Global Ionospheric Model Accuracy Analysis Using Shipborne Kinematic GPS Data in the Arctic Circle

: The global ionospheric model built by the International Global Navigation Satellite System (GNSS) Service (IGS) using GNSS reference stations all over the world is currently the most widely used ionospheric product on a global scale. Therefore, analysis and evaluation of this ionospheric product’s accuracy and reliability are essential for the practical use of the product. In contrast to the traditional way of assessing global ionospheric models with ground-based static measurements, our study used shipborne kinematic global positioning system (GPS) measurements collected over 18 days to perform a preliminary analysis and evaluation of the accuracy of the global ionospheric models; our study took place in the Arctic Circle. The data from the International GNSS Service stations near the Arctic Circle were used to verify the ionospheric total electron contents derived from the kinematic data. The results suggested that the global ionospheric model had an approximate regional accuracy of 12 total electron content units (TECu) within the Arctic Circle and deviated from the actual ionospheric total electron content value by about


Introduction
As an important component of the solar-terrestrial environment, the ionosphere has profound effects on modern radio engineering and human activities. Studying the ionosphere allows us to better understand the ionosphere itself, search for ways to overcome its potential harms, and determine methods to utilize it for our benefit. In addition, it also helps promote the study and development of earth science-related ionosphere theories and applications [1]. Many international studies have proved the potential harm of the ionosphere, the most significant of which is the impact on navigation accuracy [2][3][4][5]. Therefore, understanding the ionosphere will also promote the development of navigation and positioning technology [6,7]. The invention and rapid development of the Global Navigation Satellite System (GNSS) resulted in it becoming the main technique for ionosphere observation, as it is continuous, comprehensive, low-cost, highly accurate, and can be utilized in all types of weather [7][8][9][10][11][12][13][14][15][16].
The International GNSS Service (IGS) has been using the continuously operating GNSS reference stations around the world to develop a global ionospheric model, which has become one of the most important tools for ionosphere research and applications [17]. Therefore, analyzing and evaluating the accuracy and reliability of the IGS ionospheric product is essential for its proper use. Restricted by its ground-based observation stations, it was previously shown that the global ionospheric model published by the IGS had a lower accuracy over the sea compared to that over the land [18][19][20][21].
Although there have been some researchers who have used satellites for ocean altimetry to analyze and model the ionospheric total electron content (TEC) over the sea [22][23][24], due to inevitable systematic errors between different data sources and a limited number of existing satellites, the accuracy of the product is low. Compared to that in low-latitude and mid-latitude regions, the ionospheric structure in the polar regions is more complicated and volatile [25]. This special structure of the ionosphere makes the changing pattern of the TEC unpredictable, thereby causing the global ionospheric model to demonstrate a lower accuracy in polar regions than in low-latitude and mid-latitude regions [26]. This is particularly true in the Arctic Circle, due both to a lack of observational data from global positioning system (GPS) reference stations as well as more complicated ionospheric characteristics. Some scholars have used traditional ground-based stations to study the characteristics and effects of the Arctic ionosphere [27][28][29]. However, they could not reflect the situation well without high spatial and temporal resolution data. Therefore, analyzing and evaluating the accuracy of the global ionospheric model in the Arctic Circle is crucial for the proper application of the IGS ionospheric products in that region and related work in the future.
In our study, GNSS receivers were installed on a Chinese research vessel for an annual Arctic research expedition, which provided invaluable data for our purposes. Our study assessed the accuracy of the global ionospheric model in the Arctic Circle quantitatively using the data collected in September 2017. For many years, the IGS has been acquiring ionosphere information from the continuously operating GNSS reference stations around the world. In 1998, it approved and started implementing the TEC Ionosphere Exchange Format (IONEX) [17], which has become an important component of the IGS products and has provided abundant fundamental data for ionospheric studies around the world.
Among the four ionospheric analysis centers of the IGS, the Center for Orbit Determination in Europe and the European Space Agency modeled the global ionospheric TEC with the spherical harmonic method [30,31]. By adopting a holistic modeling approach, this method presented an effective extrapolation for the ionospheric TEC and demonstrated a certain accuracy in computing the ionospheric TEC for regions without direct observational data. However, this method failed to show the subtle changes in the regional ionospheric TEC. Alternatively, the Jet Propulsion Laboratory and Polytechnical University of Catalonia modeled the global ionospheric TEC based on global triangular grids and the model interpolation of selected reference stations, respectively [31,32]. These methods were able to effectively show the subtle changes in the ionospheric TEC of the observation region but failed to reasonable extrapolate ionospheric TEC outside the region. In addition, they generally relied on empirical models (such as the international reference ionosphere model) or mathematical interpolation (such as linear and Kriging interpolation) such that their accuracies cannot be guaranteed.
Based on some previous studies [30][31][32], the spherical harmonic method works relatively well for the interpolation and extrapolation of ionospheric TEC on a global scale and maintains the continuity and reliability of ionospheric TEC changes more effectively. Therefore, the global ionospheric model built with the spherical harmonic method was chosen for our study, and the ionospheric TEC was measured with the GPS data collected in the Arctic Circle to assess the model.
The second part of this paper introduces the details about the adopted data and methods in this study. The third part outlines the results of the accuracy assessment. The fourth part summarizes the major findings and contributions of the study and identifies a direction for future investigations.

