Regional Ionosphere Mapping with Kriging and Multiquadric Methods

Wielgosz, Paweł; Grejner‐Brzezinska, Dorota A.; Kashani, Israel

doi:10.5081/jgps.2.1.48

Cited by 85 publications

(54 citation statements)

References 6 publications

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“…Detailed information relating to the application of the OKR model in network solutions is presented in e.g. (Wielgosz et al, 2003;Al-Shaery et al, 2010, 2011.…”

Section: Application Parameters and Solution Algorithmmentioning

confidence: 99%

“…Distance-Based Linear Interpolation Method (Gao et al, 1997), Linear Combination Model (Han andRizos, 1996, 1997), Linear Interpolation Method (Wanninger, 1995), Low-Order Surface Model (Fotopoulos and Cannon, 2001)) and (ii) the geostatistical methods (e.g. Least-Squares Collocation Method (Marel, 1998;Raquet, 1998), Ordinary Kriging Method (Wielgosz et al, 2003;Al-Shaery et al, 2011)). From among these models, only Distance-Based Linear Interpolation Method does not allow the defining of the predicted values errors.…”

Section: Application Parameters and Solution Algorithmmentioning

confidence: 99%

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Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Próchniewicz

2014

Artificial Satellites

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ABSTRACT. The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

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“…Detailed information relating to the application of the OKR model in network solutions is presented in e.g. (Wielgosz et al, 2003;Al-Shaery et al, 2010, 2011.…”

Section: Application Parameters and Solution Algorithmmentioning

confidence: 99%

Section: Application Parameters and Solution Algorithmmentioning

confidence: 99%

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Próchniewicz

2014

Artificial Satellites

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“…Therefore another technique called Kriging, has been implemented (Wielgosz P. et al, 2003). This uses a slack variable, called Lagrange multiplier λ to obtain the delay in an optimum and unbiased manner.…”

Section: Ordinary Krigingmentioning

confidence: 99%

Statistical Comparison of Various Interpolation Algorithms for Grid-Based Single Shell Ionospheric Model Over Indian Region

Shukla¹,

Nagori²,

Das³

et al. 2008

J. of GPS

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Future Satellite Based Navigation Systems based on GPS, like US Wide Area Augmentation Sysytem (WAAS), are of global interest to the scientific community. Precise estimation of ionospheric delay is most crucial for successful implementation of the systems. Due to the complex ionospheric structure and large variation of Total Electron Content (TEC) in low latitudes, it is necessary to compare and validate the efficiency of the existing algorithms in this region. In this study, performances of the various interpolation algorithms for TEC calculation at ionospheric grid point (IGP) and user position for gridbased Single Shell Model have been tested for 72 test days of 2005. Based on the results obtained from this analysis, it has been found that, for the Indian region, it would be more suitable to use Ordinary Kriging in place of Planar Fit to estimate delay at an IGP (as used by US WAAS). It has also been found that Ordinary Kriging performs better than the Bilinear Interpolation technique at the user end.

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“…In addition, the resolution of these products might not be sufficient to support high quality GPS positioning, especially in the presence of local ionospheric disturbances. The need to produce regional ionosphere models for accurate positioning was investigated by many researchers (Komjathy and Langley, 1996;Hernández-Pajares et al, 1997;Hernandez-Pajares et al 1999;Liu and Gao, 2003;Wielgosz et al, 2003;Moon, 2004;Leandro and Santos 2007;Sayin et al, 2008;Maruyama, 2007;Liu et al, 2011;Liu et al, 2014;Ohashi et al, 2015 andRazin et al, 2015), where different algorithms were employed for regional ionosphere modeling such as Spherical harmonics, Spline interpolation, Gaussian process, kriging and artificial neural networks. However, due to the nonlinearity of ionosphere physical properties a highly nonlinear model a highly nonlinear wavelet network method is proposed in this paper to model and predict the temporal and spatial variations of ionosphere modeling.…”

Section: Introductionmentioning

confidence: 99%

Regional ionospheric modeling using wavelet network model

El-Diasty

2017

J. Glob. Position. Syst.

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A major error component of Global Positioning System (GPS) is the ionospheric delay. Ionopspheric error can be reduced by a dual frequency receiver using a linear combination technique that can not be applied with a single frequecy receiver. However, an accurate ionospheric error modeling for single-frequency receiver is required. Due to the nonlinearity of the ionospheric error, a highly nonlinear wavelet network (WN) method is proposed in this paper. The main objective of the paper is to develop a short-term prediction model based on a short dataset. Therefore, five GPS stations with five days of ionospheric datasets along with time and location were employed to develop the proposed WN-based ionospheric model. Four days of datasets were employed to develop the model and one day of dataset was employed to test the prediction accuracy. To validate the WN-based ionospheric model, a comparison was made between the developed WN-based ionospheric model and the CODE, JPL and IGS Global Ionospheric Map (GIM) models. It is shown that the Root-Mean-Squared (RMS) errors of the developed WNbased ionospheric model are 2.51 TECU, 2.75 TECU and 2.50 TECU (Total Electronic Content Unit) with percentage errors of about 3.4%, 3.8% and 3.4% when compared with the CODE, JPL and IGS GIM models.

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Regional Ionosphere Mapping with Kriging and Multiquadric Methods

Cited by 85 publications

References 6 publications

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Statistical Comparison of Various Interpolation Algorithms for Grid-Based Single Shell Ionospheric Model Over Indian Region

Regional ionospheric modeling using wavelet network model

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