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Ionospheric time delay corrections based on the extended single layer model over low latitude region
Geodesy and Geodynamics 10 (2019) 235e240
Contents lists available at ScienceDirect
Geodesy and Geodynamics journal homepage: http://www.keaipublishing.com/geog
Ionospheric time delay corrections based on the extended single layer model over low latitude region Sahithi Karanam, D. Venkata Ratnam*, J.R.K. Kumar Dabbakuti Department of Electronics and Communications Engineering, Koneru Lakshmaiah University, Guntur, Andhra Pradesh, 522502, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 February 2018 Received in revised form 28 January 2019 Accepted 25 February 2019 Available online 8 April 2019
Ionospheric delay error is considered to be one of the most prominent factors impacting the Global Navigation Satellite Systems (GNSS) positioning and navigation accuracies. Due to dispersive nature and anisotropic of the ionosphere above certain regions, the positioning accuracy is seriously affected when using a precision-limited model. In this paper, an attempt has been taken to estimate ionosphere-delays based on Planar Fit (PF) and Spherical Harmonic Function (SHF) models by applying the commonly used single layer Model (SLM) and an extended single layer model (ESLM) which has been explored sparsely over the region. The results show that ESLM of PF and SHF techniques performed better in estimating ionospheric delay compared to the existing SLM model. Although the performance of the ESLM approach is almost comparable to the SLM results during the quiet ionospheric conditions, the ESLM-PF and ESLMSHF models led to respective improvements of 4.66% and 7.14% over the classically used SLM model under the disturbed ionospheric conditions. In view of the uneven variability of equatorial/low latitude ionosphere above the Indian subcontinental region, the suitability of ESLM-PF and ESLM-SHF models has been emphasized and suggested for assessing its completeness and reliableness across other parts of the globe. The output of this work may be useful for high precession GNSS positioning through mitigating the ionospheric delays under quiet as well as varied ionospheric conditions across the low/equatorial latitude regions. © 2019 Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Global Navigation Satellite Systems (GNSS) Planar fit (PF) Spherical Harmonic Function (SHF) Extended single layer model (ESLM)
1. Introduction Global Navigation Satellite Systems (GNSS), Satellite Based Augmentation Systems (SBAS) and Regional Navigation Satellite Systems (RNSS) have been proposed/established in the past three decades, along with the modern technological improvements in the radio wave propagation, space-based navigation and satellite communication requirements. In the commencement, the main goal of the navigation satellite system was relative position, time transfers and the accurate navigation relative positioning [1]. Nevertheless,
* Corresponding author. E-mail address: [email protected] (D. Venkata Ratnam). Peer review under responsibility of Institute of Seismology, China Earthquake Administration.
Production and Hosting by Elsevier on behalf of KeAi
there is a certain amount of time delay in the signal as the signal travels through the ionosphere. This is a major concern of scientific development community that ultimately degrades the performance of the navigation system [2]. Further, the equatorial/low latitude region encounters significantly large ionospheric gradients and range delays due to uncertainty in the day-to-day variability associated with localized electrodynamic and wind parameters. Usually, dual-frequency GNSS receivers meet most requirements by eliminating up to 99.9% of ionospheric error with a linear combination of frequencies. However, a single-frequency GNSS receiver use the most commonly used Klobuchar model (about 55% ionospheric error correction), regional vertical ionospheric TEC map, terrestrial/satellite-based augmentation systems, or other empirical ionospheric delay error models are the best choice for ionospheric error mitigation. But, the height component of the positioning solution can only be achieved reliably if a proper ionosphere mitigation method is applied. Whichever be the source for mitigating ionospheric delay in single/dual frequency GNSS receivers, an appropriate choice of model mapping function and ionospheric shell height are
https://doi.org/10.1016/j.geog.2019.02.002 1674-9847/© 2019 Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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S. Karanam et al. / Geodesy and Geodynamics 10 (2019) 235e240
