# Harmonizing Multi-Source Remote Sensing Images for Summer Corn Growth Monitoring
## 4 Discussion  
### The Improved Kalman Filter Model  
Kalman filter is an algorithm for optimal estimation of system state which uses linear equation of system state and observation data. When we predicted the missing GF-1 image by Kalman filter, we found that the model was uncertain due to the lack of observation value. Consequently, we generated a set of observation data, firstly through ESTARFM model and applied it to Kalman filter. In our work, the result manifested that the improved Kalman filter had good performance in predicting  
Figure 9: Harmonized remote sensing images over the summer corn fields: temporal variation of NDVI and LAI (**a**), slope and difference of NDVI (**b**), rainfalls and temperatures (**c**), ET (**d**) and LE (**e**) from DOY 150 to DOY 280, 2014, in study area.  
GF-1 images. As shown in Figure 5, the harmonized images using improved Kalman filter depicted the growing and changing of summer corn well, and was in good agreement with the temporal changing curve of MODIS images which had a low spatial resolution. Importantly, compared with the ESTARFM model, the improved Kalman filter added the function of filtering on time series, and through the forward and backward filtering of Kalman filter, the weighted average was carried out according to the uncertainty to achieve a smooth effect. We used the real observations (DOY 178 and DOY 227) which were not involved in synthesis as validation data. As could be seen from the Figures 7 and 8, the synthesized dataset constructed using this methodology was highly accurate, with high temporal resolution and medium spatial resolution.  
Although there are important discoveries revealed by our studies, there are also limitations. First, the problem of missing data due to weather (e.g., clouds, raining and smog) has not been thoroughly solved. In spite of the synthesis algorithm based on multi-source data platform alleviates this problem to some extent, it is possible to not get an image for a month. Especially in our research area, this phenomenon is particularly serious. [PERSON] et al. (2016) compared four kinds of image fusion methods, including ESTARFM, and showed that the ESTARFM performed more stably than other models. However, the results of [PERSON] et al. (2017, 2018) showed that MODIS 8-day composite datasets had more acceptable correlations for distinguishing phenology variations at shorter time frames than 16-days. Long time intervals will lead to large changes in vegetation cover and NDVI due to vegetation growth, which will have a negative impact on the quality of the predicted image. To some extent, the improved Kalman filter alleviates this contradiction, but it cannot be ignored. Second, the BRDF effect of MODIS images also has a beneficial effect on the results. [PERSON] et al. (2019) reminded of the BRDF effects in MODIS images can be considerable because of the large swath width. In practice, we used NDVI to reduce the BRDF effect. Furthermore, the selection of sampling plots was done manually, which greatly reduces the image processing ability. The meaning of Equation (3) is to capture the changes of vegetation growth over time on existing low-resolution images and use it to predict the high-resolution prior estimation at the next moment. Therefore, the selection of quadrats is very important as it requires pure corn pixels. [PERSON] et al. (2018) pointed out that the higher pixel purity could improve the accuracy of LAI of time series and crop yield estimation. We selected relatively pure corn pixels manually according to land-use classification data (excluding those cloudy and serious mixed pixels). The process of manual selection was time-consuming and laborious, which greatly reduced the efficiency of the algorithm.  
In the future, we will try to introduce Synthetic Aperture Radar (SAR), which is not affected by weather conditions such as clouds and rain into the improved Kalman filter model and develop an automatic method to select sampling plots.