When ordinary principal component analysis (PCA) is employed to analyze the position time series of a regional GNSS station network, the GNSS time series are assumed to be homogeneous, and the missing data in the time series must be restored beforehand. To directly process incomplete and heterogeneous GNSS position time series, we develop the extended PCA (EPCA) and weighted EPCA approaches to solving for the missing values based on the best low-rank approximation in the spatiotemporal domain. The proposed approaches are used to process the real GNSS position time series of 24 stations in North China spanning 2011 to 2019 and successfully extract the common mode errors (CMEs). The proposed approaches are compared with modified PCA (MPCA) and weighted MPCA, in which an additional optimization criterion needs to be introduced in the frequency domain. The results show that EPCA can extract more CMEs than MPCA for both the unweighted and weighted cases. Consequently, EPCA outperforms MPCA in reducing noise and improving the accuracy of site velocity estimates. Repeated simulation experiments show that the CMEs extracted by EPCA are closer to the simulated true values than those extracted by MPCA. When the formal errors of the time series are considered, both weighted EPCA and weighted MPCA outperform their unweighted counterparts, and the former outperforms the latter. In addition, EPCA is computationally more efficient than MPCA since fewer unknowns need to be estimated.

The weighting method of the traditional fixed combination forecasting model is the only criterion considered to improve accuracy, which has some limitations. In order to improve the comprehensive prediction performance of the combined model, hierarchical structure of the combined model by selecting some parameters which can reflect the performance of the model (including prediction accuracy, robustness, sensitivity, and the amount of fitting data) is established and a kind of multiple factor and multiple criteria weighting method of combination forecasting model is put forward. Based on SVR model, GM (1, 1) model, and ARIMA model, a combination forecasting model based on Improved Analytic Hierarchy Process (AHP) is constructed and applied to a foundation pit. The experimental results show that the combined forecasting model based on improved AHP are better than the single model in precision and robustness; it also has good effect in sensitivity, which has more comprehensive prediction performance than the single models, and has good engineering and practical value.