# Satellite Attitude Determination and Map Projection Based on Robust Image Matching
## 6 Conclusions  
We have developed an automated and robust scheme for deriving satellite attitudes from satellite observation images with known satellite positions. By combining SURF and RANSAC-based algorithms, the proposed scheme optimizes the solution under satellite-specific geometry conditions. The proposed method provides accurate satellite attitude determination independently of satellite onboard attitude sensors including STT, and improved map-projection are achieved. The satellite attitude determined by the proposed method can be accurate to within \(\sim\)0.02\({}^{\circ}\), which reaches the same order of the STT accuracy. In addition, the proposed method achieves two-pixel accuracy in the map projection, as confirmed in the comparisons between the projected satellite images and the base-map images. This accuracy is acceptable for applying conventional approaches such as template matching and GCP matching. Accurate attitude determination and map projection achieved by the proposed method will improve small satellite image geometries, which contributes to provide fine-scale information about Earth. Though the proposed scheme is not applicable when no land features can be seen in a satellite image (e.g., whole cloud images and sea observations), it can be a complementary approach to STT in determining satellite attitude. The proposed approach treats image sensors as attitude sensors. Although we evaluated its performance through a map projection task in this paper, stricter evaluation may be carried out by comparing the output from the proposed approach with attitudes determined by another attitude sensor. To reduce the computational cost, we designed an early stopping mechanism for the repetitions of the RANSAC family by recognizing that it is possible to find which matched feature pairs between the satellite and base-map images strictly follow the geometrical relationship described in Section 3.1. We confirmed that when the inlier ratio exceeds 60%, the average numbers of repetitions were less \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Observation Date** & **1: 2015-10-16T03-31:07** & **2: 2015-10-16T03-31:15** \\ \hline Rotation matrix (\(\mathbf{\hat{M}}\)) & \(\left(\begin{array}{c}-0.15760437&0.78030853&0.60521026\\ 0.43610075&0.60486583&-0.66629833\\ -0.88598928&0.15892112&-0.43562263\end{array}\right)\) & \(\left(\begin{array}{c}-0.16089170&0.77993737&0.60482358\\ 0.43638362&0.60586881&-0.66520096\\ -0.88525883&0.15690979&-0.43783115\end{array}\right)\) \\ Rotation angle between two matrices & & 0.18\({}^{\circ}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Rotation matrices and rotation angle between the two observations shown in Figure 8.  
Figure 8: Sequential observations of UNIFORM-1 on 26 September 2015. The numbers represent the order of the two observations, which are temporally separated by 8 s. Base-map images are taken from OLI band 4. Contrasts in the VIS images are enhanced. than 10, which is small enough for fast computation. Even in a smaller inlier ratio case, a huge number of repetitions can be avoided by incorporating sequential observations. In addition, the feature points extracted from base-map images by the SURF descriptor can be independently prepared before each satellite observation. This preparation would reduce not only the computational cost of processing each observation, but also the amount of data storage, because the proposed method would call the SURF descriptor instead of referring to images. As the proposed method requires no specific feature descriptor, it can be combined with methods other than SURF, such as Scale-Invariant Feature Transform (SIFT) [23], Binary Robust Invariant Scalable Key-points (BRISK) [33], Oriented FAST and Rotated BRIEF (ORB) [34], and KAZE [35].