Performance Evaluation of Adjusted Spherical Harmonics Ionospheric Model Over Indian Region

The ionosphere is perceived to be a predominant source of ranging error of Global Navigation Satellite System (GNSS) signals to degrade the positional accuracy. The suitable ionospheric model is necessary to improve the positional accuracy of GNSS and Satellite-Based Augmentation System (SBAS) users. In this paper, the regional ionospheric model (RIM) over the Indian region is implemented based on the adjusted spherical harmonics function (ASHF) model from dense GPS TEC stations over the Indian region. Also, the evaluation of the different ASHF order models conducted to identify the proper order of the ASHF model for Indian low latitude ionospheric calm and adverse space weather conditions. The results confirm that the 4th order ASHF ionospheric model can identify the northern Equatorial Ionization Anomaly (EIA) TEC crest patterns over the Indian region. The comparison of the 4th order ASHF ionospheric model carried out with dual and single frequency ionospheric models like as Klobuchar model, Centre for Orbit Determination in Europe (CODE) Klobuchar model, NeQuick G model, BeiDou System (BDS2) model and CODE Global Ionospheric Maps (GIM) models. The outcome of the results indicates that the 4th Order ASHF ionospheric model would be potential for single and dual-frequency ionospheric models for GNSS and SBAS systems.


I. INTRODUCTION
The regional ionospheric Total Electron Content (TEC) model is necessary for High Frequency (HF), communication, and navigation applications to characterize local spatialtemporal and dispersive properties of the ionosphere [1]. The primary ionospheric parameter known as Total Electron Content (TEC) can be measured using dual-frequency Global Navigation Satellite System (GNSS) receivers. The single and dual-frequency ionospheric models are mandatory components to improve the positional accuracy of GNSS The associate editor coordinating the review of this manuscript and approving it for publication was Yue Zhang . and its satellite and ground-based augmentation navigation systems [2]. The range delay errors introduced in the GNSS and SBAS are highly variable and least predictable, especially in equatorial and low latitude regions due to Equatorial Ionization Anomaly (EIA) [3]. Klobuchar [4] proposed an empirical-based ionospheric broadcast model popularly known as Klobuchar ionospheric model for single-frequency GPS receivers. Klobuchar model is more straightforward and requires eight broadcasting coefficients in the navigation message of GPS satellites to compute ionospheric corrections. However, Klobuchar ionospheric model can predict 50% of actual ionospheric delays over the midlatitude region and low latitude regions [5], [6]. The major drawback of the Klobuchar ionospheric broadcast correction model is its inability to model night-time ionospheric variability due to constant offset value (5 nanoseconds). The Russian GLONASS navigation system does not equip with a single frequency ionospheric model [6]. NeQuick model requires three ionospheric broadcast coefficients which will be sent to Galileo users as part of the navigation message to represent global ionospheric behavior [7], [8]. NeQuick G model performance is better than the Klobuchar model [9]. BeiDouglobal broadcast ionospheric delay correction model (BDGIM) is developed for the BeiDou-3 navigation system [10].
BDGIM model computes ionospheric time delay using nine BDS GIM coefficients based on the modified spherical harmonic function model formulation [11]. The longterm performance analysis of the global BDGIM ionospheric model is still in the process. Indian regional navigation system called as Navigation with Indian Constellation (NAVIC) adopted Klobuchar and ionospheric grid corrections for single-frequency NAVIC users [12]. The Klobuchar ionospheric model is adopted for single frequency Japan's Quasi-Zenith Satellite System (QZSS) [1].
The Centre for Orbit Determination in Europe (CODE) has been providing Global Ionospheric Maps (GIM) with 1-hour resolution for single-frequency GNSS ionospheric delay corrections [2]. The Klobuchar like coefficients have been routinely estimated using GIM TEC maps and found that the CODE Klobuchar model with eight coefficients is better than Klobuchar model [13]. Hence, GNSS single frequency users require higher prediction accuracy in ionospheric delay estimation for positioning applications.
On the other hand, satellite-based augmentation systems (WAAS-USA, EGNOS-Europe, QZSS-Japan, GAGAN-India) adopted dual-frequency ionosphere models to provide ionospheric differential corrections and their error bounds via GEO stationary satellites. The user SBAS receiver then interpolates the ionospheric delay from surrounding four Ionospheric Grid Points (IGPs) using the Bi Linear interpolation algorithm [14]. Large temporal and spatial gradients in the ionospheric delays are significant in the equatorial and low latitude regions [15], [16]. A regional ionospheric TEC model is necessary for modeling TEC data scattered over the region of interest [17]. SBAS Ionospheric Grid-based models are generally used to estimate the ionospheric delays at the predefined ionospheric grid points and provide the values to the users [18]. Indian Satellite-based Augmentation system -GAGAN system adopted the ionospheric grid model based on a multilayer Data Fusion model developed by the Indian Space Research Organization (ISRO) [19]. However, none of these SBAS models provide model coefficients that are to be transmitted by GNSS satellites as a part of the navigation message.
Ratnam and Sarma [20] have implemented the regional ionospheric TEC model based on third-order spherical harmonic function (SHF) with 16 model coefficients. However, SHF ionospheric model produces smoother variations as compared to other ionospheric grid models over the Indian region [20]. An extended single layer model (ESLM) mapping function was implemented to eliminate ionospheric mapping error for the conversion of vertical TEC from slant TEC as part of the SHF ionospheric model [21]. Dabbakuti et al. [22] implemented the Adjusted Spherical Harmonics Function model for few ionospheric grid locations with 17 GPS TEC stations data of the 2004 year. The order suitability of the ASHF model yet to be investigated for low latitude ionospheric conditions. The suitability of the regional ASHF ionospheric model as a single frequency ionospheric broadcast model to be tested over low latitude ionospheric conditions. In this paper, an attempt has been made to identify suitable order adjusted spherical harmonic function models and 25 model coefficients for both single and dual-frequency GNSS users. The proposed model has well captured the EIA features under adverse space weather conditions.

