# Motion Estimation of Non-Cooperative Space Objects Based on Monocular Sequence Images
## 3 Results  
The calculation effect of this method will be verified by mathematical simulation. Assuming that there is a free nutation satellite in orbit, it represents a typical space non-cooperative object. Before the robot operates on the orbit, it first needs to obtain the motion state of the object.  
The mass characteristics and initial motion state of the satellite described in the object-fixed frame are as follows:  
1. The mass is \(M_{b}=3000(\text{kg})\).  
Figure 4: The equivalent translation process of the camera. The line with the arrow represents the translation between different frames. \(T_{i}\) represents the translation from the object-fixed frame to the camera-fixed frame at moment \(i\). \(\Delta R_{i}\) and \(\Delta T_{i}\) represent the rotation and translation of the camera-fixed frame from moment \(i\) to moment \(i+1\). \(\Delta L_{i}\) represents the translation of the object-fixed frame from moment \(i\) to moment \(i+1\).  
2. The moment of inertia relative to the centeriod is as follows: \[\mathbf{J}_{b}=\begin{bmatrix}5887.73&-970.31&-3193.43\\ -970.31&12708.23&-1063.51\\ -3193.43&-1063.51&9883.97\end{bmatrix}\left(\text{kg}\cdot\text{m}^{2}\right)\]
3. The initial angular velocity is \(\omega_{b}=\begin{bmatrix}1&0.2&0.1\end{bmatrix}^{\text{T}}(\circ/s)\). The centroid position of the satellite described in the camera-fixed frame is as follows: \(\begin{bmatrix}0&0&40\end{bmatrix}(\text{m})\). The internal parameter matrix of the camera is as follows: \[A=\begin{bmatrix}2909&0&1024\\ 0&2909&1024\\ 0&0&1\end{bmatrix}\]  
The above parameter selection comes from the general satellites, and they are simply a set of horizontally comparable parameters that are randomly assumed to not affect the results. The number of feature points extracted from the object needs to be greater than eight. The camera's internal parameter matrix is derived from an ideal camera with a focal length of 16 mm, the size of a single cell on the image plane is 5.5 microns, and the total number of pixels is 2048 by 2048.  
Through the object feature recognition and matching algorithm, more than eight feature points on the object are extracted and stably tracked, as shown in Figure 5. The spatial motion trajectory of the object feature points is shown in Figure 6. The tracked object image feature points and their change trajectories are shown in Figure 7.  
The attitude quaternion and angular velocity of the object are obtained by the method in this paper, as shown in Figures 8 and 9, where the red dotted curve is the result estimated by the proposed method, and the blue solid curve is the real state of the object simulation.  
Figure 5: Object feature point extraction. The object is a hypothetical satellite model. The yellow points represent the feature points of the object.  
Figure 8: Comparison of the object attitude quaternion. This figure is the comparison of the object attitude quaternion. The red dotted curve is the result estimated by the proposed method, and the blue solid curve is the real state of the object simulation.  
Figure 6: Spatial motion trajectories of the object feature points. The yellow points represent the feature points of the object. The blue curves represent the trajectories of the feature points, and the black line displays the main outline of the object.  
Figure 7: Object image feature points and their trajectories. The yellow points represent the feature points of the object in the image. The blue curves represent the trajectories of the feature points.