This experiment was performed in the same place as Experiment 7.1, therefore the UKF uses the path loss parameters identified during that experiment.
A formation of 3 MAVs and one beacon were used during this experiment.
The formation swept a 65 by 50 m large area by traveling to 16 predefined positions resulting in 48 different radiation pattern measurements. The predefined trajectory can be seen in Figure 7.6. The formation starts in the lower left corner. During the first flight described in Subsection 7.4.1 the MAVs made 23 individual measurements and the experiment was stopped due to technical difficulties but the measured data can still be used for partial localization. During the second flight described in Subsection 7.4.2 the MAVs made all 48 individual measurements. A video of the second flight can be seen on youtube. 2. Figure 7.10 contains a picture from the video depicting measurement of the individual radiation patterns. Figure 7.11 contains another picture from the video which shows the MAV formation following the predefined trajectory and localizing the beacon.
7.4.1 First flight
Figure 7.7a shows the MAV positions during this experiment along with the detected AoAs which are depicted by lines pointing from the appropriate MAV positions. Data from all 3 MAVs in formation are available only from the first
2https://youtu.be/3fBW5CertHk
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7.4. MAV Formation sweeping a large area-20 0 20 40 60
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Formation trajectory
MAV formation trajectory beacon
Figure 7.6: Predefined formation trajectory - experiment with an MAV formation sweeping a large area
3 formation positions. In the rest of the positions, only data from 2 MAVs were obtained. The correlation of estimated AoA uncertainty σθ and AoA estimation error is 0.28 at 0.19 statistical significance which is significantly lower than in the previous experiments but a correlation still exists. The RMSE of average RSSI values from the theoretical curve is 3.9 dBm.
Figure 7.7b contains the progression of UKF localization error over the number of performed filter steps. It can be seen that using the measured data the localization error dropped by approximately 20 m during the filter run. The final localization error is 9.8 m.
7.4.2 Second flight
During the second flight, the MAVs made a total number of 48 different measurements. The positions were the measurements were performed along with the detected AoAs can be seen in Figure 7.8a. The correlation ofσθ and AoA estimation error is 0.29 at 0.043 statistical significance. The average RSSI values along with the theoretical curve are shown in Figure 7.8b. The RMSE of the values from the theoretical curve is 3.45 dBm.
During this experiment, the largest number of correct measurements was
7. Real experiments
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MAV and beacon positions with detected AoA
MAV beacon detected AoA
(a) : x-y plot of MAV and beacon positions along with detected AoA
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UKF localization error over filter steps
(b) : UKF localization error
Figure 7.7: MAV positions with detected AoA and UKF localization error from first flight of formation with predefined trajectories
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MAV and beacon positions with detected AoA
MAV beacon detected AoA
(a) : x-y plot of MAV and beacon positions along with detected AoA from experiment with a formation following predefined trajectories
Dependency of average RSSI on 3D distance
measured data theoretical curve
(b) : Dependency of average RSSI on distance from formation experiment
Figure 7.8: Measured data from the second flight of MAV formation
collected therefore the data from this experiment were used for tuning the parameters of the UKF with the goal of minimizing the final localization error and the performance of the filter with these parameters was then verified on data gained from the other experiments. The UKF parameters are described in Section 4.4.4.
Figure 7.9a shows the progression of UKF localization error over the number of performed filter steps for 3 different settings of the filter. TheRSSI+AoA setting uses the filter parameters described in Section 4.4.4. It can be seen that its localization error drops to 1.66 m in 25 filter steps end then keeps slowly converging to the real beacon position. The final localization error is 0.04 m. TheAoA setting uses just the AoA data for localization which was
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7.4. MAV Formation sweeping a large areaUKF localization error over filter steps
RSSI + AoA AoA RSSI
(a) : UKF localization error for different filters
Estimated beacon position over filter steps
MAV beacon estimated position covariance ellipse
(b) : Estimated beacon position over filter steps
Figure 7.9: Localization results from the second flight of MAV formation
Figure 7.10: Measurement of radiation patterns during the second flight in the experiment with MAV formation following a predefined trajectory
done by setting the σRSS parameter to a very large value (1000 dBm) and tuning theQmatrix for the best possible localization results. In this case, the final localization error is 5.92 m. The RSSI setting uses only the RSSI data which is set by multiplying theσθ parameters by a large scalar value (1000) and tuning the Q matrix andσRSS parameter to produce a good and stable filter performance. The performance is again worse than the performance of the hybridRSSI+AoA filter and the final localization error is 3.19 m.
Figure 7.9b depicts the progression of the RSSI+AoA UKF estimated position in the xy plane. It can be seen that the estimate starts with its initial value in the first formation position and then gradually converges to the real beacon position. A covariance ellipse of the final estimate representing the 95% confidence area is plotted as well.
7. Real experiments
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Figure 7.11: Localization of the beacon during the second flight in the experiment with MAV formation following a predefined trajectory