In the Global Navigation Satellite System, ionospheric delay is a significant source of error. The magnitude of the ionosphere total electron content (TEC) directly impacts the magnitude of the ionospheric delay. Correcting the ionospheric delay and improving the accuracy of satellite navigation positioning can both benefit from the accurate modeling and forecasting of ionospheric TEC. The majority of current ionospheric TEC forecasting research only considers the temporal or spatial dimensions, ignoring the ionospheric TEC’s spatial and temporal autocorrelation. Therefore, we constructed a spatiotemporal network model with two modules: (i) global spatiotemporal characteristics extraction via forwarding spatiotemporal characteristics transfer and (ii) regional spatiotemporal characteristics correction via reverse spatiotemporal characteristics transfer. This model can realize the complementarity of TEC global spatiotemporal characteristics and regional spatiotemporal characteristics. It also ensures that the global spatiotemporal characteristics of the global ionospheric TEC are transferred to each other in both temporal and spatial domains at the same time. The spatiotemporal network model thus achieves a spatiotemporal prediction of global ionospheric TEC. The Huber loss function is also used to suppress the gross error and noise in the ionospheric TEC data to improve the forecasting accuracy of global ionospheric TEC. We compare the results of the spatiotemporal network model with the Center for Orbit Determination in Europe (CODE), the convolutional Long Short-Term Memory (convLSTM) model and the Predictive Recurrent Neural Network (PredRNN) model for one-day forecasts of global ionospheric TEC under different conditions of time and solar activity, respectively. With internal data validation, the average root mean square error (RMSE) of our proposed algorithm increased by 21.19, 15.75, and 9.67%, respectively, during the maximum solar activity period. During the minimum solar activity period, the RMSE improved by 38.69, 38.02, and 13.54%, respectively. This algorithm can effectively be applied to ionospheric delay error correction and can improve the accuracy of satellite navigation and positioning.

The study of digital elevation model (DEM) super-resolution reconstruction algorithms has solved the problem of the need for high-resolution DEMs. However, the DEM super-resolution reconstruction algorithm itself is an inverse problem, and making full use of the DEM a priori information is an effective way to solve this problem. In our work, a new DEM super-resolution reconstruction method is proposed based on the complementary relationship between internally learned super-resolution reconstruction methods and externally learned super-resolution reconstruction methods. The method is based on the presence of a large amount of repetitive information within the DEM. Using an internal learning approach to learn the internal prior of the DEM, a low-resolution dataset of the DEM rich in detailed features is generated, and based on this, the training of a constrained external learning network is constructed for the discrepancy data pair. Finally, it introduces residual learning based on the network model to accelerate the operation rate of the network and to solve the model degradation problem brought about by the deepening of the network. This enables the better transfer of learned detailed features in deeper network mappings, which in turn ensures accurate learning of the DEM prior information. The network utilizes the internal prior of the specific DEM as well as the external prior of the DEM dataset and achieves better super-resolution reconstruction results in the experimental results. The results of super-resolution reconstruction by the Bicubic method, Super-Resolution Convolutional Neural Networks (SRCNN), very deep convolutional networks (VDSR), ”Zero-Shot” Super-Resolution networks (ZSSR) and the new method in this paper were compared, and the average RMSE of the super-resolution reconstruction results of the five methods were 8.48 m, 8.30 m, 8.09 m, 7.02 m and 6.65 m, respectively. The mean elevation error at the same resolution is 21.6% better than that of the Bicubic method, 19.9% better than that of the SRCNN, 17.8% better than that of the VDSR method, and 5.3% better than that of the ZSSR method.

