## 3 Results
### Validation of Yield Estimation Models  
In this section, the established models were evaluated by validation datasets. It was found that the overall test results were similar to these obtained by the calibration dataset, demonstrating the usefulness of florescence spectral information in improving R\({}^{2}\), MAPE and RMSE of yield estimation models using vegetation indices alone (Table 7). Moreover, the fitting line of measured and estimated yields of models with flowering information were closer to the 1:1 line (Figure 7). R\({}^{2}\) of the single-growth stage model, two-growth stage model and three-growth stage model increased by 0.073, 0.037 and 0.012, respectively, with the largest increase obtained by the single growth stage model, whose MAPE and RMSE decreased by 27.3% and 19.2%, respectively.  
Additionally, it could be found that yield estimation accuracy of the single-growth stage model based on vegetation index and florescence spectral indices was equivalent to the two-growth stage model using vegetation indices alone, and the same held true for the comparison between the two-growth stage model basing on vegetation indices and florescence spectral information and the three-growth stage model basing on vegetation indices alone. This indicated that the introduction of florescence spectral information into models using spectral indices alone not only helped reduce the number of remote  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Growth Stage Combination** & **Florescence Information** & \(\mathbf{R^{2}}\) & **MAPE (\%)** & **RMSE (kg/ha)** \\ \hline Single-growth stage & No & 0.748 & 5.74 & 548.61 \\  & Yes & 0.799 & 5.06 & 489.91 \\ Two-growth stage & No & 0.833 & 4.74 & 446.45 \\  & Yes & 0.869 & 3.98 & 396.02 \\ Three-growth stage & No & 0.838 & 4.7 & 439.7 \\  & Yes & 0.861 & 4.33 & 419.58 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparisons of the yield estimation models with and without considering florescence spectral information for the modeling dataset.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Growth Stage Combination** & **Florescence Information** & \(\mathbf{R^{2}}\) & **MAPE (\%)** & **RMSE (kg/ha)** \\ \hline Single-growth stage & No & 0.738 & 7.04 & 405.92 \\  & Yes & 0.811 & 5.12 & 328.10 \\ Two-growth stage & No & 0.791 & 6.83 & 391.68 \\  & Yes & 0.828 & 6.04 & 376.16 \\ Three-growth stage & No & 0.795 & 6.17 & 360.54 \\  & Yes & 0.807 & 6.06 & 373.31 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparisons of the yield estimation models with and without considering florescence spectral information for the validation dataset.  
sensing data acquisition, but also realized the accurate rice yield estimation at an earlier time. Compared to the three-growth stage models using vegetation indices alone, the two-growth stage model using vegetation indices and florescence spectral indices was more likely to be a preferred model for rice yield estimation (Figure 8).  
Figure 8: Scatter plots of measured yield vs. estimated yield derived from the original vegetation index-based model and the optimization model introducing florescence spectral information for modeling datasets of (**a**) single growth stage (**b**) two-growth stage (**c**) three-growth stage, and validation datasets of (**d**) single-growth stage (**e**) two-growth stage and (**f**) three-growth stage.