## 4 Experimental Results and Discussion
### Practical Experiments and Analysis
#### 4.2.2 SAR Tracking System  
As shown in Figures 16 and 17, the UAV is equipped with one D3160 type SAR. The UAV is a six-rotor UAV with mass being 20 kg and velocity range being 0 m/s-20 m/s. The D3160 type SAR is a kind of micro-SAR system and the parameters are as follows: mass: 4 kg, operating frequency band: X or Ku, detection range: 10 km, resolution: 0.3 m. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Mean Absolute Error of Longitude (m)**} & \multicolumn{2}{c}{**Mean Absolute Error of Latitude (m)**} \\ \cline{2-5}  & **Mean** & **Standard Deviation** & **Mean** & **Standard Deviation** \\ \hline EKF & 8.6533 & 7.9816 & 8.2107 & 7.0044 \\ CKF & 8.4154 & 7.5127 & 8.0109 & 6.8135 \\ UKF & 6.9018 & 6.5011 & 6.9271 & 6.6102 \\ AUKF & 4.4225 & 4.0118 & 4.8159 & 4.6825 \\ NAUKF & 3.0156 & 2.8105 & 2.8192 & 2.4947 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison for NAUKF in INS/GPS navigation system. Figure 15: Latitude error comparison for NAUKF in INS/GPS navigation system. The SAR can detect the pitch angle \(\varphi_{1}\), azimuth \(\varphi_{2}\) and distance \(d\) of the target vehicle relative to the UAV, and the measurement equation is  
\[\mathbf{Z}=\left[ \begin{array}{c}d\\ \varphi_{1}\\ \varphi_{2}\end{array} \right]=\left[ \begin{array}{c}\sqrt{\left(x_{U}-x_{t} \right)^{2}+\left(y_{U}-y_{t}\right)^{2}+\left(z_{U}-z_{t}\right)^{2}}\\ \arctan\left(\frac{z_{U}-z_{t}}{\sqrt{\left(x_{U}-x_{t}\right)^{2}+\left(y_{U} -y_{t}\right)^{2}}}\right)\\ \arctan\left(\frac{y_{U}-y_{t}}{x_{U}-x_{t}}\right)\end{array} \right] \tag{51}\]  
where \(\left[x_{U},y_{U},z_{U}\right]^{\mathrm{T}}\) is the position of UAV; \(\left[x_{t},y_{t},z_{t}\right]^{\mathrm{T}}\) is the position of the target vehicle. In the experiment process, both the pitch angle and azimuth measurement had the drift rate, and the distance measurement had the deviation for the SAR, but the precise statistics about the sensor faults and noises are still unknown. In Figure 18, the target vehicle is driving on the expressway, and the initial position of the UAV and the target vehicle is, respectively, East longitude 108.933195\({}^{\circ}\), North latitude 34.188183\({}^{\circ}\), and an altitude of 1.50 km and East longitude 108.938962\({}^{\circ}\), North latitude 34.187501\({}^{\circ}\), and an altitude of 436.05 m. The experiment test time is designed as 1000 s with the sample period being 1 s, and the end point of the UAV and the target vehicle is, respectively, East longitude 109.130943\({}^{\circ}\), North latitude 34.245275\({}^{\circ}\), and an altitude of 1.50 km and East longitude 108.145231\({}^{\circ}\), North latitude 34.239740\({}^{\circ}\), an altitude of 436.76 m.  
Figure 16: The experimental unmanned aerial vehicle (UAV). Figure 17: The UAV loaded tracking equipment; (**a**): SAR (synthetic aperture radar); (**b**): Antenna. When the IMM and CPIMM methods are used, the target model description is the same as the numerical simulation. Four filtering methods including IMM-UKF, IMM-NAUKF, CPIMM-UKF, and CPIMM-NAUKF were used in the experiment, and these algorithms were evaluated by the estimation error shown by Equation (50).