# An Optimized Vector Tracking Architecture for Pseudo-Random Pulsing CDMA Signals
## 5 Simulation and Results
### Simulation Setup  
Figure 6 shows the block diagram of the self-developed simulation scheme. First, the position and velocity of the receiver are preset in the trajectory generator. Then, the IF PRPS can be produced according to the fixed pseudolite position. This paper assumes that there is no multipath signal and that the pseudolite net is synchronous. Therefore, the PRPS is transmitted through the Gaussian channel, and it will be captured and tracked by the receiving module. Finally, the position, velocity, doppler, and code phase error results are used to evaluate the performance of different vector tracking structures.  
The simulation in this paper is established on a self-defined XYZ coordinate system. This process does not affect the evaluation of vector tracking performance but avoids the transformation between coordinate systems. The parameters of the PRPS are listed in Table 1. The total number of pseudolite is 10 in the simulation.  
Figure 6: Block diagram of the simulation scheme.  
The reference trajectory is shown in Figure 7, the blue dot is the starting point, the blue arrow represents the direction of motion, and the yellow five-pointed star is the endpoint. The reference velocity and acceleration are presented in Figure 8a,b, respectively.  
The dynamic process of the receiver is described as follows:  
1. The receiver is in a static state during 0\(\sim\)7 s, and the relative coordinate of the starting point is \([-90,120,0]\) (m).
2. Conduct a constant acceleration movement in the \(+x\) direction with an acceleration of 10 m/s and a duration of 2 s.
3. Stop acceleration and maintain a constant velocity state for 1 s.
4. Make a 1/4 circular motion with a circle radius of 50 m.
5. The receiver moves toward the \(-y\) direction and keeps moving at a constant speed for 1.382 s.
6. Apply a constant acceleration in the \(+z\) direction. The acceleration is 10 m/s, and the duration is 1 s.
7. Stop acceleration and maintain a constant velocity state for 1 s.
8. Perform a deceleration movement in the \(+z\) direction until \(V_{z}=0\) and the acceleration is \(-10\) m/s.  
\begin{table}
\begin{tabular}{l c} \hline RF (\(f_{c}\)) & 1575.42 MHz \\ IF (\(f_{IF}\)) & 24 MHz \\ code frequency & 10.23 MHz \\ code length & 1023 chips \\ duty cycle of the pulse pattern (\(d\)) & 0.1 \\ Timeslot Period (\(T_{s}\)) & 0.1 ms \\ Frame Period (\(T_{f}\)) & 1 ms \\ Number of Timeslots in one Frame (\(N_{s}\)) & 10 \\ Number of Frames (\(N_{f}\)) & 200 \\ Super Frame Period (\(T_{p}\)) & 200 ms \\ \hline \end{tabular}
\end{table}
Table 1: Main parameters of PRPS.  
Figure 7: Reference trajectory.  
* Keep a uniform speed in the \(-y\) direction for 1 s.
* Make a 1/4 circular motion with a circle radius of 50 m.
* The receiver moves toward the \(-x\) direction and keeps moving at a constant speed for 1.382 s.
* Perform a deceleration movement in the \(-x\) direction until \(V_{x}=0\) and the acceleration is \(-10\) m/s.
* The receiver remains stationary for 3 s.  
The dynamic process described above lasts for a total time of 30 s and the coordinate of end point is \([-71.5,-98.3,20.0]\) (m).