## 3 Results
### Model Status Update DA  
Ensemble Kalman filter (EnKF) is an assimilation algorithm that combines the advantages of ensemble prediction and Kalman filter. It was first proposed by [PERSON] and later described in detail by [PERSON] et al. [147; 148]. The model state update assimilation process is shown in Figure 8. Its core operational mechanism involves two main stages: prediction and update [149; 150]. Its core mechanism is shown in Formulas (4)-(9) [74; 151; 152]:  
* Forecast \[X_{i,k+1}^{f}=M_{k,k+1}\Big{(}X_{i,k}^{h}\Big{)}+\omega_{i,k},\ \omega_{i,k}\sim N(0,Q_{k})\] (4) where, \(X_{i,k+1}^{f}\) represents the predicted value of the \(i\) th state variable at time \(k+1\), \(X_{i,k}^{h}\) represents the estimated value of the \(i\)th state variable at time \(k\), \(X_{i,k}^{h}\) represents the state transition matrix from time \(k\) to time \(k+1\), \(\omega_{i,k}\) represents the model error, which obeys the Gaussian distribution with mean 0 and covariance matrix \(Q_{k}\). * Update  
Figure 8: Crop model framework of wheat LAI assimilation SAFY based on sentinel-2 remote sensing images [74]. \[X_{i,k+1}^{\mu}=X_{i,k+1}^{f}+K_{k+1}\Big{[}Y_{k+1}^{o}-H_{k+1}\Big{(}X_{i,k+1}^{ f}\Big{)}+v_{i,k}\Big{]},\;v_{i,k}\sim\;N(0,Q_{k}) \tag{5}\]  
\[\overline{X}_{k+1}^{\mu}=\frac{1}{N}{\sum_{i=1}^{N}}X_{i,k+1}^{\mu} \tag{6}\]  
\[K_{k+1}=P_{k+1}^{f}H^{T}\Big{(}Hp_{k+1}^{f}H^{T}+R_{k}\Big{)}^{-1} \tag{7}\]  
\[P_{k+1}^{f}=\frac{1}{N-1}{\sum_{i=1}^{N}}\Big{(}X_{i,k+1}^{f}-H\Big{(} \overline{X}_{k+1}^{f}\Big{)}\Big{)}\Big{(}X_{i,k+1}^{f}-\Big{(}\overline{X}_{ k+1}^{f}\Big{)}\Big{)}^{T} \tag{8}\]  
\[Hp_{k+1}^{f}H^{T}=\frac{1}{N-1}{\sum_{i=1}^{N}}\Big{[}H\Big{(}X_{i,k+1}^{f} \Big{)}-H\Big{(}\overline{X}_{k+1}^{f}\Big{)}\Big{]}\Big{[}H\Big{(}X_{i,k+1}^{ f}\Big{)}-H\Big{(}\overline{X}_{k+1}^{f}\Big{)}\Big{]}^{T} \tag{9}\]  
where \(X_{i,k+1}^{\mu}\) is the updated estimate of the \(i\)th state variable, \(K_{k+1}\) represents the Kalman gain, \(Y_{k+1}^{o}\) is the new observation value, \(H_{k+1}\) is the observation matrix, and \(v_{i,k}\) is the observation error, which follows the Gaussian distribution with the mean of 0 and the covariance matrix of \(Q_{k}\). \(\overline{X}_{k+1}^{\mu}\) represents the average estimate of all state variables, \(P_{k+1}^{f}\) represents the prediction error variance matrix, and \(R_{k}\) is the observed noise covariance. It is found that the EnKF model is most widely used in precision agriculture assimilation, especially in combination with WOFOST, CERES, and SAFY swb models [153]. In addition, the model is often assimilated as physicochemical parameters (such as LAI, SM, NDVI) for yield prediction, and more results have been achieved [154]. Recent DA studies show that EnKF focuses on in-depth exploration of uncertainties associated with multi-source RS assimilation and model blending errors. Some researchers have integrated diverse RS data sources, such as MODIS, Landsat-8, HJ-1 A/B, and Sentinel-2, into the EnKF framework to optimize CGMs simulation performance [155; 156]. Other studies have combined MCMC algorithms [157] or hybrid complex evolutionary algorithms with EnKF to recalibrate CGMs parameters and assimilate time-series data like LAI into the models, significantly enhancing simulation accuracy [135]. [PERSON] et al. effectively improved the estimation method for winter wheat yields by employing an EnKF strategy to assimilate spatiotemporal LAI into the CERES wheat model, considering factors such as observation error, assimilation stage uncertainty, and temporal-spatial scale variability [5]. Despite these advancements, EnKF still faces several challenges in the field of precision agriculture that require resolution. In general, EnKF is built upon the assumption of Gaussian distributions for system state and observation errors.