In 1960, R.E. Kalman published his famous paper describing a recursive solution, the Kalman filter, to the discrete-data linear filtering problem. In the following decades, thanks to the continuous progress of numerical computing, as well as the increasing demand for weather prediction, target tracking, and many other problems, the Kalman filter has gradually become one of the most important tools in science and engineering. With the continuous improvement of its theory, the Kalman filter and its derivative algorithms have become one of the core algorithms in optimal estimation. This paper attempts to systematically collect and sort out the basic principles of the Kalman filter and some of its important derivative algorithms (mainly including the Extended Kalman filter (EKF), the Unscented Kalman filter (UKF), the Ensemble Kalman filter (EnKF)), as well as the scope of their application, and also to compare their advantages and limitations. In addition, because there are a large number of applications based on the Kalman filter in data assimilation, this paper also provides examples and classifies the applications of both the Kalman filter and its derivative algorithms in the field of data assimilation.

Ultraviolet B (UV-B) radiation plays a multifaceted role in human health, inducing DNA damage and representing the primary source of vitamin D for most humans; however, current U.S. UV exposure models are limited in spatial, temporal, and/or spectral resolution. Area-to-point (ATP) residual kriging is a geostatistical method that can be used to create a spatiotemporal exposure model by downscaling from an area- to point-level spatial resolution using fine-scale ancillary data. A stratified ATP residual kriging approach was used to predict average July noon-time erythemal UV (UVEry) (mW/m2) biennially from 1998 to 2012 by downscaling National Aeronautics and Space Administration (NASA) Total Ozone Mapping Spectrometer (TOMS) and Ozone Monitoring Instrument (OMI) gridded remote sensing images to a 1 km spatial resolution. Ancillary data were incorporated in random intercept linear mixed-effects regression models. Modeling was performed separately within nine U.S. regions to satisfy stationarity and account for locally varying associations between UVEry and predictors. Cross-validation was used to compare ATP residual kriging models and NASA grids to UV-B Monitoring and Research Program (UVMRP) measurements (gold standard). Predictors included in the final regional models included surface albedo, aerosol optical depth (AOD), cloud cover, dew point, elevation, latitude, ozone, surface incoming shortwave flux, sulfur dioxide (SO2), year, and interactions between year and surface albedo, AOD, cloud cover, dew point, elevation, latitude, and SO2. ATP residual kriging models more accurately estimated UVEry at UVMRP monitoring stations on average compared to NASA grids across the contiguous U.S. (average mean absolute error [MAE] for ATP, NASA: 15.8, 20.3; average root mean square error [RMSE]: 21.3, 25.5). ATP residual kriging was associated with positive percent relative improvements in MAE (0.6–31.5%) and RMSE (3.6–29.4%) across all regions compared to NASA grids. ATP residual kriging incorporating fine-scale spatial predictors can provide more accurate, high-resolution UVEry estimates compared to using NASA grids and can be used in epidemiologic studies examining the health effects of ambient UV.

Forest is the largest vegetation carbon pool in the global terrestrial ecosystem. The spatial distribution and change of forest biomass are of importance to reveal the surface spatial variation and driving factors, to analyze and evaluate forest productivity, and to evaluate ecological function of forest. In this study, broad-leaved forests located in a typical state nature reserve in northern subtropics were selected as the study area. Based on ground survey data and high-resolution remote sensing images, three machine learning models were used to identify the best remote sensing quantitative inversion model of forest biomass. The biomass of broad-leaved forest with 30-m resolution in the study area from 1998 to 2016 was estimated by using the best model about every two years. With the estimated biomass, multiple leading factors to cause biomass temporal change were then identified from dozens of remote sensing factors by investigating their nonlinear correlations. Our results showed that the artificial neural network (ANN) model was the best (R² = 0.8742) among the three, and its accuracy was also much higher than that of the traditional linear or nonlinear models. The mean biomass of the broad-leaved forest in the study area from 1998 to 2016 ranged from 90 to 145 Mg ha⁻¹, showing an obvious temporal variation. Instead of biomass, biomass change (BC) was studied further in this research. Significant correlations were found between BC in broad-leaved forest and three climate factors, including average daily maximum surface temperature, maximum precipitation, and maximum mean temperature. It was also found that BC has a strong correlation with the biomass at the previous time (i.e., two years ago). Those quantitative correlations were used to construct a linear model of BC with high accuracy (R² = 0.8873), providing a new way to estimate the biomass change of two years later based on the observations of current biomass and the three climate factors.

Current multimodal learning in smart feature extraction and classification has reshaped the landscape of remote sensing. The recent developments in smart feature extraction mainly rely on different machine learning and data mining algorithms as powerful classifiers to improve prediction accuracy. This article presents an innovative ensemble learning algorithm for integrated data and classifier fusion via higher order singular value decomposition (IDCF-HOSVD). Based on the fused data, different analytical, semiempirical, and empirical classifiers can be selected and applied to perform information retrieval that can be further synergized via a tensor flow based feature extraction scheme over the classifier space. When preserving core fused image patterns via HOSVD, the final step of IDCF-HOSVD helps rank the contributions from different classifiers via nonlinear correlation information entropy. Practical implementation of the IDCF-HOSVD algorithm was assessed through its application to map the seasonal water quality conditions in Lake Nicaragua, Central America.