## 4 Experimental Results and Discussion
### Experiments on Simulation Datasets  
We use Matlab to simulate the motion process of a ground vehicle, including varying accelerated motion and yaw rotations. The average speed during the 30-min simulation period is 3.67 m/s. Based on the true trajectory, the INS measurements were generated at 100 Hz. The measurement models of accelerometer and gyroscope are described in Equations (8) and (9). Here, we use the NovAtel SPAN-CPT system as a reference for the determination of inertial navigation parameters. Its specifications are given in Table 1[15]. In our simulation, the constant bias of the accelerometer was set as a three-component vector in the body frame as follows:  
\[\mathbf{b}_{a}=(45,-33,40)mg \tag{25}\]  
The constant bias of the gyroscope in the body frame was:  
\[\mathbf{b}_{g}=(20,-20,20)^{\circ}/\text{hr} \tag{26}\]  
The random noise was drawn from a zero-mean Gaussian distribution, the root power spectral density (PSD) of the accelerometer and gyroscope were set as follows, respectively:  
\[\mathbf{\sigma}_{a}=0.55 mg/\sqrt{Hz} \tag{27}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Fiber Optic Gyros**} & \multicolumn{3}{c}{**Micro-Electro-Mechanical**} \\  & & **System (MEMS) Accelerometers** \\ \hline Bias & \(20^{\circ}/\text{hr}\) & Bias & 50 mg \\ \hline Angular Random Walk & \(0.00667^{\circ}/\sqrt{\text{hr}}\) & Bias Stability & \(\pm 0.75\text{mg}\) \\ \hline Scale Factor & 1500 ppm & Scale Factor & 4000 ppm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance specifications of SPAN-CPT. \[\sigma_{g}=0.00667^{\circ}/\sqrt{\mathrm{hr}} \tag{28}\]  
The scale factor and cross-coupling errors of the accelerometer and gyroscope were:  
\[\mathbf{M}_{a}=\left[ \begin{array}{ccc}2500&-750&500\\ -375&-3000&625\\ -625&250&1000\end{array} \right]\mathrm{ppm} \tag{29}\]  
\[\mathbf{M}_{g}=\left[ \begin{array}{ccc}1000&-400&300\\ 0&-800&-210\\ 0&0&-430\end{array} \right]\mathrm{ppm} \tag{30}\]  
Besides supplying consumer-grade inertial sensor measurements, GNSS measurements were generated at 1 Hz. Our simulation of satellite motion as well as GNSS pseudorange and carrier phase observations were also implemented in Matlab. To obtain ECEF Cartesian positions and the velocities of simulation satellites in the constellation, we use the matlab program created by [PERSON] [17] for reference. It assumes that the satellites are evenly distributed on a circular orbit. When generating GNSS pseudorange observations, we considered ionosphere errors, troposphere errors, ephemeris errors, satellite clock errors, receiver noise, and multipath. When generating the GNSS carrier phase, the receiver noise and multipath are set to smaller values. In order to test the performance of the proposed ARPD-RTK/INS algorithm under different conditions, we designed an experimental group and a control group with different satellite visibility, as listed hereafter:  
* Scene A: Control group. From 0 s to 1800 s, there are sufficient satellite measurements with no cycle slips occurring. * Scene B: Experimental group. From 0 s to 1800 s, the total number of satellites in view is more than four, but there exist frequent changes in satellite visibility. The visibility of satellites is shown in Figure 7. In Figure 7a,b, the red points represent invisible satellites, and the black points represent available observations. Figure 7c,d depict the number of visible satellites for the control and experimental groups, respectively. In the simulation environment, the standard deviation of the carrier phase noise is 5 mm, and the standard deviation of the pseudorange noise is 30 cm. Figure 8 shows the position errors of different RTK solutions in the ECEF frame. Table 2 compares the accuracy and fix rate of these algorithms numerically.