A modified Klobuchar model for single-frequency GNSS users over the polar region

Bi, Tong; An, Jiachun; Yang, Jian; Liu, Shulun

doi:10.1016/j.asr.2016.10.029

Cited by 21 publications

(4 citation statements)

References 19 publications

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“…In contrast to the GPS model, the Klobuchar BeiDou model operates using geographic instead of geomagnetic coordinates. The vertical ionospheric delay of Klobuchar can be determined using the formula [ 41 , 42 , 43 ]:

where:…”

Section: Methodsmentioning

confidence: 99%

Analysis of GPS/EGNOS Positioning Quality Using Different Ionospheric Models in UAV Navigation

Grunwald

Ciećko

Kozakiewicz

et al. 2023

Sensors

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Unmanned aerial vehicles (UAVs) have become very popular tools for geoinformation acquisition in recent years. They have also been applied in many other areas of life. Their navigation is highly dependent on global navigation satellite systems (GNSS). The European Geostationary Navigation Overlay Service (EGNOS) is intended to support GNSSs during positioning, mainly for aeronautical applications. The research presented in this paper concerns the analysis of the positioning quality of a modified GPS/EGNOS algorithm. The calculations focus on the source of ionospheric delay data as well as on the aspect of smoothing code observations with phase measurements. The modifications to the algorithm concerned the application of different ionospheric models for position calculation. Consideration was given to the EGNOS ionospheric model, the Klobuchar model applied to the GPS system, the Klobuchar model applied to the BeiDou system, and the NeQuick model applied to the Galileo system. The effect of removing ionospherical corrections from GPS/EGNOS positioning on the results of the determination of positioning quality was also analysed. The results showed that the original EGNOS ionospheric model maintains the best accuracy results and a better correlation between horizontal and vertical results than the other models examined. The additional use of phase-smoothing of code observations resulted in maximum horizontal errors of approximately 1.3 m and vertical errors of approximately 2.2 m. It should be noted that the results obtained have local characteristics related to the area of north-eastern Poland.

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where:…”

Section: Methodsmentioning

confidence: 99%

Analysis of GPS/EGNOS Positioning Quality Using Different Ionospheric Models in UAV Navigation

Grunwald

Ciećko

Kozakiewicz

et al. 2023

Sensors

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“…At mid-latitudes, the correction percentage of the LSTM forecast model relative to the reference data is even more than 90%, which is comparable to the RIM data, while Klobuchar is only about 40%, an improvement of about 50%. It is known from the previous paper (Bi et al, 2017) that the Klobuchar model is too poor in position accuracy mainly in the U direction. Due to the limitation of RIM data coverage, the correction percentage of RIM is only about 60% for high latitude stations except NMER.…”

Section: Performance In Spp Solutionmentioning

confidence: 97%

LSTM-based short-term ionospheric TEC forecast model and position accuracy analysis

Xie

Dai

Zhu

et al. 2022

Preprint

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Ionospheric delay is one of the major error sources in global navigation satellite system (GNSS) single point positioning (SPP). Some empirical models have been proposed to correct ionospheric delay, which, however, are limited by the low accuracy. The single-point time-series-based ionospheric total electron content (TEC) forecast method theoretically introduces model error and the accumulation of forecast error increases during a day. Therefore, based on the regular variation characteristics of the ionosphere, to improve the forecast accuracy of the ionosphere, we propose a long short-term memory (LSTM) short-term forecast model using discrete GNSS data and ionospheric space environment data in the same period of multiple days. The LSTM ionospheric forecast model is constructed based on the 2014 single-site GNSS data from different regions (low, mid, and high latitude regions) of the Crustal Movement Observation Network of China (CMONOC). The results are compared with the Klobuchar model, CMONOC regional ionosphere maps (RIM) data, and GNSS derived TEC measurements. The performance of each model in the SPP is also compared and analyzed to further examine the feasibility of the LSTM ionospheric forecast model. The comprehensive statistical analysis shows that: i) LSTM forecast model is consistent with GNSS-TEC observations at high, mid, and low latitudes, and the forecast error is less than 3 TECu, which is much better than that of the Klobuchar model and RIM model, and is robust to anomalous values. The mean absolute error (MAE) and root mean square error (RMSE) of the LSTM forecast model decrease with increasing latitude. ii) When being used in SPP, the LSTM forecast model brings significant improvement to position accuracy, which is overall better than the RIM and Klobuchar models. The RMSE of 3D position error is 2–4 m for the LSTM forecast model, 2–5 m for the RIM model, and 4–5 m for the Klobuchar model. iii) In terms of geographic location, for 3D position accuracy, it is highest at mid-latitudes followed by high latitudes and worst at low latitudes. For the percentage of 3D position corrections relative to the reference, it is highest at high latitudes followed by mid-latitudes, and lowest at low latitudes. The percentage of LSTM forecast model is 85%-90% at low latitudes, which is better than Klobuchar's 40%-80% and RIM's 75%-85%. Such percentage is over 90% at mid-latitudes, which is comparable to the RIM and about 50% better than the Klobuchar model. It is noteworthy that the LSTM performs even better than the reference data at high latitudes.

