• Journal of Positioning, Navigation, and Timing
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• v.12 no.2
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• pp.113-119
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• 2023

Satellite navigation systems, with the exception of the GLObal NAvigation Satellite System (GLONASS), adopt ionosphere models and provide ionospheric coefficients to single-frequency users via navigation messages to correct ionospheric delay, the main source of positioning errors. A Global Navigation Satellite System (GNSS) mostly has its own ionospheric models: the Klobuchar model for Global Positioning System (GPS), the NeQuick-G model for Galileo, and the BeiDou Global Ionospheric delay correction Model (BDGIM) for BeiDou satellite navigation System (BDS)-3. On the other hand, a Regional Navigation Satellite System (RNSS) such as the Quasi-Zenith Satellite System (QZSS) and BDS-2 uses the Klobuchar Model rather than developing a new model. QZSS provides its own coefficients that are customized for its service area while BDS-2 slightly modifies the Klobuchar model to improve accuracy in the Asia-Pacific region. In addition, BDS broadcasts multiple ionospheric parameters depending on the satellites, unlike other systems. In this paper, we analyzed the different ionospheric models of GPS, QZSS, and BDS in Korea. The ionospheric models of QZSS and BDS-2, which are based in Asia, reduced error by at least 25.6% compared to GPS. However, QZSS was less accurate than GPS during geomagnetic storms or at low latitude. The accuracy of the models according to the BDS satellite orbit was also analyzed. The BDS-2 ionospheric model showed an error reduction of more than 5.9% when using GEO coefficients, while in BDS-3, the difference between satellites was within 0.01 m.

• Journal of Positioning, Navigation, and Timing
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• v.13 no.1
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• pp.63-73
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• 2024

NeQuick G is the ionosphere model utilized by Galileo single-frequency users to estimate the ionospheric delay on each user-satellite link. The model is characterized by the effective ionization level (Az) index, determined by a modified dip latitude (MODIP) and broadcast coefficients derived from daily global space weather observations. However, globally fitted Az coefficients may not accurately represent ionosphere within local area. This study introduces a method for regional ionospheric modeling that searches for locally optimized Az coefficients. This approach involves fitting TEC output from NeQuick G to TEC data collected from GNSS stations around Korea under various ionospheric conditions including different seasons and both low and high solar activity phases. The optimized Az coefficients enable calculation of the Az index at any position within a region of interest, accounting for the spatial variability of the Az index in a polynomial function of MODIP. The results reveal reduced TEC estimation errors, particularly during high solar activity, with a maximum reduction in the RMS error by 85.95%. This indicates that the proposed method for NeQuick G can effectively model various ionospheric conditions in local areas, offering potential applications in GNSS performance analyses for local areas by generating various ionospheric scenarios.

• International Journal of Aeronautical and Space Sciences
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• v.5 no.1
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• pp.94-100
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• 2004

Ionospheric time delay is the biggest error source for single-frequency DGPSapplications, including time transfer and Wide Area Differential GPS (WADGPS).Currently, there are many attempts to develop real-time ionospheric time delayestimation techniques to reduce positioning error due to the ionospheric time delay.Klobuchar model is now widely used for ionosphehc time delay calculation forsingle-frequency users. It uses flat surface at night time and cosine surface atdaytime[1], However, the model was developed for worldwide ionosphere fit, it isnot adequate for local area single-frequency users who want to estimateionospheric time delay accurate1y[2]. Therefore, 3-D ionosphere model usingtomographic estimation has been developed. 3-D tomographic inversion modelshows better accuracy compared with prior a1gorithms[3]. But that existing 3-Dmodel still has problem that it requires many coefficients and measurements forgood accuracy. So, that algorithm has Umitation with many coefficients incontinuous estimation at the small region which is obliged to have fewermeasurements.In this paper, we developed an modified 3-D ionosphehc time delay modelusing tomography, which requires only fewer coefficients. Because the combinationsof our base coefficients correspond to the full coefficients of the existing model, ourmodel has equivalent accuracy to the existing. We confirmed our algorithm bysimulations. The results proved that our modified algohthm can perform continuousestimation with fewer coefficients.