II. METHODOLOGY
Airports Authority of India (AAI) and Indian Space Research Organization (ISRO) operating 26 GPS TEC stations under the GPS Aided Geo Augmented Navigation (GAGAN) TEC network over the Indian region (Fig. 1). This GAGAN network of 26 GPS dual-frequency receivers being a part of Space-Based Augmentation System (SBAS) program are useful to monitor and model the ionospheric TEC conditions. These 26 GPS dual-frequency receivers will provide the SBAS ionosphere differential corrections over the Indian region. The GPS TEC observations like slant TEC (STEC), GPS week, GPS time, PRN number, elevation angle, azimuthal angle information from all the GPS network receivers (Manufacturer: Novatel, Model: GSV4000B) over India are considered. The Receiver Independent Exchange (RINEX) format of the GPS receivers provides all STEC observations using code combined with VOLUME 8, 2020 carrier pseudo-range measurements with a 1-min time resolution. Kalman filter estimation procedure was used to remove the satellite and receiver instrumental biases [23]. VTEC values are calculated from STEC measurements based on elevation-dependent mapping function, assuming the thin shell height of the ionosphere as 350 km [24], [28], [29]. The corresponding ionospheric pierce point latitude and longitudes of all satellites concerning GPS stations are computed. In order to avoid multipath effects on GPS signals, the elevation masking angle is considered as 40 • [28], [29]. GPS-TEC data from 26 locations over the Indian region is considered during March, June, September, and December 2015 year to evaluate the performance of selected ionospheric models. The data collected for these seasons ASHF model estimates ionospheric delay using the Fourier series expansion method with the sum of latitudinal Legendre function and longitudinal sine and cosine terms. The mathematical expression for mapping the regional vertical total electron content (VTEC) using the adjusted spherical harmonics function (ASHF) model is given by [25].
: mapping function el : satellite elevation angle R e : represents earth radius (6378 km) h iono : thin shell height from the earth (350 km) m and n: order and degree φ r and λ r : adjusted latitude and longitude of the IPP φ 0 and λ 0 : geographic latitude and sun-fixed longitude θ max : half-angle of the spherical cap coordinate system C nm and S nm : ASHF model coefficients to be estimated using regional GPS-TEC data P nm : normalized associated Legendre functions.
The ASHF approach includes a surface model is characterized by the order of expansion m = 2, 3, 4, 5,6, 7, 8, 9, 10 including the coefficients n = 4, 9, 16, 25, 36, 49, 64, 81, 100 respectively. The order and degree of ASHF model describe the resolution of the model, and it depends upon the region and the number of measurements.
The Legendre function P nm is given by [26], The measurements of the spherical harmonic's expansion Eq. (1) is re-organized in matrix notations as given in below Eq. (3).
. . . where, The ASHF model coefficients are valid over the geographical area of interest to compute regional ionospheric delay, in turn, represent regional ionospheric behavior.