Mathematic Models, Data Sets, and Analysis Methods
The spherical harmonic model of the global ionospheric TEC is described as [10]: where VTEC(ϕ, λ) represents the vertical TEC (VTEC) at the intersect pierce point (IPP;(ϕ, λ)); ϕ and λ represent the latitude and longitude of the ionospheric IPP, respectively; n dmax represents the maximum degree in spherical harmonics; ∼ P nm (sin ϕ) = MC(n, m) · P nm (sin ϕ) represents the normalized Legendre function with the n th degree and the m th order; MC(n, m) represents the normalized function shown in Equation (2) below; and ∼ A nm and ∼ B nm represent parameters in the model that are to be estimated:

Shipborne Kinematic GPS Data from the Arctic Research Expeditions
In 2017, a GNSS monitoring receiver set was brought onboard a Chinese research vessel operating in the Arctic region. The receiver Trimble NetR9 was used together with an antenna called TRM57971.00. The receiver was used to track GPS signals and transmit data, including pseudo-range (C1C, C2W) and carrier-phase measurements (L1C, L2W). The actual route of the Chinese research vessel was in the area between 66 • N and 77 • N. The sailing time was from September 1 to 22, 2017 (the data for September 6, 10, 16, and 20 was missing). The ionospheric TEC information on the satellite signal path was gathered from the dual-frequency data received by the receiver. This information formed the basis of the accuracy and reliability assessment for the global ionospheric model in the Arctic Circle.
The data from the IGS GNSS reference stations (RESO and THU2) near the Arctic Circle for September 1 to 3, 2017 were collected to verify the reliability of the shipborne kinematic GPS measurements. The actual route taken by the Chinese research vessel for its operation within the Arctic Circle and the location of IGS GNSS reference stations are shown in Figure 1. represent parameters in the model that are to be estimated:

Shipborne Kinematic GPS Data from the Arctic Research Expeditions
In 2017, a GNSS monitoring receiver set was brought onboard a Chinese research vessel operating in the Arctic region. The receiver Trimble NetR9 was used together with an antenna called TRM57971.00. The receiver was used to track GPS signals and transmit data, including pseudo-range (C1C, C2W) and carrier-phase measurements (L1C, L2W). The actual route of the Chinese research vessel was in the area between 66°N and 77°N. The sailing time was from September 1 to 22, 2017 (the data for September 6, 10, 16, and 20 was missing). The ionospheric TEC information on the satellite signal path was gathered from the dual-frequency data received by the receiver. This information formed the basis of the accuracy and reliability assessment for the global ionospheric model in the Arctic Circle.
The data from the IGS GNSS reference stations (RESO and THU2) near the Arctic Circle for September 1 to 3, 2017 were collected to verify the reliability of the shipborne kinematic GPS measurements. The actual route taken by the Chinese research vessel for its operation within the Arctic Circle and the location of IGS GNSS reference stations are shown in Figure 1.

