Efficient Approximation for a Fully Populated Variance-Covariance Matrix in RTK Positioning
Publication: Journal of Surveying Engineering
Volume 144, Issue 4
Abstract
Global navigation satellite system (GNSS) observations have been shown to be physically correlated. Disregarding the physical correlations in a variance-covariance matrix (VCM) will lead to adverse impacts on GNSS applications. Typically, physical correlations have three types in a fully populated VCM: spatial, cross, and temporal correlations. However, such a fully populated VCM cannot be easily estimated and inverted, especially in real-time kinematic (RTK) positioning. The authors propose an efficient approximation approach for processing these physical correlations. This method appropriately considers the significant covariance elements and efficiently transforms the time-dependent VCM to a time-independent block diagonal matrix. As an example, 10 data sets of BeiDou code and phase observations with different baseline lengths and receivers were collected. The results showed that this proposed method had fewer covariance elements to be estimated, thus decreasing the number of unknowns when using (co)variance component estimation (VCE). In addition, the proposed method had lower computation burden than the multiple-epoch method. For instance, the computation efficiency was increased by more than 50% in the case of the 60-epoch data window. It can also provide more realistic baseline solutions and precisions compared with the traditional single-epoch method.
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Acknowledgments
This study was sponsored by the National Natural Science Foundation of China (41574023, 41622401, and 41731069), the Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee (17511109501, 17DZ1100802, and 17DZ1100902), the National Key Research and Development Program of China (2016YFB0501802), and the Fundamental Research Funds for the Central Universities. The authors gratefully acknowledge the editor and two reviewers for giving constructive comments that helped improve this paper.
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Published In
Journal of Surveying Engineering
Volume 144 • Issue 4 • November 2018
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© 2018 American Society of Civil Engineers.
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Received: Nov 2, 2017
Accepted: Apr 6, 2018
Published online: Jun 29, 2018
Published in print: Nov 1, 2018
Discussion open until: Nov 29, 2018
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