Mapping GPS positional errors using spatial linear mixed models

Militino, Ana F.; Ugarte, M. D.; Iribas, J.; Lizarraga-Garcia, Enrique

doi:10.1007/s00190-013-0638-z

Cited by 6 publications

(6 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(IV) Measuring the emission rate of an aerosol also faces with measurement error which studied by Bémer et al (2002). (V)Finally, the altitude as a GPS information faces with measurement error as well, which discussed in previously mentioned study Militino et al (2013).…”

Section: Piemonte Datasetmentioning

confidence: 93%

Analysis of Gaussian Spatial Models with Covariate Measurement Error

Tadayon¹,

Rasekh²

2019

J. of Stat. Sci.

View full text Add to dashboard Cite

Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated variances and so an inappropriate inference. In this paper, the Gaussian spatial model is fitted based on covariate measurement error. For this purpose, we adopt the Bayesian approach and utilize the Markov chain Monte Carlo algorithms and data augmentations to carry out calculations. The methodology is illustrated using simulated data.Gaussian Spatial Model, Measurement Error, Bayesian Analysis MSC 2010: 62H11, 62F15.

show abstract

Section: Piemonte Datasetmentioning

confidence: 93%

Analysis of Gaussian Spatial Models with Covariate Measurement Error

Tadayon¹,

Rasekh²

2019

J. of Stat. Sci.

View full text Add to dashboard Cite

show abstract

“…Le‐Gallo and Fingleton () considered the case of cross‐sectional spatial regression models with MEs in the explanatory variables and demonstrated that ME in an independent variable is one reason why ordinary least squares estimates may not be consistent. Militino, Ugarte, Iribas, and Lizarraga‐Garcia () addressed the quality of the Global Positioning System measurements using a likelihood‐based approach for the analysis of positional errors based on a spatial linear mixed model. In line with the observations in the work of Li et al (), Huque, Bondell, and Ryan () showed that the presence of covariate MEs can lead to significant sensitivity of parameter estimation to the choice of the spatial correlation structure.…”

Section: Introductionmentioning

confidence: 99%

Spatial models for non‐Gaussian data with covariate measurement error

Tadayon

Torabi

2018

Environmetrics

View full text Add to dashboard Cite

Spatial models have been widely used in the public health setup. In the case of continuous outcomes, the traditional approaches to model spatial data are based on the Gaussian distribution. This assumption might be overly restrictive to represent the data. The real data could be highly non‐Gaussian and may show features like heavy tails and/or skewness. In spatial data modeling, it is also commonly assumed that the covariates are observed without errors, but for various reasons, such as measurement techniques or instruments used, uncertainty is inherent in spatial (especially geostatistics) data, and so, these data are susceptible to measurement errors in the covariates of interest. In this paper, we introduce a general class of spatial models with covariate measurement error that can account for heavy tails, skewness, and uncertainty of the covariates. A likelihood method, which leads to the maximum likelihood estimation approach, is used for inference through the Monte Carlo expectation–maximization algorithm. The predictive distribution at nonsampled sites is approximated based on the Markov chain Monte Carlo algorithm. The proposed approach is evaluated through a simulation study and by a real application (particulate matter data set).

show abstract

“…Kriging (see e.g., [10]), though originating in the field of mining, is developed to fully account for spatio-temporal information on data [10]. Since then, it has become a powerful tool in geostatistics and spatial statistics to handle spatially and/or temporally correlated and irregularly distributed data and has been widely applied to other fields such as hydrology [11], climatology [12], soil science [13], ecology [14], Geo-Information System (GIS) [15], atmosphere science [16], geophysics [17] and geodesy [18]. Since 2002, it has been shown to be efficient for ionospheric delay estimation as well.…”

Section: Introductionmentioning

confidence: 99%

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

Huang

Zhang

et al. 2017

Sensors

View full text Add to dashboard Cite

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 × 1016 electrons/m2) 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.

show abstract

Mapping GPS positional errors using spatial linear mixed models

Cited by 6 publications

References 44 publications

Analysis of Gaussian Spatial Models with Covariate Measurement Error

Analysis of Gaussian Spatial Models with Covariate Measurement Error

Spatial models for non‐Gaussian data with covariate measurement error

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

Contact Info

Product

Resources

About