Ionospheric TEC Information Extracted from Dual-Frequency GPS Data
GPS data can be classified into code-phase and carrier-phase measurements. As the code pseudo-range has a lower accuracy, information about the absolute TEC of the ionosphere that is

Ionospheric TEC Information Extracted from Dual-Frequency GPS Data
GPS data can be classified into code-phase and carrier-phase measurements. As the code pseudo-range has a lower accuracy, information about the absolute TEC of the ionosphere that is obtained using the code pseudo-range alone usually has a low accuracy as well [33,34]. Alternatively, due to the inclusion of integer-ambiguity parameters for two frequencies, the carrier-phase measurement can only obtain information about the relative TEC of the ionosphere [35].
To acquire highly accurate information about the absolute TEC of the ionosphere, this study adopted the carrier-phase smoothed pseudo-range method and extracted the ionospheric TEC information from the dual-frequency GPS data. The function expression is given as follows [17]: where P 1 and P 2 represent the values of the code pseudo-ranges at different frequencies; f 1 and f 2 represent the frequencies corresponding to carrier signals L 1 and L 2 , respectively; F(α) represents the projection function, which can convert the ionospheric TEC value in the ionospheric IPP direction into the ionospheric VTEC value at that point (the function mainly depends on the relative zenith distance α between the satellite and the ionospheric IPP); c represents the speed of light in a vacuum; and DCB s and DCB r represent the difference code biases (DCBs) of the satellite and the receiver, respectively. Therefore, from the equation above, highly accurate absolute TEC information from the ionosphere can be obtained after determining the DCB in the satellite and the receiver.

Estimation of Kinematic GPS-Difference Code Biases of the Receiver
DCBs in the satellite and the receiver are significant errors in the ionospheric TEC calculation. While DCB in the satellite can be corrected using IGS products, DCB in the receiver can be estimated accurately only with its own observational data. Unlike the IGS, which estimates DCB simultaneously when modeling the global ionospheric model, we describe the trend of changes in the ionosphere above the kinematic GPS monitoring stations with a generalized trigonometric series [35], with the DCB of the receiver for one day estimated as a constant. The model, using a generalized trigonometric series, considers both the gradient of regional changes [36,37] and the cyclic nature of the ionosphere for one day, it is therefore more suitable for the accurate simulation of the ionospheric delay occurring above the kinematic GPS reference stations. The model using the generalized trigonometric series is shown as: where ϕ 0 represents the latitude of the center of the regional ionospheric TEC model; h represents the function related to the standard time t at the IPP; n max , m max , and k max represent the maximum orders of the polynomial function and the trigonometric function, respectively; and E nm , C k , S k represent the coefficients in the model that are to be estimated. Other parameters are the same as the corresponding symbols in Equation (1).

Results
Information about a clean absolute TEC of the ionosphere was obtained by correcting the VTEC value at the ionospheric IPP with the estimated values of DCB in the satellite and the receiver with the method discussed in Section 2.3. Taking that "clean" absolute TEC of the ionosphere as the reference, the ionospheric TEC was calculated for the corresponding time and location using the IONEX file interpolation. The direct ionospheric TEC variation is given in Figure 2. It can be seen that the irregularity of the ionosphere in the Arctic Circle makes it difficult to describe. To prove the reliability of shipborne data, direct changes in the ionospheric TEC calculated by the shipborne data and the IGS reference stations data are compared. The results are shown in Figure  3. When the ship sailed near the IGS reference stations, the shape and magnitude of the ionospheric TECs were similar. This confirms the reliability of the shipborne data. Meanwhile, the shipboard data can reflect abnormal changes in the ionosphere in the Arctic Circle, which is more advantageous in the Arctic region where the IGS reference stations are sparse. Then, the difference between the global ionosphere model TEC and the actual ionospheric TEC was obtained. The probability distribution of the difference is given in Figure 4. It can be seen that the overall difference between the global ionospheric model TEC and the ionospheric TEC obtained from the kinematic data is about 3 to 6 total electron content units (TECu). Overall, this deviation is about 4 TECu. To prove the reliability of shipborne data, direct changes in the ionospheric TEC calculated by the shipborne data and the IGS reference stations data are compared. The results are shown in Figure 3. When the ship sailed near the IGS reference stations, the shape and magnitude of the ionospheric TECs were similar. This confirms the reliability of the shipborne data. Meanwhile, the shipboard data can reflect abnormal changes in the ionosphere in the Arctic Circle, which is more advantageous in the Arctic region where the IGS reference stations are sparse. To prove the reliability of shipborne data, direct changes in the ionospheric TEC calculated by the shipborne data and the IGS reference stations data are compared. The results are shown in Figure  3. When the ship sailed near the IGS reference stations, the shape and magnitude of the ionospheric TECs were similar. This confirms the reliability of the shipborne data. Meanwhile, the shipboard data can reflect abnormal changes in the ionosphere in the Arctic Circle, which is more advantageous in the Arctic region where the IGS reference stations are sparse. Then, the difference between the global ionosphere model TEC and the actual ionospheric TEC was obtained. The probability distribution of the difference is given in Figure 4. It can be seen that the overall difference between the global ionospheric model TEC and the ionospheric TEC obtained from the kinematic data is about 3 to 6 total electron content units (TECu). Overall, this deviation is about 4 TECu. Then, the difference between the global ionosphere model TEC and the actual ionospheric TEC was obtained. The probability distribution of the difference is given in Figure 4. It can be seen that the overall difference between the global ionospheric model TEC and the ionospheric TEC obtained from the kinematic data is about 3 to 6 total electron content units (TECu). Overall, this deviation is about 4 TECu. The root mean square error (RMSE) of the daily deviation was counted. This value was used to represent the accuracy of the model value relative to the measured value. The expression of RMSE is given as follows:  Table 1 with the corresponding dates The root mean square error (RMSE) of the daily deviation was counted. This value was used to represent the accuracy of the model value relative to the measured value. The expression of RMSE is given as follows: where N represents the number of samples; X model represents the model value; and X shipborne represents the measured value. The results are summarized in Table 1 with the corresponding dates of observation. The last item in the table denotes the overall accuracy during the measurement period. The result is shown in Figure 5. During the test, the highest accuracy was observed on September 1, and the worst accuracy was observed on September 8. The overall accuracy was approximately 12 TECu. The result is shown in Figure 5. During the test, the highest accuracy was observed on September 1, and the worst accuracy was observed on September 8. The overall accuracy was approximately 12 TECu.

