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Soil moisture time series data are usually nonlinear in nature and are influenced by multiple environmental factors. The traditional autoregressive integrated moving average (ARIMA) method has high prediction accuracy but is only suitable for linear problems and only predicts data with a single column of time series. The gated recurrent unit neural network (GRU) can achieve the prediction of time series and nonlinear multivariate data, but a single nonlinear model does not yield optimal results. Therefore, a hybrid time series prediction model, BAG, combining linear and nonlinear characteristics of soil moisture, is proposed in this paper to achieve the identification process of linear and nonlinear relationships in soil moisture data so as to improve the accuracy of prediction results. In BAG, block Hankel tensor ARIMA (BHT-ARIMA) and GRU are selected to extract the linear and nonlinear features of soil moisture data, respectively. BHT-ARIMA is applied to predict the linear part of the soil moisture, and GRU is used to predict the residual series, which is the nonlinear part, and the superposition of the two predicted results is the final prediction result. The performance of the proposed model on five real datasets was evaluated. The results of the experiments show that BAG has a higher prediction accuracy compared with other prediction models for different amounts of data and different numbers of environmental factors. Full article

This study aims to use remote sensing (RS) time-series data to explore the intrinsic relationship between crop growth and yield formation at different fertility stages and construct a high-precision winter wheat yield estimation model applicable to short time-series RS data. Sentinel-2 images were acquired in this study at six key phenological stages (rejuvenation stage, rising stage, jointing stage, heading stage, filling stage, filling-maturity stage) of winter wheat growth, and various vegetation indexes (VIs) at different fertility stages were calculated. Based on the characteristics of yield data continuity, the RReliefF algorithm was introduced to filter the optimal vegetation index combinations suitable for the yield estimation of winter wheat for all fertility stages. The Absolutely Objective Improved Analytic Hierarchy Process (AOIAHP) was innovatively proposed to determine the proportional contribution of crop growth to yield formation in six different phenological stages. The selected VIs consisting of MTCI(RE2), EVI, REP, MTCI(RE1), RECI(RE1), NDVI(RE1), NDVI(RE3), NDVI(RE2), NDVI, and MSAVI were then fused with the weights of different fertility periods to obtain time-series weighted data. For the characteristics of short time length and a small number of sequences of RS time-series data in yield estimation, this study applied the multiplexed delayed embedding transformation (MDT) technique to realize the data augmentation of the original short time series. Tucker decomposition was performed on the block Hankel tensor (BHT) obtained after MDT enhancement, and the core tensor was extracted while preserving the intrinsic connection of the time-series data. Finally, the resulting multidimensional core tensor was trained with the Autoregressive Integrated Moving Average (ARIMA) model to obtain the BHT-ARIMA model for wheat yield estimation. Compared to the performance of the BHT-ARIMA model with unweighted time-series data as input, the weighted time-series input significantly improves yield estimation accuracy. The coefficients of determination (R²) were improved from 0.325 to 0.583. The root mean square error (RMSE) decreased from 492.990 to 323.637 kg/ha, the mean absolute error (MAE) dropped from 350.625 to 255.954, and the mean absolute percentage error (MAPE) decreased from 4.332% to 3.186%. Besides, BHT-ARMA and BHT-CNN models were also used to compare with BHT-ARIMA. The results indicated that the BHT-ARIMA model still had the best yield prediction accuracy. The proposed method of this study will provide fast and accurate guidance for crop yield estimation and will be of great value for the processing and application of time-series RS data. Full article