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“…Generally, real‐time Global Navigation Satellite System (GNSS) users often apply the following approaches to correct ionospheric delays. The first one is the broadcast ionosphere models, such as Klobuchar and its refined models for Global Positioning System (GPS) (Bi et al., 2017; Chen et al., 2017; Klobuchar, 1987; N. Wang et al., 2016), NeQuickG model for GALILEO (Leitinger et al., 2005; Montenbruck & González‐Rodríguez, 2019; Nava et al., 2008), broadcast ionospheric model and its improvements for Beidou Navigation Satellite System (BDS) (N. Wang et al., 2018, 2021; Yuan et al., 2019), Neustrelitz Total Electron Content Model (NTCM) and its modifications for the next‐generation GNSS (Hoque & Jakowski, 2015; Hoque et al., 2017, 2018, 2019; X. Zhang et al., 2017). However, their accuracy is limited since they mainly use empirical equations to calculate ionospheric delays.…”

Section: Introductionmentioning

confidence: 99%

Method and Validation of Real‐Time Global Ionosphere Modeling Constraint by Multi‐Source GNSS/LEO Data

Chen,

Ren,

et al. 2024

Space Weather

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This study applies the zero‐differenced integer ambiguity method, named PPP‐Fixed, to extract real‐time ionospheric data and eliminate the latencies of rapid/final Global Ionosphere Maps (GIMs). The PPP‐Fixed method is also used to derive ionospheric data for post‐processed GIM generation, named SGG Post‐GIM, combined with low earth orbit satellite data. The obtained hardware delays are applied to revise real‐time ionospheric data. Meanwhile, the estimated multi‐source ionospheric model is regarded as historical data to estimate an ionospheric prediction model for constraint using the semi‐parameter model. Then, the Kalman filter is employed to estimate the parameters to generate real‐time GIM. Finally, the accuracy of estimated real‐time GIM, named SGG RT‐GIM, and SGG Post‐GIM is assessed. During the experimental period, the mean differences of SGG Post‐GIM and SGG RT‐GIM relative to GIMs provided by the international Global Navigation Satellite System service, named IGSG, are −0.46 and −0.57 Total Electron Content Unit (TECU), respectively. The corresponding Root Mean Square (RMS) values are 1.64 and 3.08 TECU. Over the test period, the mean positioning errors of the single‐frequency precise point positioning corrected by IGSG, SGG Post‐GIM, SGG RT‐GIM, and Klobuchar model are 0.14, 0.19, 0.21, and 0.25 m in the horizontal direction, respectively, while the corresponding errors are 0.36, 0.33, 0.38, and 0.64 m in the up direction. Further, the mean biases of experimental days for the self‐consistency assessment are 0.06, −0.01, and −0.07 TECU for IGSG, SGG Post‐GIM, and SGG RT‐GIM, respectively. The corresponding RMS values are 1.19, 1.15, and 1.57 TECU.

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A modified Klobuchar model for single-frequency GNSS users over the polar region

Cited by 21 publications

References 19 publications

Analysis of GPS/EGNOS Positioning Quality Using Different Ionospheric Models in UAV Navigation

Analysis of GPS/EGNOS Positioning Quality Using Different Ionospheric Models in UAV Navigation

LSTM-based short-term ionospheric TEC forecast model and position accuracy analysis

Method and Validation of Real‐Time Global Ionosphere Modeling Constraint by Multi‐Source GNSS/LEO Data

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