Conclusions
The global ionospheric model from the IGS generally has a relatively low accuracy when used in the polar regions, and it is often difficult to obtain a reliable assessment of the accuracy of the ionospheric products in that region with the existing ground-based GNSS observation stations. In this study, using the shipborne kinematic GPS data from a Chinese Arctic expedition, the DCB values were accurately estimated with a model based on a generalized trigonometric series; these values were then used to perform a detailed assessment of the accuracy and reliability of the global ionospheric model; our study was conducted in the Arctic Circle.
The data from IGS reference stations near the Arctic Circle were used to verify the ionospheric total electron content from the shipborne kinematic GPS measurements. The assessment results indicated that the TEC from the kinematic GPS measurements is reliable, and the overall difference between the global ionospheric model TEC and the actual ionospheric TEC is about 3 to 6 TECu in

Conclusions
The global ionospheric model from the IGS generally has a relatively low accuracy when used in the polar regions, and it is often difficult to obtain a reliable assessment of the accuracy of the ionospheric products in that region with the existing ground-based GNSS observation stations. In this study, using the shipborne kinematic GPS data from a Chinese Arctic expedition, the DCB values were accurately estimated with a model based on a generalized trigonometric series; these values were then used to perform a detailed assessment of the accuracy and reliability of the global ionospheric model; our study was conducted in the Arctic Circle.
The data from IGS reference stations near the Arctic Circle were used to verify the ionospheric total electron content from the shipborne kinematic GPS measurements. The assessment results indicated that the TEC from the kinematic GPS measurements is reliable, and the overall difference between the global ionospheric model TEC and the actual ionospheric TEC is about 3 to 6 TECu in

Conclusions
The global ionospheric model from the IGS generally has a relatively low accuracy when used in the polar regions, and it is often difficult to obtain a reliable assessment of the accuracy of the ionospheric products in that region with the existing ground-based GNSS observation stations. In this study, using the shipborne kinematic GPS data from a Chinese Arctic expedition, the DCB values were accurately estimated with a model based on a generalized trigonometric series; these values were then used to perform a detailed assessment of the accuracy and reliability of the global ionospheric model; our study was conducted in the Arctic Circle.
The data from IGS reference stations near the Arctic Circle were used to verify the ionospheric total electron content from the shipborne kinematic GPS measurements. The assessment results indicated that the TEC from the kinematic GPS measurements is reliable, and the overall difference between the global ionospheric model TEC and the actual ionospheric TEC is about 3 to 6 TECu in the Arctic Circle. Further, the accuracy of the global ionospheric model was approximately 12 TECu in the region.
For a better assessment of the accuracy and reliability of the global ionospheric model in the Arctic Circle, future work has been designed to collect and analyze GNSS data acquired from the multi-GNSS receivers on board an Arctic research vessel to extend the scope of the ionospheric model assessment with more data sets.