## 1 Introduction  
Winter wheat is one of the major food crops in China. By monitoring and estimating winter wheat yield, the growth status of wheat in the field can be obtained in a timely manner, which is an important reference for food market supply and its stability supply [1]. In addition, by keeping track of winter wheat yield, the government can adjust grain reserves, and import and export policies in a timely manner to achieve stable market supply and price control, which is important for maintaining market order, increasing farmers' income, and ensuring national food security [2]. With the advancement of satellite technology and image processing algorithms, remote sensing technology can quickly obtain wide-area and high-resolution image data of vast agricultural fields, thereby achieving near real-time monitoring and prediction of crop growth and yield [3]. The principle of remote sensing monitoring of crop yield is to observe and analyze the characteristics of crop reflection, radiation, or absorption of electromagnetic energy in different spectral bands, establish models related to crop yield, and infer crop growth and yield [4; 5]. To achieve near real-time crop yield prediction based on remote sensing technology, it is necessary to quickly obtain parameter data for high-precision and wide-area models. How to efficiently obtain the parameters for a wide-range yield model based on remote sensing data has become an urgent and essential issue to be addressed. A large number of yield estimation studies, especially winter wheat yield, have been conducted based on remote sensing technology, such as empirical statistical models [6], light use efficiency models [7], crop models [8], and machine learning models [9; 10]. Light use efficiency (LUE) models have been shown to accurately and widely estimate winter wheat yield [7; 11]. The fraction of absorbed photosynthetically active radiation (_f_PAR) is an essential variable in the calculation of vegetation gross primary productivity (GPP) based on LUE models, and it is one of the important parameters in ecological balance and carbon sink estimation [12]. _f_PAR is defined as the ratio of photosynthetically active radiation (PAR) absorbed by crops or vegetation cover to the total incident photosynthetically active radiation and represents the ability of vegetation to perform photosynthesis, participate in carbon cycling, and maintain energy balance. In addition, _f_PAR is an important parameter in many ecosystem productivity models, crop yield estimation models, and gross primary productivity estimates [13]. Rapid and accurate estimation of _f_PAR can improve the accuracy of crop yield estimates, which is important for crop management and food security. Current methods for obtaining _f_PAR can be categorized into four main approaches: (1) Ground-based measurements, where instruments such as Sunscan and AccuPAR are used to measure multiple canopy incidence, canopy reflectance, ground incidence and ground reflectance at measurement points to calculate _f_PAR; (2) Estimation of vegetation indices using remote sensing, which indirectly calculates _f_PAR by establishing linear or non-linear relationships between vegetation indices and _f_PAR [14; 15]; (3) Physical models, such as the porosity method and three-dimensional radiation transfer models, which estimate _f_PAR by simulating the transmission and absorption of light in vegetation based on the spectral characteristics of the vegetation and environmental factors. Often LAI and _f_PAR are inverted together, as LAI estimation also uses radiation transfer models [16; 17]; (4) Machine learning, which involves constructing radiation transfer models between _f_PAR and remote sensing data using methods such as remote sensing data and neural networks. Ground-based measurements are laborious and time-consuming at large scales. Machine learning methods require a large number of training samples, and the transferability of the trained models has yet to be verified [18; 19].