Gravity Recovery and Climate Experiment (GRACE) satellites can effectively monitor terrestrial water storage (TWS) changes in large-scale areas. However, due to the coarse resolution of GRACE products, there is still a large number of deficiencies that need to be considered when investigating TWS changes in small-scale areas. Hence, it is necessary to downscale the GRACE products with a coarse resolution. First, in order to solve this problem, the present study employs modeling windows of different sizes (Window Size, WS) combined with multiple machine learning algorithms to develop a new machine learning spatial downscaling method (MLSDM) in the spatial dimension. Second, The MLSDM is used to improve the spatial resolution of GRACE observations from 0.5° to 0.25°, which is applied to Guantao County. The present study has verified the downscaling accuracy of the model developed through the combination of WS3, WS5, WS7, and WS9 and jointed with Random Forest (RF), Extra Tree Regressor (ETR), Adaptive Boosting Regressor (ABR), and Gradient Boosting Regressor (GBR) algorithms. The analysis shows that the accuracy of each combined model is improved after adding the residuals to the high-resolution downscaled results. In each modeling window, the accuracy of RF is better than that of ETR, ABR, and GBR. Additionally, compared to the changes in the TWS time series that are derived by the model before and after downscaling, the results indicate that the downscaling accuracy of WS5 is slightly more superior compared to that of WS3, WS7, and WS9. Third, the spatial resolution of the GRACE data was increased from 0.5° to 0.05° by integrating the WS5 and RF algorithm. The results are as follows: (1) The TWS (GWS) changes before and after downscaling are consistent, decreasing at −20.86 mm/yr and −21.79 mm/yr (−14.53 mm/yr and −15.46 mm/yr), respectively, and the Nash–Sutcliffe efficiency coefficient (NSE) and correlation coefficient (CC) values of both are above 0.99 (0.98). (2) The CC between the 80% deep groundwater well data and the downscaled GWS changes are above 0.70. Overall, the MLSDM can not only effectively improve the spatial resolution of GRACE products but also can preserve the spatial distribution of the original signal, which can provide a reference scheme for research focusing on the downscaling of GRACE products.

The launch of GRACE satellites has provided a new avenue for studying the terrestrial water storage anomalies (TWSA) with unprecedented accuracy. However, the coarse spatial resolution greatly limits its application in hydrology researches on local scales. To overcome this limitation, this study develops a machine learning-based fusion model to obtain high-resolution (0.25°) groundwater level anomalies (GWLA) by integrating GRACE observations in the North China Plain. Specifically, the fusion model consists of three modules, namely the downscaling module, the data fusion module, and the prediction module, respectively. In terms of the downscaling module, the GRACE-Noah model outperforms traditional data-driven models (multiple linear regression and gradient boosting decision tree (GBDT)) with the correlation coefficient (CC) values from 0.24 to 0.78. With respect to the data fusion module, the groundwater level from 12 monitoring wells is incorporated with climate variables (precipitation, runoff, and evapotranspiration) using the GBDT algorithm, achieving satisfactory performance (mean values: CC: 0.97, RMSE: 1.10 m, and MAE: 0.87 m). By merging the downscaled TWSA and fused groundwater level based on the GBDT algorithm, the prediction module can predict the water level in specified pixels. The predicted groundwater level is validated against 6 in-situ groundwater level data sets in the study area. Compare to the downscaling module, there is a significant improvement in terms of CC metrics, on average, from 0.43 to 0.71. This study provides a feasible and accurate fusion model for downscaling GRACE observations and predicting groundwater level with improved accuracy.

To improve the reliability of the Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) feature extraction, this paper uses a correlation coefficient combined with the traditional variational mode decomposition (VMD), proposing a new correlation variational mode decomposition (CVMD). In contrast to previous studies, the CVMD denoises the sequences before feature extraction and it is the first time that be used in the GPS and GRACE. First, the correlation between the intrinsic mode function (IMF) and the original sequence is obtained to denoise the original sequence. Moreover, the algorithm reuses the VMD to obtain the IMF components with different frequencies. Then the Lomb Scargle (L-S) spectral analysis and energy density are used to obtain the trend-, seasonal, and residual items. Second, the features of the GPS and GRACE time series are extracted based on the CVMD and multidimensional ensemble empirical mode decomposition (MEEMD) to verify the availability of the CVMD. The results indicate that the CVMD is more superior to the MEEMD in feature extraction. Third, the CVMD is used to extract the trend- and seasonal terms of GPS and GRACE in the North China Plain (NCP). The conclusions are as follows: (1) the seasonal items of GRACE are used to correct the GPS sequences, and the average reduction of the weighted root mean square (WRMS) of each GPS station is 0.69, which demonstrates a strong consistency between the seasonal terms of the GPS sequence and GRACE sequence; (2) during 2003-2015, the mean slope of vertical displacements is 0.20 ± 0.07 mm / yr, and the uplift rate increases substantially (1.66 ± 0.62 mm / yr) after 2013. Then, the temporal and spatial relationship between rainfall and crustal load-deformation in the NCP is analyzed, and it is found that the crustal load-deformation is primarily related to rainfall, while human activities play a leading role in the southwestern regions where agricultural irrigation is relatively strong.

A pulse phase estimation of an X-ray pulsar with the aid of vehicle orbital dynamics is proposed. The original continue-time X-ray pulsar signal model is modified to be a term of vehicle position and velocity varying with time, and a modified definition of pulse time of arrival is given. The modified signal model is further linearized around the predicted position and velocity of the vehicle to the second order. The initial phase and the coefficients of the extended signal model can be estimated by maximum likelihood estimator. Some simulations are performed to verify the method and show the method has robustness to the initial error within initial state of the vehicle and is capable of handling the phase-estimation problem for pulsars with low fluxes.

In order to enhance the independent viability of high-orbit satellites, an X-ray pulsar-based navigation (XNAV)/celestial navigation system (CNS) integrated navigation method is proposed. An improved kinematic and static filter is derived to fulfil data fusion that can obtain an optimal estimation for global use. In the filter, unscented transformation is used to reduce linearization error, and the technique of separate-bias is used to reduce the impacts of systematic errors in XNAV measurements. The results of simulations have shown that the proposed navigation system can reach a positioning accuracy of less than 100 m, an improved performance over separate XNAV and CNS.