^{2}I_{3}&TI_{3}\\ \frac{1}{2}T^{2}I_{3}&TI_{3}&I_{3}\end{array} \right] \tag{34}\]  
Measurement noise covariance matrix  
\[R^{2}=\left[ \begin{array}{ccc}\textbf{diag}(\textbf{{R}}_{code,\textbf{1}} \end{array} , \begin{array}{ccc}\textbf{{R}}_{carrier,\textbf{1}}\end{array}  \cdots\cdots\cdots\textbf{{R}}_{code,\textbf{n}}\end{array}, \begin{array}{ c}\textbf{{R}}_{carrier,\textbf{n}}\end{array} \right]^{2} \tag{35}\]  
The simulation first takes the root-mean-square error of the frequency as the evaluation index. Through 500 Monte Carlo experiments, the relationship curve between the RMS frequency error of the channel and the carrier-to-noise ratio CNR is obtained. The definition of RMSE is as follows:  
\[RMSE=\sqrt{\frac{1}{M}\sum_{i=1}^{M}\left( \begin{array}{c}X_{n}(\text{k})- \hat{X}_{n}^{i}(k|k)\end{array} \right)^{2}} \tag{36}\]  
The movement process of the carrier is as follows: the number of signal channels during 0 s-25 s is 12; during this period, the carrier moves in a straight line at a constant speed. After that, during 26 s-120 s, the number of channels with signals drops to three or fewer, which means that the carrier is in a weak signal environment at this time. During the period of 26\(-\)60 s, it is still moving in a straight line at a constant speed. Then, during 60\(-\)85 s, the carrier periodically performs a highly dynamic movement as shown  
Figure 2: The trajectory of the receiver relative to the Beidou satellite. (**a**) Acceleration model for highly dynamic motion; (**b**) Jerk model for highly dynamic motion. Reprinted from ref. [24].