**3. Test and Validation**

*3.1. Simulation*

Faults are simulated and added to data from UAV flight tests to test the proposed quality control algorithm. The UAV flight data were collected in Nantou City, Taiwan, shown in Figure 2. The UAV used in the test is AXH-E230 from AVIX Technology (Toronto, ON, Canada), and it was flown semi-automatically with a smart power control module to perform autonomous intelligent navigation flight mission. The onboard equipment setup included: (1) a dual-frequency GNSS receiver, Trimble BD 982 (Sunnyvale, CA, USA), with a sampling rate of 10 Hz for the raw pseudorange measurements collection; (2) a STIM-300 IMU (Sensonor, Horten, Norway), with a sampling rate of 100 Hz for UAV acceleration and angular rate collection; (3) an on-board VLP-16 Velodyne Lidar (San Jose, CA, USA) to provide centimeter-level positioning accuracy for the reference trajectory generation in the experiment. The speed of UAV was less than 10 m/s during the flight, and the height was about 60 m AGL (with the ground elevation around 120 m). The fault scenarios in Table 2 were specified in order to compare the proposed algorithm with the traditional IMU/GNSS tightly-coupled (TC) without fault exclusion, the TC with traditional w-test quality control (FDE TC), and the TC with Robust filter (AKF TC) in [31].

**Figure 2.** Unmanned aerial vehicle (UAV) flight trajectory.


**Table 2.** The defined scenarios.

In the different scenarios above, for each selected satellite, an error of 10 m, 30 m, or 50 m was injected into the pseudo-range observation of the satellite during the corresponding fault duration. Based on the derivations in [32], UAV flight in the urban environment is subjected to multipath interference to produce similar errors, with error magnitudes less than 10 m having little impact on the satellite navigation and positioning results, and is hence ignored as constituting failure. At the same time, considering the characteristics of UAV in urban low-altitude areas, fault duration is selected as 30 s. In order to verify the validity of the algorithm, in terms of accuracy, this paper uses the Root Mean Square Error (RMSE) metric to compare the performance of the TC, FDE TC, AKF TC, and the proposed methods. The errors of the position, calculated from the candidate algorithms, are shown in Figure 3. The RMSE of the positions for the candidate algorithms are represented in Table 3.

**Figure 3.** The positioning error of TC, FDE TC, AKF TC, and the proposed algorithm in the four fault scenarios.

**Table 3.** Comparison of algorithm performance between TC, FDE TC, AKF TC, and the proposed algorithm in the different fault scenarios.


It can be seen, in Figure 3, that TC position error increases rapidly after pseudorange errors are introduced in the four scenarios. This indicates that, without FDE, the IMU/GNSS integrated navigation positioning quality is seriously degraded and results in divergence in the filter estimated results. Therefore, quality control of the GNSS measurement is essential. Meanwhile, by observing the position errors of the FDE TC in different scenarios, it can be seen that, in most cases, when two satellites simultaneously fail, the performance of FDE TC is poor. Only when one satellite has a 30 m step error, and one satellite has a 50 m step error, does FDE TC correctly identify the two faulty satellites in all epochs and eliminate them.

In the other three scenarios, however, the corresponding faulty satellites could not be correctly detected and excluded in all epochs by FDE TC, resulting in a large positioning error. In scenario 3, the maximum positioning error of the FDE TC method even exceeds that of the traditional TC. This is mainly because, in scenario 3, the two satellites add the same step error. As a result, the test statistics of other satellites are strongly correlated with the two faulty satellites, resulting in the maximum test statistics exceeding the traditional w-test threshold. When the satellite with the maximum test statistics exceeding the threshold is eliminated based on a traditional w-test, the redundancy of the observation data is further reduced, so the remaining faulty satellite cannot be detected in the subsequent traditional w-test. The satellite faults still exist in the GNSS measurements, so the positioning performance of the FDE TC is comparable to that of the traditional TC without FDE. It can be seen from Table 3 that the FDE TC, in the above four different scenarios, has similar accuracy to the traditional TC in some cases. However, in scenarios 1 and 2, the FDE TC can still eliminate all faulty satellites in some epochs, but the faulty satellites cannot be correctly eliminated all the time by FDE TC. As a result, the positioning performance of FDE TC is improved by 49% and 62% compared with the traditional TC, respectively. On the other hand, although AKF TC cannot eliminate faults, it reduces the weight of fault observations, thus ensuring the navigation performance to a certain extent. The positioning performance of AKF TC is improved by 35%, 52%, 61%, and 67% compared with the traditional TC, respectively.

However, compared with the above algorithm, the proposed algorithm significantly improves positioning accuracy. This also shows that the proposed algorithm can correctly detect the satellites with the step errors in the above four different cases. The 3D positioning RMSE of the algorithm proposed in this paper, in four different fault scenarios, is 2.98 m. Compared with 9.62 m, 13.04 m, 17.36 m, and 20.73 m of the traditional TC, the accuracy is improved by 69.07%, 77.17%, 82.85%, and 85.64%, respectively. In summary, the above results show that the algorithm proposed in this paper can correctly detect the faulty satellites in the real-data field scenarios with the simulated step errors. Compared with the traditional TC, FDE TC, and AKF TC, it is able to provide a significant improvement in the position solutions.