III. RESULTS AND DISCUSSIONS
To evaluate the suitability order of the ASHF model, 26      phenomenon can be observed apparently in low-latitude regions (15)(16)(17)(18)(19)(20) • N), during 10:00 and 13:00 LT (IST=UTC+ 5hrs:30 min) for 4 th order ASHF model during both geomagnetic quiet and disturbed days ( Fig. 2 and 3). The temporal and spatial variations of ionospheric TEC values measured from GPS measurements and the TEC peak distributions discussed in [31]. Whereas an unusual EIA peak distribution could be observed for the 2 nd , 3 rd , and 5 th order ASHF models with the peaks extend from 10 • N to 30 • N during 05 March 2015 (Fig. 2). Moreover, during geomagnetic disturbed day, 17 March 2015, except for the 4 th order ASHF model, for the remaining orders, the ASHF TEC distributions are comparatively uneven with respect to the temporal and spatial TEC distributions (Fig. 3). Hence, 4 th order ASHF model is considered as a RIM model over the Indian region due to the low statistical error values recorded for this order as shown in Table 1. Table 1 shows the comparison of maximum, minimum, mean, standard deviation, and the RMSE values of the ASHF model for the different orders (2 nd , 3 rd , 4 th , and 5 th orders) considered in the present analysis over Indian region. It is evident from the observations that the proposed 4 th order ASHF model has less RMSE and reasonable statistical values when compared with observed data over the Indian region during both the geomagnetic quiet and disturbed days . The entry formation of EIA TEC structures noticed at 6.00 hrs. UTC (11.30 local time) with maximum TEC of 40 TECU. The complete EIA occurred at 9.00 hrs UTC (14.30 local time) with maximum TEC (80 TECU) around 20 • N latitudes (Fig.5).
The enhanced EIA TEC structures are noticed from 07.00 to13.00 hrs UTC between the latitude range of 10 • to 20 • degrees. The maximum TEC intensity of 80 TECU occurred at 10.00 hrs UTC (Fig. 4). The 4 th order ASHF model can capture both ionospheric quiet and disturbed EIA characteristics.

A. COMPARISON OF 4 th ORDER ASHF MODEL WITH DUAL-FREQUENCY TEC MODELS
The performance of the 4 th order ASHF model evaluated CODE-GIM model. To generate reference TEC maps by Assimilated Indian Regional Vertical Total Electron Content (AIRAVAT) model [17]. Fig. 6a shows observed latitudinal TEC profiles at 80 • E longitudinal cross-section. The maximum TEC intensity of 80 TECU is observed at 11.00 hrs. UTC (16.30 LT) for the observed TEC map. Fig. 6b shows that Kp values are less than 3 indicate quiet ionospheric conditions. The northern EIA crest TEC structures are noticed at 9.00 hrs. UTC with maximum TEC intensity of 78 TECU (Fig. 6c). From Fig.6c-6f show TEC results of CODE-GIM, and ASHF model. The 4 th order ASHF is performed well compared to the CODE-GIM model. The TEC biases calculated by subtracting the observed and model TEC values. The 4th order ASHF model outperforms from CODE-GIM model. The maximum TEC biases value noted as 11TECU.
The proposed 4 th order ASHF model performance compared to disturbed conditions (Fig.7). The early formation EIA TEC structures have occurred at 06.00 hrs. UTC (11.30LT) (Fig.7a). Fig.7b shows that Kp variations indicate disturbed ionospheric conditions. The disturbed EIA TEC structures (enhanced TEC intensities) are all well captured by AIRVAT (Observation) and 4 th order ASHF models except the CODE GIM model. The biases of TEC results indicate that the ASHF model attains minimum bias TEC values as compared to CODE-GIM model. The proposed 4 th order ASHF model is a strong contender of a near real-time ionospheric model for SBAS systems, especially for low and equatorial regions.

