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1、 · 812 · DING Meng et al. / Chinese Journal of Aeronautics 24(2011 807-815 No.6 On the basis of six initial FPs, we use In_M2+OI to study error changes when the number of FPs increases along three different directions. Fig. 5a, 5b, 5c, 5d, 5e, 5f and 5a, 5b, 5c, 5d, 5e, 5f, show the averag

2、e errors in the attitude angles and distances when FPs are added along the vertical tail. Fig. 5a, 5b, 5c, 5d, 5e, 5f and 5a, 5b, 5c, 5d, 5e, 5f, show average errors of attitude angles and distances when FPs are added along the wings and horizontal tails symmetrically. True values are a yaw angle of

3、 3°, pitch angle of 2°, roll angle of 3°, tx = 15, ty = 0, and tz = 4.5. Figure 5 shows that the error in pose estimation does Fig. 5 Errors as FPs are added along three different directions. not change significantly as the number of FPs increases. It has been noted that FPs are the p

4、rojections of intensity output from particular beacons (such as an LED beacon fixed on wings, horizontal tails and the vertical tail of a tanker in the image plane 14. Therefore, an increase in the number of FPs will decrease the imperceptibility of the tanker. Additionally, it will increase the com

5、putational complexity and further reduce real-time performance. Therefore, the following simulation experiments only select six FPs for pose estimation. 4.2. Error dependence on the configuration of FPs We now discuss the effect of the FP configuration on the accuracy of the pose estimation. In the

6、experiment, 10 groups of configurations are selected in terms of different separations of FPs (Fig. 6. Each configuration has six FPs located on the wings, horizontal tails and vertical tail. Fig. 7 presents the error in pose estimation using In_M2+OI for the same level of Gaussian noise but differe

7、nt configurations of FPs. True values are a yaw angle of 5°, pitch angle of 5°, roll angle of 5°, tx = 15, ty = 0, and tz = 5. The experiment results show that the error reduces as the separation of FPs increases for the same number of FPs and noise level. Therefore, while considering

8、 the field-of-view of the camera, the separation of particular beacons fixed on the surface of the tanker should be as great as possible. No.6 DING Meng et al. / Chinese Journal of Aeronautics 24(2011 807-815 · 813 · Fig. 6 Different configurations of FPs. in attitude angle is small. There

9、fore, the rotation matrix can be set initially to the identity matrix in the phase of commencing refueling and during refueling. Fig. 7 Errors for different configurations of FPs. 4.3. Accuracy and robustness In pose estimation, accuracy refers to the difference between true and estimated values. Ro

10、bustness relates to the error distribution when different levels of Gaussian noise are added to both coordinates of the image points to generate perturbed image points. This type of error is also referred to as the estimation error versus image pixel noise and is induced by the distance between a co

11、rresponding FP and real-image point in the image plane. The standard deviation denotes the level of Gaussian noise. In this experiment, the camera representing the UAV is moved along the route of the refueling, the pose parameters are estimated employing the two initialization methods and OI algorit

12、hm, and we evaluate the measurement error and resistance to noise. For the same level of Gaussian noise, Fig. 8 presents measurement errors of the attitude angle and distance during refueling relative to measured values for the three different methods. The simulation of the variation in rotation ang

13、le and position of the UAV shows that the method combining In_M2 and the OI algorithm is the most stable and accurate. This demonstrates that the precision of the initial value obtained with the linear method is very low when the variation · 814 · DING Meng et al. / Chinese Journal of Aero

14、nautics 24(2011 807-815 No.6 Fig. 8 Comparisons of values estimated employing three methods and the true value. Fig. 9 shows the estimation error obtained with In_M2+OI for different Gaussian noise in UAV refueling simulations. The results show that the robustness of the distance estimation is greater than that of the attitude angle estimation, and as the UAV approaches, the parameter estimation becomes more precise. Fig. 9 Errors for different levels of noise. 5. Conclusions This paper describes an approach for pose estimation with an OI algorithm. The approach is implemented

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