Impact of Approximate Implementation manner in Klobuchar Model

This paper focuses on the approximations that John A. Klobuchar made in mid 70s in his famous algorithm of ionospheric correction model for single frequency GPS receiver. At that time Klobuchar used a system of fixed geomagnetic north pole coordinates which are not accurate nowadays according to the International Geomagnetic Reference Field and to the World Magnetic Model because the geomagnetic poles move slowly. In addition, Klobuchar had to do other trigonometry simplifications in his implementation to avoid sophisticated computations. In order to evaluate this approximate implementation in a single frequency GPS receiver, ionospheric time and range delay are estimated on the entire day of January 1st 2010, using a different implementation in MATLAB. The required GPS data is obtained from recorded RINEX files at UDMC near DAMASCUS, SYRIA. In this comparative study, we reformulated the standard equations of Klobuchar model and examined the influence of its approximations on the ionospheric range delay and found a non- negligible bias in order of ten centimeters, whereas the influence of the movement of the geomagnetic poles was in order of few centimeters.

Analysis of the BDGIM Performance in BDS Single Point Positioning

The broadcast ionospheric model is mainly used to correct the ionospheric delay error for single-frequency users. Since the BeiDou global ionospheric delay correction model (BDGIM) is a novel broadcast ionospheric model for BDS-3, its performance was analyzed through single point positioning (SPP) in this study. Twenty-two stations simultaneously receiving B1C, B2a, B1I and B3I signals were selected from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) tracking networks for the SPP experiments. The differential code bias (DCB) parameters were used to correct the hardware delays in the signals of B1C and B2a. The results showed that the BDGIM performs the best in high-latitude areas, and can effectively improve the positioning accuracy compared with the Klobuchar model. The average 3D positioning accuracy of the four civil signals can reach 3.58 m in high-latitude areas. The positioning accuracies with the BDGIM in the northern hemisphere are better than those in the southern hemisphere, and the global average 3D positioning accuracy of the four civil signals is 4.60 m. The performance of the BDGIM also shows some seasonal differences. The BDGIM performs better than the Klobuchar model on the days of spring equinox and winter solstice, while the opposite is true on the days of summer solstice and autumn equinox. On the day of winter solstice, the average 3D accuracies with the BDGIM on the signals of B1C, B2a, B1I and B3I are 4.13 m, 5.32 m, 4.40 m and 4.49 m, respectively. Although the SPP accuracies are to some extent affected by the geomagnetic storm, the BDGIM generally performs better and are more resistant to the geomagnetic storm than the Klobuchar model.

Smartphone Positioning and Accuracy Analysis Based on Real-Time Regional Ionospheric Correction Model

As one of the main errors that affects Global Navigation Satellite System (GNSS) positioning accuracy, ionospheric delay also affects the improvement of smartphone positioning accuracy. The current ionospheric error correction model used in smartphones has a certain time delay and low accuracy, which is difficult to meet the needs of real-time positioning of smartphones. This article proposes a method to use the real-time regional ionospheric model retrieved from the regional Continuously Operating Reference Stations (CORS) observation data to correct the GNSS positioning error of the smartphone. To verify the accuracy of the model, using the posterior grid as the standard, the electron content error of the regional ionospheric model is less than 5 Total Electron Content Unit (TECU), which is about 50% higher than the Klobuchar model, and to further evaluate the impact of the regional ionosphere model on the real-time positioning accuracy of smartphones, carrier-smoothing pseudorange and single-frequency Precise Point Positioning (PPP) tests were carried out. The results show that the real-time regional ionospheric model can significantly improve the positioning accuracy of smartphones, especially in the elevation direction. Compared with the Klobuchar model, the improvement effect is more than 34%, and the real-time regional ionospheric model also shortens the convergence time of the elevation direction to 1 min. (The convergence condition is that the range of continuous 20 s is less than 0.5 m).

Influence of the Ionospheric Delay on Designation of an Aircraft Position

The article presents and describes research results concerning determination of an impact of the ionospheric correction upon the positioning accuracy of an aircraft. The main objective of examinations was to verify three ionospheric models (the Klobuchar model, SBAS model and IONEX model) in determining aircraft coordinates. In the framework of the conducted simulations, the authors determined the aircraft coordinates by means of the SPP code method in the GPS system. The article presents a comparison of the determined aircraft coordinates in the SPP code method in relation to an accurate solution in the RTK-OTF differential technique. Based on the obtained results, it was found that e use of the SBAS and IONEX model is exploited to improve the positioning accuracy of an aircraft in relation to the Klobuchar model, from 20% to 72%, in the geocentric XYZ frame. The obtained findings of a simulation indicate that the ionospheric correction in the SBAS and IONEX models may be used to improve the performance of aircraft coordinates in air navigation.

