## 4 Experimental Results and Analysis
### Manual Selection for Spectra Reflectance Template  
The manual selection of spectra reflectance template inversion is selecting an effective IMF combination to provide the initial population for OCA, which can accelerate the convergence speed of OCA. The reflectance curve \(R_{k_{1}k_{2}}^{i}\) is the ratio of the Ceres envelope to the solar envelope. The Ceres envelope is the sum of some IMFs and Ceres residual spectra, while the solar envelope is the envelope of the solar spectra. The expression of the reflectance curve is shown in Equation (23).  
\[R_{k_{1}k_{2}}^{i}=\left.\left(C_{a}^{i}+\sum_{m=k_{2}}^{9}h_{a}^{im}\right) \right/\left(C_{s}+\sum_{m=k_{1}}^{9}h_{s}^{m}\right), \tag{23}\]  
where \(k_{1}\) = 1,2,..., M and \(k_{2}\) = 1,2,..., \(M\) are the initial number of levels selected of the solar IMFs and the IMFs of Ceres, respectively.  
The velocimetry errors of the manual selection of spectra reflectance template inversion for Ceres are shown in Table 3. The maximal error in Table 3 is 5776 m/s, and the minimal one is 1.24 m/s. With a significant difference between them, we can see that it is crucial to select the reflectance template. The effective reflectance curve is applied for the measured solar spectrum, which can effectively reduce the influence of reflectivity on the asteroid; otherwise, the velocimetry is seriously abnormal. Taking the referential velocity difference as the baseline, the error of the velocimetry, by the traditional Taylor method, is 2.85 m/s, and the errors in bold type in Table 3 are lower than that. We can see that the levels of effective combinations of IMFs are concentrated in levels 7-9 of the asteroid spectrum and levels 4-9 of the solar spectrum. Among them, k\({}_{1}\) = 4, k\({}_{2}\) = 7 is the best combination of IMFs.  
The measurement accuracy of OCA using the manually selected population is significantly higher than that of the random initial population, and its convergence speed is much faster than that of the random initial population. This shows that the effective combination of manually selected IMFs as the initial group can accelerate the convergence speed and improve the measurement accuracy. The favourable template selected manually has a positive impact on improving the accuracy of the celestial Doppler difference velocimetry. In Section 4.4, we use several swarm intelligence algorithms to sea  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\begin{array}{c}\text{{Solar}}\\ \text{{k}}_{2}\end{array}\) & \(\begin{array}{c}\text{{K}}_{1}\\ \text{{k}}_{1}\end{array}\) & \(\begin{array}{c}\text{{2}}\\ \text{{3}}\end{array}\) & \(\begin{array}{c}\text{{4}}\\ \text{{5}}\end{array}\) & \(\begin{array}{c}\text{{6}}\\ \text{{7}}\end{array}\) & \(\begin{array}{c}\text{{8}}\\ \text{{9}}\end{array}\) \\ \hline
1 & 855.2 & 3313 & 561.9 & 502.6 & 490.4 & 486.4 & 478.7 & 480.6 & 478.8 \\
2 & 2406 & 3313 & 1834 & 779.1 & 757.2 & 749.1 & 739.5 & 740.1 & 738.1 \\
3 & 1527 & 3313 & 1004 & 929.1 & 918.4 & 919.8 & 916.4 & 917.2 & 916.6 \\
4 & 477.6 & 5776 & 331.3 & 301.5 & 298.9 & 303.2 & 303.0 & 304.2 & 304.6 \\
5 & 104.1 & 5776 & 63.57 & 42.63 & 40.53 & 44.19 & 44.01 & 44.31 & 44.61 \\
6 & 50.79 & 2396 & 24.63 & 3.45 & **1.96** & 4.77 & 4.77 & 5.07 & 5.25 \\
7 & 46.17 & 1813 & 22.11 & **1.24** & **2.25** & **2.13** & **2.02** & **2.43** & **2.67** \\
8 & 45.39 & 1747 & 21.87 & **1.3** & **2.55** & **2.07** & **1.96** & **2.31** & **2.55** \\
9 & 45.63 & 1740 & 21.93 & **1.24** & **2.67** & **2.01** & **2.02** & **2.31** & **2.61** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Velocimetry errors of the manual selection.  
build reflectance templates. We apply them to celestial Doppler difference velocimetry and compare the error and convergence of these algorithms.