#### *3.2. Field Test*

In order to further validate the performance of the proposed algorithm in an urban environment, a field test was carried out in a deep urban environment in Taipei. The experimental data acquisition equipment contained a low-cost IMU Stim-300 and a GNSS receiver Trimble BD 982, with a sampling rate of 250 Hz and 1 Hz, respectively. The reference trajectory was obtained by an integrated high-grade GNSS receiver and iNAV-RQH IMU with the commercial software NovAtel Inertial Explorer. The experimental test environment is shown in Figure 4, and the reference trajectory is shown in Figure 5. PDOP values during the test are always very high, with the highest value above 16, exhibiting the characteristics of the deep urban environment, as seen in Figure 6. The number of visible satellites is shown in Figure 7.

In order to evaluate the performance of the proposed algorithm, the results of the proposed algorithm are compared with those of the traditional TC, FDE TC, and AKF TC. The errors in position, velocity, and altitude, calculated from the algorithms, are shown

in Figures 8–10. The accuracies (RMSE) of the position, velocity, and altitude for the algorithms are given in Tables 3–6.

**Figure 4.** Environments of field test.

**Figure 5.** Vehicle trajectory in field test.

From Figure 8 and Table 3, the AKF TC position RMSE is 4.40 m in the horizontal direction and 8.94 m in the vertical direction (Down), which is an improvement of 11.65% and 17.15% compared to the 4.98 m and 10.79 m of the TC. The FDE TC vertical position RMSE is 9.66 m, whose performance is not as good as AKF TC, but the performance is better in the horizontal direction. However, neither is as much improved as the algorithm

proposed in this paper. The position RMSE of the algorithm proposed is 3.79 m and 7.51 m in the horizontal and vertical directions. The results represent improvements of 23.90% and 30.40% compared to TC without FDE, 7.79% and 22.26% over FDE TC, as well as 13.86% and 15.88% over AKF TC, respectively. As shown in Figure 11, the algorithm proposed in this paper has a better performance in urban environments in the horizontal directions.

**Figure 6.** PDOP in field test.

**Figure 7.** Visible satellite number in field test.

**Figure 8.** The position error of TC, FDE TC, AKF TC, and the proposed algorithm in field test.

**Figure 9.** The velocity error of TC, FDE TC, AKF TC, and the proposed algorithm in field test.

**Figure 10.** The altitude error of TC, FDE TC, AKF TC, and the proposed algorithm in field test.


**Table 4.** The position RMSE of TC, FDE TC, AKF TC, and the proposed algorithm in field test.

**Table 5.** The velocity RMSE of TC, FDE TC, AKF TC, and the proposed algorithm in field test.



**Table 6.** The altitude RMSE of TC, FDE TC, AKF TC, and the proposed algorithm in field test.

**Figure 11.** Trajectory comparison for TC, FDE LC, AKF TC, and the proposed algorithm in field test.

It can be seen from Figure 9 and Table 5 that the horizontal and vertical velocity RMSE of the traditional TC scheme without FDE are 0.98 m/s and 1.07 m/s, with the corresponding values, from the proposed algorithm, of 0.59 m/s and 0.72 m/s. These correspond to improvements of 40% and 33%, respectively. While the AKF TC gives an RMSE for horizontal velocity of 0.89 m/s, the performance in the vertical direction deteriorates by 13.08% due to its inability to be accurately adjusted, specifically, for the errors caused by multipath signals and NLOS that are common in urban areas. Compared with the 0.73 m/s and 0.93 m/s of FDE TC, the proposed algorithm in this paper improves by 19% and 23%. This shows that correct fault detection and elimination is effective for quality control.

For the performance of altitude determination in Figure 10 and Table 6, pitch, roll, and yaw RMSE of the traditional TC scheme without FDE are 2.70◦, 1.39◦, and 3.43◦, with the corresponding values from the FDE TC of 2.62◦, 1.38◦, and 2.28◦. These correspond to improvements of 2.96%, 0.72%, and 33.53%, respectively. It is worth noting that the correction of yaw information has always been a difficult problem in the GNSS/IMU integrated navigation algorithm, and the yaw RMSE of FDE TC has dropped by 27.6%. This further illustrates the importance of quality control. While the AKF TC gives an RMSE for pitch angle of 2.33◦, the performance in the roll angle deteriorates by 2.88%, and

there is less improvement in the yaw angle. The proposed algorithm has improved the estimation results of pitch angle, roll angle, and yaw angle by 2%, 8%, and 1% compared with FDE TC, respectively. Although the performance of the proposed algorithm in this paper is not good in the pitch angle, compared with AKF TC, the overall performance of the proposed algorithm in this paper is better, which improves by 11.19% and 27.60% in roll and yaw angles.