Behavior of Broadcast Ionospheric-Delay Models from GPS, Beidou, and Galileo Systems

The GNSS observations suffer from different types of errors that could affect the achieved positioning accuracy based on the receiver type used. Single-frequency receivers are widely used worldwide because of its low cost. The ionospheric delay considers the most challenging error for single-frequency GNSS observations. All satellite navigation systems, except GLONASS, are advising their users to correct for the ionospheric delay using a certain model. Those models’ coefficients are sent to users in the system’s navigation message. These models are different in their accuracy and behavior based on its foundation theory as well as the updating rate of their coefficients. The GPS uses Klobuchar model for mitigating the ionospheric delay. BeiDou system (BDS-2) adopts a slightly modified Klobuchar model that resembles GPS ICA (Ionospheric Correction Algorithm) with eight correction parameters but is formulated in a geographic coordinate system with different coefficients in origin and updating rate. Galileo system uses a different model (NeQuick model). This article investigates the behavior of the three models in correcting the ionospheric delay for three stations at different latitudes during 3 months of different states of ionospheric activity, comparing with International GNSS Service-Global Ionospheric Maps (IGS-GIMs). It is advised from this research’s outputs to use the GPS model for mitigating the ionospheric delay in low-latitude regions during the state of low-and medium-activity ionosphere. It is advised to use the BeiDou model for mitigating the ionospheric delay in mid-latitude regions during different states of ionospheric activity. It is advised to use the Galileo model for mitigating the ionospheric delay in high-latitude regions during different states of ionospheric activity. Also, the Galileo model is recommended for mitigating the ionospheric delay for low-latitude regions during the state of high-activity ionosphere.

NIGHTTIME TEC VARIATION ANALYSIS OF KLOBUCHAR MODEL BASED ON IGS DATA IN CHINA

In order to further study the variation characteristics of the nighttime ionospheric accuracy of the Klobuchar model and the correlation between the nighttime ionospheric accuracy of the Klobuchar model and solar activity intensity. In this paper, a method for comparative analysis on solar activity intensity in the high, medium and low solar activity years has been proposed. The GIM provided by the IGS Center from 2008 to 2018 are treated as reference values to analyze the nighttime accuracy of the Klobuchar model for annual, seasonal, and monthly changes in high solar activity, medium solar activity and low solar activity. The results are: (1) The nighttime accuracy of the Klobuchar model is best in the medium solar activity, followed in the low solar activity and the worst in the high solar activity. (2) The Bias and RMS of the Klobuchar model at nighttime had obviously semi-annual and seasonal variations in high and medium solar activity. (3) The nighttime accuracy of the Klobuchar model did not vary with Bias and RMS changes at nighttime.

On Global Ionospheric Maps based winter-time GPS ionospheric delay with reference to the Klobuchar model

Modelling of the ionospheric Total Electron Content (TEC) represents a challenging and demanding task in Global Navigation Satellite Systems (GNSS) positioning performance. In terms of satellite Positioning, Navigation and Timing (PNT), TEC represents a significant cause of the satellite signal ionospheric delay. There are several approaches to TEC estimation. The Standard (Klobuchar) ionospheric delay correction model is the most common model for Global Positioning System (GPS) single-frequency (L1) receivers. The development of International GNSS Service (IGS) Global Ionospheric Maps (GIM) has enabled the insight into global TEC dynamics. GIM analyses in the Northern Adriatic area have shown that, under specific conditions, local ionospheric delay patterns differ from the one defined in the Klobuchar model. This has been the motivation for the presented research, with the aim to develop a rudimentary model of the TEC estimation, with emphasis on areas where ground truth data are not available. The local pattern of the ionospheric delay has been modelled with wave functions based on the similarity of waveforms, considering diurnal differences in TEC behavior from defined TEC patterns. The model represents a spatiotemporal winter-time ionospheric delay correction with the Klobuchar model as a basis. The evaluation results have shown accurate approximation of the local pattern of the ionospheric delay. The model was verified in the same seasonal period in 2007, revealing it successfulness under pre-defined conditions. The presented approach represents a basis for the further work on the local ionospheric delay modelling, considering local ionospheric and space weather conditions, thus improving the satellite positioning performance for single-frequency GNSS receivers.