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Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation t...

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Autores principales: Huang, Ling, Zhang, Hongping, Xu, Peiliang, Geng, Jianghui, Wang, Cheng, Liu, Jingnan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5375754/
https://www.ncbi.nlm.nih.gov/pubmed/28264424
http://dx.doi.org/10.3390/s17030468
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author Huang, Ling
Zhang, Hongping
Xu, Peiliang
Geng, Jianghui
Wang, Cheng
Liu, Jingnan
author_facet Huang, Ling
Zhang, Hongping
Xu, Peiliang
Geng, Jianghui
Wang, Cheng
Liu, Jingnan
author_sort Huang, Ling
collection PubMed
description Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 10(16) electrons/m(2)) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.
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spelling pubmed-53757542017-04-10 Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction Huang, Ling Zhang, Hongping Xu, Peiliang Geng, Jianghui Wang, Cheng Liu, Jingnan Sensors (Basel) Article Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 10(16) electrons/m(2)) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area. MDPI 2017-02-27 /pmc/articles/PMC5375754/ /pubmed/28264424 http://dx.doi.org/10.3390/s17030468 Text en © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Huang, Ling
Zhang, Hongping
Xu, Peiliang
Geng, Jianghui
Wang, Cheng
Liu, Jingnan
Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction
title Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction
title_full Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction
title_fullStr Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction
title_full_unstemmed Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction
title_short Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction
title_sort kriging with unknown variance components for regional ionospheric reconstruction
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5375754/
https://www.ncbi.nlm.nih.gov/pubmed/28264424
http://dx.doi.org/10.3390/s17030468
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