the essential aspects to portray and mitigate the associated delay error for relatively precise positioning [3]. In fact, the ionospheric time delays due to each GNSS signal is usually determined from the TEC by assuming a layer of maximum electron density and its corresponding ionospheric pierce point (IPP) height. Moreover, the reliability of the TEC in two-dimensional (2-D) representation depends primarily on the source GNSS stations distribution and the spatiotemporal gradient modeling of TEC over a region. For the 2-D approaches, the two types of errors usually limit the accuracy of the normal selection of the single-layer model (SLM), i.e., a) error relating to model mapping function (or mapping function errors) and b) error caused by ignoring the horizontal gradients of electron density along the ray path [4]. In order to evaluate the improvement of the accuracy with respect to the standard models such as Inverse-Distance-Weight (IDW), Bilinear model, Kriging Model (KRM), Modified planar fit model (MPFM), Minimum Mean Square Model (MMSE), Spherical Harmonic Analysis (SHA) and Adjusted spherical harmonic analysis (ASHA), it seems one can inspect how precisely the mapping function (MF) is modeled, that denotes, the unknown height variation of the electron density profile is converted into a predetermined form. In the recent years, many researchers have been put their efforts in estimating and mitigating the ionospheric time delays based ionospheric modeling techniques with standard models [5e10]. These studies have been carried out mainly in place of the model performance analysis of the SBAS services over the region. Their results confirm that these models provide different model accuracies under different ionospheric conditions based on the SLM method [11]. However, the major challenge for any ionospheric model is the irregular distribution of ionospheric electron density, where any Single Layer Model (SLM) missing the detection of ionospheric irregularity. Following the aforesaid gaps in the regular SLM approach, the Jet Propulsion Laboratory (JPL) proposed an Extended Single Layer Model (ESLM) mapping function that has been successfully used in the Centre for Orbit Determination in Europe (CODE) Global Ionosphere Maps (GIM) to represent the global VTEC distribution in the time domain [12]. In addition, studies of Sparks et al. (2000) demonstrated that the ionospheric correction based on the ESLM model provides better results than the single layer model [4]. In the present paper, an attempt was made to estimate the ionospheric time delays from regional network of TEC data through using ESLM with the planar fit (PF) and the Spherical Harmonics Function (SHF) techniques over the equatorial/low latitude Indian Sub-continental region. 2. Data and methodology In the current study, GPS-TEC data from 17 GNSS stations are considered during July 2004, which are operating under the GAGANTEC network in the Indian region. The position of GNSS stations covers a stretch between geomagnetic equator to the equatorial anomaly crest and beyond with a ð5ο x 5ο Þ grid spacing in latitude and longitude. Initially, retrieved TEC data from all stations is preprocessed, followed by the PF and SHF techniques. A brief outline of the methodology followed has been presented in Fig. 1.
Fig. 1. Flowchart for estimating the ionospheric time delays.
"
"
Mðh; elÞ ¼ 1
cosðel:aÞ 1þ
#2 #1 2
h Re
Iv; IPPðx; yÞ is the ionospheric delay xeast and ynorth determine the user locations in the east direction and north direction coordinates and ao ; a1 ; a2 are the planar fit coefficients. Mðh; elÞ is the extended single-layer model (ESLM). The hs ,Re , el are referred to the thinshell height (506.7 km), earth radius (6378 km) and satellite elevation angle respectively. Additionally, the parameter ‘a’ is the constant term with a value of 0.9782.
2.2. SHF model The ionospheric single-shell approximation depending on the SHF is illustrated as follows [13].
STECðq; lÞ ¼
n X m X
P nm ½cosðqÞfCnm cosðmlÞ þ Snm sinðmlÞg
n¼0 m¼0
(2)
2.1. Planar fit model The ionospheric GPS-TEC measurements can be modeled with the frequently utilized single layer approximation depending on the planar fit model is given as [8].
h
Iv; IPPðx; yÞ ¼ Mðh; elÞ ao þ a1 x where
east
þ a2 y
north
i
(1)
VTEC ¼ STEC Mðh; elÞ
l; q is the geographic longitude and latitude of the IPP.
(3)
Cnm ; Snm is the unspecified Spherical Harmonic Coefficients of order m and degree n. P nm ½cosðqÞ is the normalized associated Legendre function. Compute the PF and SHF model coefficients by using weighted least square method as suggested by Menke et al. [14].
S. Karanam et al. / Geodesy and Geodynamics 10 (2019) 235e240
237
2.3. Truth data
3. Results and discussions
At a specific location, for a certain epoch, the vertical Ionospheric delays and their latitudes and longitudes of Ionospheric Pierce Point (IPP) due to the visible satellites are measured. Vertical ionospheric delays are taken into account at the corresponding IPP locations. Among them, the vertical ionospheric delay of the satellite with maximum elevation is considered a “truth data,” so that the error of conversion to vertical bias is less. For example, to estimate the vertical ionosphere time delay at ð25+ N; 75o EÞ Ionospheric Grid Point (IGP), the IPP equivalent to the highest elevation at each epoch is considered as an unknown point, and the measured vertical delays of the same are considered as “truth data” [15]. The vertical IGP delay is estimated at these IPPs using the data from surrounding stations, namely, Jodhpur, Delhi, Ahmedabad and Bhopal (Fig. 2).
