# A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series
## 1 Introduction  
Land surface temperature (LST) is one of the most important physical parameters in surface-atmosphere interactions, and is of great importance in many related disciplines such as global environmental change and ecological evolution [1]. As a dynamic thermal equilibrium parameter, the land surface temperature is impacted by the land surface energy balance (SEB) process. It is a dynamically changing time series parameter. In addition, land surface temperatures that are obtained by remote sensing inversion are transient samples that can have temporal or spatial gaps or can be unstable as a result of the effects of factors such as the two-way reflection of clouds and land objects [2, 3]. Additionally, the distribution of an LST obtained by remote sensing inversion in land SEB studies is often inaccurate due to factors such as the indirectness and morbidity of the remote sensinginversion data. To overcome the problems of missing and low-quality data, Moderate Resolution Imaging Spectroradiometer (MODIS) products deliver level three 10-day and monthly synthetic data. However, although applying interpolation and iteration to such data solves the problem of temporal and spatial gaps in the data to some degree, missing and inaccurate data are still severe problems that affect studies of regional land surface energy parameters, directly affecting the accuracy and effects of subsequent land surface process modeling [4]. Data assimilation is a method in which new observational data are merged during the dynamic execution of a numerical model based on the data's temporospatial distribution as well as the data's observational and background errors [5; 6; 7]. The core of land surface data assimilation is to merge direct and indirect data from difference sources and different resolutions in the dynamic framework of land surface process modeling to accurately and consistently estimate each component of the hydrological and energy cycles of the land surface. By integrating surface models and satellite data using data assimilation, [PERSON] established a framework for the assimilation of multisource remote sensing data combined with the simultaneous estimation of states and parameters to provide accurate estimates of soil moisture on the Tibetan Plateau, providing a practical method for improving simulation accuracy when determining soil moisture [8]. [PERSON] used above-ground biomass (AGB) from Zhejiang Province to assimilate MODIS LAI (leaf area index) products, which resulted in the assimilated LAI spatio-temporal data being much more accurate compared to the observed LAI, and the changes in the assimilated LAI time series were consistent with the seasonal dynamics of bamboo forest growth [9]. As research regarding land surface data assimilation continues to become more in depth, optimization algorithms that are suitable for land surface data assimilation are being developed rapidly. Since the 1960s, the Kalman filter algorithm has been widely used in the fields of Global Positioning System (GPS) navigation, aircraft orbit correction, human-robot interaction, radar systems and missile tracking, and deformation monitoring [10; 11; 12; 13; 14]. Recently, it has been applied to practical studies, such as those on sensor data merging and microeconomics [15; 16]. In addition to applications in industrial and socio-economical areas, the Kalman filter has been used in meteorology and Earth sciences. [PERSON] et al. and [PERSON] introduced ground meteorological observations and meteorological satellite data and assimilated them using the Kalman filter. The reconstructed time series of solar radiation exhibited greater consistency with the in situ data set than with the time series before the optimization [17; 18]. [PERSON] et al. developed a data assimilation framework using Kalman filtering to simultaneously assimilate satellite soil moisture retrievals from the Soil Moisture Active Passive (SMAP) and Soil Moisture and Ocean Salinity (SMOS) missions using the Australian Water Resources Assessment Landscape model (AWRA-L).