B. COMPARISON OF ASHF MODEL WITH SINGLE FREQUENCY IONOSPHERIC MODELS
The advantage of the 4 th order ASHF model provides 25 model coefficients to estimate ionospheric delays over the Indian region. The ASHF model coefficients will be broadcasted to single-frequency GNSS users for ionospheric delay corrections. Furthermore, the ASHF model validated with Klobuchar model (Klob), CODEKlob model (Klobucharstyle coefficients provided by the Center for Orbit Determination in Europe (CODE), BeiDou System (BDS2) and NeQuick G models. Fig.8 and Fig. 9 shows single frequency ionospheric models (Klob, CODEKlob, BDS-2, and VOLUME 8, 2020   The minimum TEC bias values of 7 TECU attained for the ASHF model (Fig. 8). The maximum bias values reached 15 TECU for the Klobuchar model. The bias value of all VOLUME 8, 2020  single frequency ionospheric models is larger for disturbed days conditions than quiet day conditions ( Fig. 8 and Fig. 9). It is observed that the 4 th order ASHF model captures EIA TEC structures well when compared to BDS-2, CODEKlob, and Klobuchar and NeQuick G models. Thus, the proposed 4 th order ASHF model can be useful as a regional single frequency ionospheric model for GNSS users over the Indian region.  The 4 th order ASHF model provides the lowest RMSE of 7.07 TECU and 6.60 TECU for quiet and disturbed ionospheric conditions of September 2015. The RMSE values lower for December solstice quiet day as compared to June solstice month (Table.2). Several authors [11], [32] have reported that the RMSE values of RIM models could be in the range of 3.8−16.2 TECu. Araujo-Pradere et al. (2007) [33] have reported that the accuracy of a RIM over the US is ∼2 TECU, which could be due to the low solar activity and mid latitude region. The maximum RMSE value for the proposed ASHF model is in the range of 6-13 TECu during the various seasons of the 24th high solar activity period, 2015 over Indian regions. The maximum RMSE is observed during March Equinox, June solstice and minimum RMSE is observed during December solstice and September Equinox  periods. The vertical ionospheric delays during the disturbed days are quite low compared to quiet days due to the decrease in EIA during the disturbed days. Moreover, the performance of the proposed model, ASHF with 4 th order has been compared with the dual frequency global ionospheric models (CODE GIM model, AIRAVAT as Observation model) and single frequency global ionospheric models (BDS2 model,Klobuchar model, NeQuick G model and CODEKlob model) as shown in Fig. 10 and 11 respectively. The performance of the 4 th order ASHF model is tested with IGS GPS Stations (Bangalore, Port Blair, Lucknow, and Hyderabad) for 15 March 200015 data. IGS GPS TEC observations processed with GPS toolbox [27]. The maximum ionospheric time delay 80TECUnoted for Lucknow GPS station, whereas maximum ionospheric delay of 40TECU at Port Blair (near the equatorial station).
The 4th order ASHF model is following with all ionospheric models for estimating the diurnal ionospheric characteristics. The 4 th order ASHF model is closely following the observed TEC values at Hyderabad, Bangalore, Port Blair, and Lucknow. Fig.12 illustrates 4th order ASHF model performance with different time update interval for broadcasting the coefficients in the form of a GNSS satellite navigation message. The ionospheric delay variations are becoming smoother as time update interval increases. The proposed twenty-five ASHF model coefficients can be uploaded to GNSS/NavIC satellites as part of the navigation message within a one-hour update interval. Table 3 shows the comparison of position errors such as minimum, maximum, mean, and standard deviation values of the ASHF model with the different single frequency ionospheric models (Klobuchar model, NeQuick G model, and CODKlob models) over Bangalore IGS station. It is evident from the observations that the proposed 4 th order ASHF model has lesser position errors (north, east, and up) compared with Klobuchar,NeQuick G and CODKlob models during the geomagnetic quit day (15-03-2015).
The proposed ASHF model is validated with other conventional ionospheric models in terms of the Single Point Positioning (SPP) method using GLAB software [34]. Figure 13 illustrates the positioning errors of SPP solutions at Bangalore station. It is found that the proposed regional ionospheric model, ASHF model outperforms the global ionospheric models in terms of north, east, and up errors. Further, it is also noticed that the Nequick G model provides less positional errors as compared to CODEKlob and Klobuchar model as shown in Figure 13.

IV. CONCLUSION
The regional ionosphere TEC broad model based on the 4 th order ASHF model is constructed for estimating the vertical ionospheric delay at different grid points using empirical data collected from 26 GPS TEC stations distributed throughout India. The performance of the proposed ASHF model validated in capturing the Equatorial Ionization Anomaly (EIA) patterns over the Indian region during the geomagnetic storm and quiet periods for the 2015data. The proposed 4th order ASHF model exhibits consistent better accuracy with dualfrequency models like CODE-GIM during all the geomagnetic conditions. The presented results show that adjusted spherical harmonics expansion model (with order = 4) estimates the ionospheric delays with high accuracy for SBAS application. The 4th order ASHF order driven by 25 coefficients alone and has the feasibility to act as regional GPS ionospheric broadcast model, i.e., broadcasting of these coefficients to NavIC/GNSS users. The RMSE values lower for December solstice month as compared to June solstice month.
The ASHF model coefficients can be valid up to one hour, respectively. It is suggested that a one-hour update interval of ASHF model coefficients for the GNSS/NavIC system is sufficient to represent dynamic and random ionospheric spatial-temporal variations in the Indian region.
KONDAVEETI SIVA KRISHNA received the M.Tech. degree in digital electronics and communication systems. He is currently a Senior Research Fellow (ISRO NGP-10 Project) and a Research Scholar with the Space Technology and Atmospheric Research Laboratory, Department of Electronics and Communication Engineering, Koneru Lakshmaiah Education Foundation, India. His research interests include ionospheric total electron content study, ionospheric total electron content modeling, study of ionospheric single frequency GPS receivers, developing algorithms of DCBs, and development ionospheric total electron content modeling using GPS aided GEO augmented navigation measurements. VOLUME 8, 2020