A Neural network (NN) is a promising tool for the tomographic inversion of the ionosphere. However, existing research has adopted an unbalanced cost function for training purposes and a preset image for constraint purposes, resulting in the output image being dominated by measurements. To address these problems, we proposed an NN-based tomographic model with a balance cost function and a dynamic correction process (BCDC) for ionosphere inversion. The cost function is composed of two balance terms corresponding to the measurements and the selected constraints, respectively. The produced image in the forward process of the NN is corrected dynamically by fitting each vertical profile with orthogonal basis functions (EOFs) and the Chapman function and then by smoothing the voxels of each layer with a moving window approach horizontally. The corrected image is then used to calculate the slant total electron content (STEC) parameter, which is further translated into the term of the cost for the vertical and horizontal constraints. Experiments were carried out to validate the BCDC method and compared with a recently developed tomographic method and the international reference ionosphere (IRI) model. Results show that the parameters derived from the BCDC model demonstrate good consistency with the observations. Comparing with the reference methods, the BCDC method performs better in the validations of vertical profiles, F₂ layer peak density (N_mF₂), STEC parameter and vertical total electron content map. Further analysis also shows that a balance cost function is of benefit to achieve an image of better quality.

Ionospheric tomography is a popular technique for ionosphere imaging. Though dozens of models have been proposed in the past decades, their inflexibilities in constraints, dependencies on background and lacks of constraint on dark voxels remain headache. Several means were taken in our developed model, named EOF-based multiscale tomographic model (EMST). In EMST, a series of sub-models characterized by different scales are established. A new scale is continuously added to the previous model to capture the structures of different scales by taking each EOF as a new scale. The captured structures are then consolidated by using them to restrain the subsequent models. This ensures a rigid but also a flexible model. Then, the background dependency problem is alleviated by an initial model that can give a rough estimation on the ionosphere without any background. Finally, the VTEC map is used to additionally restrain the voxels, especially the dark voxels, in EMST. A few tests were conducted to validate our model, compare it with the Frazaneh model, and discuss the means. Results show that our model outperforms the reference model in vertical profile, F2 layer peak density (NmF2), slant total electron content (STEC) and vertical total electron content (VTEC) comparisons. Its average improvements over the Farzaneh model reach to 4.93%, 28.69% and 40.89% in NmF2, STEC and VTEC, respectively. Besides, evidences also show that the EMST model is less dominated by the prior model and can be benefited from the multiscale strategy and the VTEC constraint.

Support for region queries is crucial in geographic information systems, which process exact queries through spatial indexing to filter features and subsequently refine the selection. Although the filtering step has been extensively studied, the refinement step has received little attention. This research builds upon the QR-tree index, which decomposes space into hierarchical grids, registers features to the grids, and builds an R-tree for each grid, to develop a new QRB-tree index with two levels of optimization. In the first level, a bucket is introduced in every grid in the QR-tree index to accelerate the loading and search steps of a query region for the grids within the query region. In the second level, the number of candidate features to be eliminated is reduced by limiting the features to those registered to the grids covering the corners of the query region. Subsequently, an approach for determining the maximal grid level, which significantly affects the performance of the QR-tree index, is proposed. Direct comparisons of time costs with the QR-tree index and geohash index show that the QRB-tree index outperforms the other two approaches for rough queries in large query regions and exact queries in all cases.