The climate anomaly in the Amazon River basin (ARB) has a very important influence on global climate change and has always been the focus of scientists from all over the world. To fill the 11-month data gap between Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions, we fused the TWSC results from six GRACE solutions by using the generalized three-cornered hat and the least square method to improve the reliability of TWSC results, and then combined Swarm data to construct an uninterrupted long time series of a TWSC-based drought index (GRACE/Swarm-DSI). The drought index was used to detect and characterize the drought events in the ARB between 2003 and 2020. The results show that GRACE/Swarm-DSI has a strong correlation with Self-Calibrating Palmer Drought Severity Index (SCPDSI) (0.6345), Standardized Precipitation Evapotranspiration Index-3 (SPEI-3) (0.5411), SPEI-6 (0.6377) and SPEI-12 (0.6820), and the Nash–Sutcliffe efficiency between GRACE/Swarm-DSI and the above four drought indices are 0.3348, 0.2786, 0.4044 and 0.4627, respectively. Eleven drought events were identified in the ARB during the study period, and the 2005, 2010 and 2016 droughts are the most severe and the longest. The correlation between GRACE/Swarm-DSI and precipitation (PPT) (the correlation coefficient is 0.55 with a 2-month delay) is higher than that of evapotranspiration (ET) (the correlation coefficient is −0.18 with a 12-month delay). It explains that less PPT is the main cause of drought events in the ARB. The influence of PPT is greater in the plains than the one in the mountains and the response time of GRACE/Swarm-DSI to PPT is 1~2 months in most regions. Our results provide a certain reference for the hydrological application of the Swarm model in filling the gap between GRACE and GRACE-FO missions.

The precise positioning of dynamic and static objects such as vehicles and pedestrians is a key technology. A global navigation satellite system signal is the primary signal source required to achieve precise positioning, and the optimal estimation method used in precise positioning is Kalman filtering (KF). Standard KF can only achieve optimal estimation results under the conditions that the mathematical model has been determined and the noise characteristics are known. However, when there are measurement outliers and prior noise information deviations, the accuracy of KF cannot be guaranteed. To effectively solve the above problems, a combined adaptive robust Kalman filter (CARKF) algorithm is proposed. First, the influence of measurement outliers on KF accuracy is resisted using the robust Kalman filter method. Then, the influence of an anomalous innovation on its autocorrelation sequence and cross-correlation sequence is resisted by the robust estimator for correlated observations based on the IGGIII method, to ensure the correct estimation of the correlation function sequence of the filtered innovation statistics. Finally, the autocovariance least-squares method is used to eliminate the coupling effect between noise covariances and accurately estimate the unknown noise covariance information. Moreover, an iterative strategy is adopted to eliminate the effect of errors caused by prior noise covariance deviations. The results of the three experiments show that the CARKF method can not only effectively resist the influence of measurement outliers on filtering accuracy and noise covariance valuation but also overcome the influence of errors caused by prior noise deviations and accurately simultaneously estimate two kinds of unknown noise covariance information.

Atmospheric refraction is an important factor that affects the positioning accuracy of optical high-resolution satellite imaging. Current calculation methods do not consider regional change characteristics in the atmosphere; the atmospheric division model is rough and does not conform to reality. This article studies atmospheric refraction in optical remote sensing satellite observations, provides a formula for calculating the strict refraction of a multilayer atmosphere, and shows a new method for calculating atmospheric refraction error. We use a ray-tracing method to calculate the light propagation path in the atmosphere and continuously layer the atmosphere according to the height difference of 100 m. Different from general calculation methods, we prove that a regional atmospheric model can calculate the atmospheric refraction index more accurately than using the empirical model. As the off-nadir angle gradually increases, the calculation results in this article are better than the current commonly used methods. We use WorldView-2 images of the Qinghai–Tibet Plateau region in China for the experiments. When the off-nadir angle is less than 32°, the positioning accuracy improves by 6–47%. Compared with the standard atmospheric model, the regional atmospheric model improves positioning accuracy by 2–18%. This method reflects the continuous variation in the atmospheric refractive index with the vertical distribution of the atmosphere and amended regional meteorological conditions. Model errors caused by overly simple atmospheric division are avoided, andthe positioning accuracy of optical remote sensing images is increased.