Hexagonal discrete global grid systems are multi-resolution frameworks for earth data and have attracted much attention in research towards the next generation of geographic information system. Each resolution of the framework divides the earth into a hexagonal grid of cells and cell codes are used instead of Cartesian coordinates to organize and query data. Aperture (the ratio of cells between resolutions) 4 systems have structural advantages compared with aperture 3 and 7, but haven’t been fully developed. In this manuscript, we examine the aperture 4 hexagon hierarchy on uniform tiles (HHUT) and modify the coding method. We propose two HHUT-based cell navigation methods, one for regular and the other for irregular areas. We demonstrate the utility and high efficiency of the proposed methods in two applications. Results show that the proposed method for an irregular area is on average 400 times faster than DGGRID, the conventional library. The proposed method for a regular area is on average seven times faster than the hexagon lattice quad tree method and approaches that of H3. The modified coding and novel cell navigation methods proposed here indicate high efficiency, superior data organization and broad application prospects.

Hexagonal discrete global grid systems are the preferred data models supporting multisource geospatial information fusion. Related research has aroused widespread concern in the academic community, and hierarchical indexing algorithms are one of the main research focuses. In this paper, we propose an algorithm for indexing the cell of a ringed spatial area based on a hexagonal lattice quad-tree (HLQT) structure and the indexing characteristics. First, we design a single-resolution indexing algorithm in which indexing starts from the initial quad tree and expands ring by ring using coding operations, and a quad-tree structure is applied to accelerate this process. Second, the hierarchical indexing algorithm is implemented based on single-resolution indexing, and a pyramid hierarchical model is established. Finally, we perform comparison experiments with existing algorithms. The results of the experiments indicate that the single-level indexing efficiency of the proposed algorithm is approximately twice that of the traditional method and that the hierarchical indexing efficiency is approximately 67 times that of the traditional method. These findings verify the feasibility and superiority of the algorithm proposed in this paper.

Discrete global grid systems (DGGSs) are an emerging multiresolution 3D model used to integrate and analyze big earth data. The characteristic of multiresolution is usually realized by hierarchically subdividing cells on the sphere using certain refinement. This paper introduces mixed aperture three- and four- icosahedral hexagonal DGGSs using two types of refinement, the various combinations of which can provide more resolutions compared with pure aperture hexagonal DGGSs and can flexibly design the aperture sequence according to the target resolutions. A general hierarchy-based indexing method is first designed, and related indexing arithmetics and algorithm are developed based on the indexing method. Then, the grid structure on the surface of the icosahedron is described and by projection spherical grids are obtained. Experiments show that the proposed scheme is superior to pure aperture schemes in choosing grid resolutions and can reduce the data volume by 38.5% in representing 1-km resolution raster dataset; using the proposed indexing arithmetics to replace spherical geometry operations in generating discrete spherical vector lines based on hexagonal cells can improve the generation efficiency.

Discrete Global Grid System (DGGS) is a new multi-resolution geospatial data modeling and processing scheme for the digital earth. The icosahedron is commonly regarded as an ideal polyhedron for constructing DGGSs with small distortions; however, the shape of its face is triangular, making it difficult to incorporate the matrix structure used for geospatial data storage and parallel computing. To overcome this limitation, this study utilizes the rhombic triacontahedron (RT) as the basic polyhedron to construct DGGSs. An equal-area projection between the surface of RT and the sphere is developed and used to design a grid-generation algorithm for the aperture 4 hexagonal DGGS based on RT. Compared with the equal-area DGGS based on the icosahedron, the proposed scheme results in smaller angular projection distortions, with the mean and standard deviation decreasing by 41.6% and 30.9%, respectively. The grid cells of the RT DGGS also achieve more optimized geometric characteristics in shape compactness, length deviation, and angle deviation than those in the icosahedron DGGS. Additionally, the cross-surface computation efficiency provides advantages in code conversion to latitude and longitude and proximity queries. Furthermore, the use of RT offers a new and better framework within the context of DGGS research and application.

Vectors are a key type of geospatial data, and their discretization, which involves solving the problem of generating a discrete line, is particularly important. In this study, we propose a method for constructing a discrete line mathematical model for a triangular grid based on a “weak duality” hexagonal grid, to overcome the drawbacks of existing discrete line generation algorithms for a triangular grid. First, a weak duality relationship between triangular and hexagonal grids is explored. Second, an equivalent triangular grid model is established based on the hexagonal grid, using this weak duality relationship. Third, the two-dimensional discrete line model is solved by transforming it into a one-dimensional optimal wandering path model. Finally, we design and implement the dimensionality reduction generation algorithm for a discrete line in a triangular grid. The results of our comparative experiment indicate that the proposed algorithm has a computation speed that is approximately 10 times that of similar existing algorithms; in addition, it has better fitting effectiveness. Our proposed algorithm has broad applications, and it can be used for real-time grid transformation of vector data, discrete global grid system (DGGS), and other similar applications.

Current bias compensation methods for distributed localization consider the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements noise, but ignore the negative influence by the sensor location uncertainties on source localization accuracy. Therefore, a new bias compensation method for distributed localization is proposed to improve the localization accuracy in this paper. This paper derives the theoretical bias of maximum likelihood estimation when the sensor location errors and positioning measurements noise both exist. Using the rough estimate result by MLE to subtract the theoretical bias can obtain a more accurate source location estimation. Theoretical analysis and simulation results indicate that the theoretical bias derived in this paper matches well with the actual bias in moderate noise level so that it can prove the correctness of the theoretical derivation. Furthermore, after bias compensation, the estimate accuracy of the proposed method achieves a certain improvement compared with existing methods.