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The volatility of the cumulative displacement of landslides is related to the influence of external factors. To improve the prediction of nonlinear changes in landslide displacement caused by external influences, a new combined forecasting model of landslide displacement has been proposed. Variational modal decomposition (VMD) was used to obtain the trend and fluctuation sequences of the original sequence of landslide displacement. First, we established a stacked long short time memory (LSTM) network model and introduced rainfall and reservoir water levels as influencing factors to predict the fluctuation sequence; next, we used a threshold autoregressive (TAR) model to predict the trend sequence, following which the trend and fluctuation prediction sequence were superimposed to obtain the cumulative predicted displacement of the landslide. Finally, the VMD-stacked LSTM-TAR combination model based on the variational modal decomposition, stacked long short time memory network, and a threshold autoregressive model was built. Taking the landslide of Baishuihe in the Three Gorges Reservoir area as an example, through comparison with the prediction results of the VMD-recurrent neural network-TAR, VMD-back propagation neural network-TAR, and VMD-LSTM-TAR, the proposed combined prediction model was noted to have high accuracy, and it provided a novel approach for the prediction of volatile landslide displacement.

Time-differenced carrier phase velocity estimations (TDCPVE) and Doppler velocity estimations (DVE) are two commonly used methods for precise velocity estimation with a stand-alone GPS receiver. As TDCPVE require a minimum of four satellites for parameter estimation, the time-differenced velocity estimation (TDVE) model was developed by combining the TDCPVE model and time-differenced pseudo-range velocity estimation model. A limitation of the TDVE is that it can show reduced solution availability, particularly during harsh conditions. DVE model theory is stricter than that of the TDVE model, which yields more reliability when vehicle maneuverability is strong. However, its accuracy is low due to the low precision of Doppler observations. Nevertheless, the advantages and disadvantages of the TDVE and DVE are complementary. This study presents a TD–DVE method by combining the two models. This method can achieve improved performance by fully using all useful information contained in the GPS and Doppler observations. Static and dynamic data were used to verify and analyze the performance of the TD–DVE. The results show that the accuracy of the TD–DVE was improved compared with the DVE. Compared with the TDVE method, TD–DVE has a much higher solution rate at poor observation conditions and improved accuracy during changing vehicle dynamic conditions. Overall, the TD–DVE model enhances the robustness of the individual velocity estimation methods and improves usability.

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