## 3 Results
### Model Status Update DA
However, in practical applications, nonlinear factors such as extreme weather, pests and diseases, light, temperature, moisture, and fertilizer may cause state variables to deviate from Gaussian distributions, exhibiting non-Gaussian characteristics like heavy tails or sharp peaks and leading to inaccurate covariance calculations. Although EnKF can calculate the covariance of prior state vectors using samples from the prior distribution, its effectiveness can be limited when dealing with non-Gaussian properties. Consequently, non-parametric methods like Particle Filtering and Iterative Expectation-Maximization (EM) algorithms, all Gaussian assumptions, emerge as strong alternatives to EnKF [158; 159]. Furthermore, EnKF usually estimates the covariance matrix by the differences between the set members. However, when dealing with high-dimensional systems, smaller integration sizes can lead to underestimation or overestimation of covariance, manifested by filter divergence or over-reliance on observed data [160; 161]. To address this problem, common strategies include introducing an inflation factor to increase Kalman gain and adopting an adaptive mechanism to dynamically adjust covariance matrix parameters based on historical filter performance and observed data characteristics [162]. In the future, the Schur product (also known as the Hadamard product), which refers to a new matrix formed by the product of the corresponding elements of two matrices in the context of data assimilation, can be used to localize the covariance matrix, that is, to preserve only the covariance between the observation points and the model states that are spatially close. The covariance between distant points is set to zero (or smaller) or the Gaspari-Cohn function ([PERSON] proposed a smooth truncation function in 1999), which is often used as a localized kernel, that is, the smooth decay from the center (i.e., the observed position) outward to zero, ensuring that the covariance of the neighboring region is fully utilized, and the covariance of the distance between the two points is set to zero. Distant covariances are gradually ignored, and other methods are expected to reduce the number of conditions in the covariance matrix, thereby improving the estimation accuracy [163]. In addition, EnKF faces challenges in dealing with discontinuous processes such as threshold effects, saturation phenomena, or discrete events [164], as the assimilation results are no longer significantly updated or improved despite the input of new observational data after the data reach a certain threshold. There are two main coping strategies: the first is to convert non-Gaussian observations to approximate Gaussian distributions through techniques such as piecewise linearization, logarithmic transformations, Box-Cox transformations, and TPCM pairing [165]. The second option is to take the non-Gaussian process model directly and solve for the Kalman gain using the Jacobian matrix or Newton iterative methods, although this may increase the computational cost [136]  
It is noteworthy that recent EnKF research highlights that enhancing its scalability and adaptability is crucial when confronted with complex nonlinearity, non-stationarity, uncertainties, and model errors arising from high-resolution RS, unmanned aerial vehicle hyperspectral data, and extreme climates and changing farming systems [166]. Specific strategies include explicitly incorporating model error terms, implementing weighted fusion of multiple models, adopting advanced smoothing-filtering algorithms like Ensemble Square Root Filter (EnSRF) [167], and exploring ML-based automatic parameter adjustment algorithms and feedback mechanisms [168; 169]. These measures hold promise to bolster EnKF's performance in complex agricultural RS applications, preparing it to tackle future challenges.