• Journal of Astronomy and Space Sciences
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• v.27 no.2
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• pp.117-122
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• 2010

An ionospheric error simulation is needed for creating precise Global Positioning System (GPS) signal using GPS simulator. In this paper we developed Klobuchar coefficients n ${\alpha}_n$ and ${\beta}_n$ (n = 1, 2, 3, 4) generation algorithms for simulator and verified accuracy of the algorithm. The algorithm extract those Klobuchar coefficients from broadcast (BRDC) messages provided by International GNSS Service during three years from 2006 through 2008 and curve-fit them with sinusoidal and linear functions or constant. The generated coefficients from our developed algorithms are referred to as MODL coefficients, while those coefficients from BRDC messages are named as BRDC coefficients. The maximum correlation coefficient between MODL and BRDC coefficients was found for ${\alpha}_2$ and the value was 0.94. On the other hand, the minimum correlation was 0.64 for the case of ${\alpha}_1$. We estimated vertical total electron content using the Klobuchar model with MODL coefficients, and compared the result with those from the BRDC model and global ionosphere maps. As a result, the maximum RMS was 3.92 and 7.90 TECU, respectively.

• Journal of the Institute of Convergence Signal Processing
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• v.5 no.2
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• pp.143-150
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• 2004

In this paper, a recursive digital filter realization for an ionospheric channel model is proposed. This realization is in the form of a cascade of identical second-order all-pass filters, and is determined by only three parameters; two coefficients of an all-pass section, and the number of sections. The values of these parameters are optimized by a nonlinear optimization algorithm called the "downhill simplex method", so that the resulting time delay function closely approximates that of the ionospheric channel model. Comparing with the nonrecursive digital filter realization, it can be shown that the proposed recursive-digital-filter-realization is advantageous in points of view for the numbers of filter coefficients and the realization.

• Journal of Astronomy and Space Sciences
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• v.28 no.1
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• pp.71-77
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• 2011

Ionospheric error modeling is necessary to create reliable global navigation satellite system (GNSS) signals using a GNSS simulator. In this paper we developed algorithms to generate Klobuchar coefficients ${\alpha}_n$, ${\beta}_n$ (n = 1, 2, 3, 4) for a GNSS simulator and verified accuracy of the algorithm. The eight Klobuchar coefficients were extracted from three years of global positioning system broadcast (BRDC) messages provided by International GNSS service from 2006 through 2008 and were fitted with Fourier series. The generated coefficients from our developed algorithms are referred to as Fourier Klobuchar model (FOKM) coefficients, while those coefficients from BRDC massages are named as BRDC coefficients. The correlation coefficient values between FOKM and BRDC were higher than 0.97. We estimated total electron content using the Klobuchar model with FOKM coefficients and compared the result with that from the BRDC model. As a result, the maximum root mean square was 1.6 total electron content unit.

• Journal of Advanced Navigation Technology
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• v.27 no.6
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• pp.841-848
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• 2023

The Klobuchar ionospheric model included in global positioning system (GPS) navigation messages provides ionospheric correction information to single-frequency users. This ionospheric model accuracy has a significant impact on the accuracy of navigation solutions. We examine the GPS navigation messages from 1993 to 2022 and analyze their accuracy, presence of coefficients and accuracy of the Klobuchar model. Early GPS navigation messages often did not include ionospheric data, and even when they did include ionospheric models, the accuracy was often quite low. From 2002, when the accuracy of the ionospheric model was stabilized, until 2022, the accuracy of the ionospheric model is analyzed by comparing it with the ionospheric model of the International GNSS Service (IGS). Changes in accuracy per day and per year and accuracy differences along geomagnetic latitude are analyzed.