## 4 Experimental Results and Discussion
### Practical Experiments and Analysis
#### 4.2.1 INS/GPS Integrated Navigation System  
As shown in Figures 11 and 12, the vehicle loaded integrated navigation system included a NV-IMU300 type INS, a JAVAD Lexon-GGD12T type GPS receiver, and a NovAtel DL-V3 GPS receiver on the vehicle, and another NovAtel DL-V3 GPS receiver was located at the Earth Reference Station. The working frequency of the GPS was 20 Hz. The maximum distance between the vehicle and the Earth Reference Station had to be less than 60 km, which ensured that the positioning precision of the vehicle was better than 0.1 m.  
Let the geographic coordinate system be the navigation coordinate system with three directions of East, North, Up. Define the system states as  
\[\mathbf{X}(t)=\big{[}\psi,\theta,\gamma,v_{E},v_{N},v_{U},L,\lambda,h,\varepsilon_ {x},\varepsilon_{y},\varepsilon_{z},\
abla_{x},\
abla_{y},\
abla_{z}\big{]}^{T} \tag{46}\]  
where \(\psi,\theta,\gamma\) represent the heading angle, the pitch angle, and the roll angle of the vehicle, respectively; \(v_{E},v_{N},v_{U}\) are components of the velocity along the East, North, and Up directions, respectively; \(L,\lambda,h\) are components of the position along the East, North, and Up directions, respectively; \(\varepsilon_{x},\varepsilon_{y},\varepsilon_{z}\) represent the drift of the gyro; \(\
abla_{x},\
abla_{y},\
abla_{z}\) represent the bias of the accelerator. The state space model is  
\[\dot{\mathbf{X}}(t)==\mathbf{f}[\mathbf{X}(t)]+\mathbf{W}(t) \tag{47}\]  
the concrete equations of which can be found in [45]. Select the velocity and position outputs of the GPS as the measurement variables:  
\[\mathbf{Z}=[v_{EG},v_{NG},v_{UG},L_{G},\lambda_{G},h_{G}]^{T} \tag{48}\]  
where \(v_{EG},v_{NG},v_{UG}\) are components of the velocity measured via GPS along the East, North, and Up directions, respectively; \(L_{G},\lambda_{G},h_{G}\) are components of the position measured via GPS along East, North, and Up directions, respectively. The velocity and position information measured via GPS can be used as a reference to confirm the position error of the INS/GPS. The measurement equation is  
\[\mathbf{Z}_{k}=\mathbf{H}_{k}\mathbf{X}_{k}+\mathbf{V}_{k} \tag{49}\]  
where \(\mathbf{H}_{k}=[\mathbf{O}_{6\times 3},\mathbf{O}_{6\times 6},\mathbf{O}_{6\times 6}]\). In the experiment process, the initial position was as follows: East longitude 108.891227\({}^{\circ}\), North latitude 34.286866\({}^{\circ}\), and an altitude of 437.92 m. Components of the velocity along the East, North, and Up directions were, respectively, \(-8\) m/s, \(-35\) m/s, and 0 m/s; the drift of the gyro was 0.12\({}^{\circ}\)/h, and the white noise was 0.02\({}^{\circ}\)/h; the bias of the accelerator was 10\({}^{-3}\) g, and the white noise was 10\({}^{-4}\) g; the positioning and position precision of the GPS were 5 m and 0.05 m/s; the other initial parameters were the same as the those described in the simulation section. The experiment test time was designed as 500 s with the sample period being 1 s, and the end point of the vehicle was East longitude 108.995683\({}^{\circ}\), North latitude 34.285292\({}^{\circ}\), and an altitude of 438.01 m. The practical road condition was the urban highway, and the real route of the vehicle is shown in Figure 13.  
Figure 11: The experimental vehicle. Figure 12: The vehicle loaded navigation equipment. Figure 13: The real route of the vehicle in navigation.