## 5 Experiments and Discussion
### Image Motion Compensation Simulation  
Using a two-axis frame camera as the experimental subject, the aircraft operates at an altitude of 3000 m with a speed-to-height ratio of 0.04 and a roll scanning rate of 40\({}^{\circ}\)/s. The actual attitude variation curve of a single flight strip during aircraft operation, shown in Figure 10, is used as input to perform LOS stabilization simulation for the proposed image motion compensation algorithm. The exposure start point is set at a 45\({}^{\circ}\) backward-squint ground point, where the roll planning angle is 0\({}^{\circ}\) and the pitch planning angle is 45\({}^{\circ}\), with an exposure stabilization time of 30 ms for each exposure. Figure 10: Aircraft attitude angle: (**a**) yaw; (**b**) pitch; (**c**) roll. Figure 9: 3D variation of deviation for approximate and exact algorithms with roll angle and initial pitch angle: (**a**) compensation angle deviation; (**b**) pitch angle deviation. Equation (8) enables the calculation of the camera planning angles under attitude disturbances, providing both the real-time and planned values of the camera roll angle \(\phi_{C}\) and pitch angle \(\theta_{C}\), as shown in Figure 11. It can be observed that due to attitude disturbances, the pitch angle and roll angle of the camera must be adjusted accordingly. The next step is to compute the compensation angles using the image motion compensation algorithm to stabilize the LOS. After applying the backward-squint image motion compensation algorithm in Equation (22), the comparison between the compensated LOS vector and the target LOS normalized vector is shown in Figure 12. The two vectors exhibit a high degree of overlap, which is consistent with the previous computational analysis. Figure 13 shows the trajectory of the central LOS ground projection point during whisk-broom imaging exposure. The image indicates that the displacement in the \(x\)-direction during exposure is 1.37 \(\times\) 10\({}^{-4}\) m, while the displacement in the \(y\)-direction is 2.78 \(\times\) 10\({}^{-3}\) m. Considering the 45\({}^{\circ}\) backward-squint imaging condition, the actual imaging altitude is given by 3000/cos 45\({}^{\circ}\) = 4242 m. Consequently, the central LOS stabilization deviation of the proposed image motion compensation algorithm is calculated as 0.032 \(\upmu\)rad in the \(x\)-direction and 0.65 \(\upmu\)rad in the \(y\)-direction, which is better than 0.01 pixels. This  
Figure 11: Real-time and planned angle values after attitude disturbance: (**a**) pitch; (**b**) roll. Figure 12: Comparison of the compensated and target LOS vector. demonstrates the accuracy of the image motion compensation algorithm in stabilizing the central LOS. Figure 14 illustrates the updates of the aircraft position and the real-time ground projection point over six successive steps within a single compensation cycle during backward-squint imaging when the aircraft roll angle is \(0^{\circ}\). Due to the forward motion of the aircraft, the camera's imaging position shifts incrementally in the negative \(x\)-direction, as shown in the magnified schematic on the left. The magnified schematic on the right presents the trajectory variations of the ground projection boundary points. To analyze the influence experienced by each ground projection boundary point during the scan compensation process, Figure 15a-d presents the ground projection trajectories of the four boundary points in the figure. These correspond to the upper, right, left, and lower boundary points, respectively. During the 30 ms compensation cycle, the displacement  
Figure 14: Aircraft position and ground projection point trajectory for backward-squint imaging with a roll angle of \(0^{\circ}\). Figure 13: Trajectory curve of the ground projection point of the central LOS. along the x and y directions ranges from approximately 5 to 7 m. The motion trajectories of the boundary points indicate that the displacement is primarily driven by rotational scanning.