The planar fit and SHF ionospheric models are employed by the GPS-TEC data. To investigate the IGP delay variations over the Indian region, we selected a typical quiet day (July 05, 2004) having the 3hourly Kp index in the range (0 ¼ Kp 2) and a disturbed day (July 23, 2004) with the 3-hourly Kp index (0 ¼ Kp < 9). The vertical ionospheric time delays at six IGP location between 10o N to 30o E latitude and 80o E to 90o E longitude are examined with a spacing of 10o . It is observed from the Fig. 3 that the IGP delays show an almost similar diurnal pattern with the increase in magnitude at sunrise to attain a peak around 12.00e15.00 hrs LT during quiet days and 14.00e17.00 hrs Lt during disturbed days and later declines to reach the minimum value after midnight. The vertical delay is varied from 1.27 m to 5.88 m LT (Fig. 3a) for quiet day. The vertical delay is varied from 1.44 m to 7.54 m LT (Fig. 3b) for disturbed day. Fig. 4 shows the estimation of ESLM-SHF Vertical ionospheric delays at six IGP locations for quiet and disturbed days (July 05 and 25, 2004). It is observed that the vertical delay is varied from 0.99 m to 6.28 m (Fig. 4a) for quiet day. The vertical delay is varied from 1.21 m to 7.63 m (Fig. 4b) for disturbed day. 3.1. Performance evaluation of ESLM model
Fig. 2. Locations of GPS-TEC stations (red triangle) of the GAGAN network, ionospheric grid points (IGPs) (black circle) and consolidated IGPs (green dot) for evaluation of models over Indian region.
Fig. 5 depicts the vertical ionospheric delay corresponding to the PF and SHF separately associated with SLM and ESLM at a selected IGP location (25 N and 75 E) on a quiet day. It is observed from the figure that the greatest vertical delay in the PF model is 5.97 m (SLM), 6.11 m (ESLM) whereas the corresponding minimum values are 1.11 m and 1.15. Similarly, the maximum vertical delays in SHF model are 6.21 m (SLM), 6.38 m (ESLM) along with the respective minimum values 0.66 m and 0.67 m. In Fig. 6, we plotted the vertical ionospheric delay corresponding to the PF and SHF by employing both SLM and ESLM at the IGP location (25 N and 75 E) on the disturbed day (February18, 2015). It is observed from the figure that the greatest vertical delays in the PF model are 7.60 m (SLM), 7.75 m (ESLM) and their minimum values are 1.33 m and 1.36 m. The corresponding SHF model values are 7.72 m (SLM), 7.97 m (ESLM) with
Fig. 3. Estimation of ESLM-Planar fit vertical ionospheric delays at six IGP locations for quiet and disturbed days (July 05 and 25, 2004).
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S. Karanam et al. / Geodesy and Geodynamics 10 (2019) 235e240
Fig. 4. Estimation of ESLM-SHF Vertical ionospheric delays at six IGP locations for quiet and disturbed days (July 05 and 25, 2004).
Fig. 5. Vertical ionospheric delay variations at an IGP location (25 N and 75 E) on a typical quiet day July 05, 2004.
the respective minimum values remaining at the levels of 1.17 m and 1.20 m. It is also proved that, at each IGP the vertical delays are relatively higher during the disturbed days when compared to the quiet days due to the improved EIA during the disturbed days considering the involvement of external electric field at the equatorial zone operating the pattern over the region and regular electrojet strength [16]. To evaluate the performance of ESLM over the IGP region (25 N, 75 E) location is studied in this study. The performance accuracy between the model vertical delays and the truth observation values has been determined using Root Mean Square Error (RMSE). The RMSE for both the models are determined from the considered two days as show in Fig. 7.
For the quiet day, the planar fit residuals are 1.55 m (SLM) and 1.52 (ESLM). When using a SHF approach, the residuals are 1.48 m (SLM) and 1.44 (ESLM). For the disturbed day, the planar fit residuals are 1.93 m (SLM) and 1.84 (ESLM). Whereas the SHF approaches, the residuals are 1.82 m (SLM) and 1.69 (ESLM). Hence, it is confirmed that the ESLM of PF and SHF models show better performance in estimating the ionospheric delays relative to that of the regular SLM models. The ESLM-PF improved the delay estimation by 4.66% and the ESLM-SHF model improved by 7.14% as compared to their counterparts using the SLM approach. Hence, applicability of ESLM model has been emphasized in this study for relatively better determining the ionospheric delay over the region. The performance could be further verified at different
S. Karanam et al. / Geodesy and Geodynamics 10 (2019) 235e240
239
Fig. 6. Vertical ionospheric delay variations at an IGP location (25 N and 75 E) on a typical disturbed day July 25, 2004.
conditions, so the implementation of ESLM model for more accurate monitoring of ionospheric delay error and their mitigations improving navigation and positioning precisions over the low latitude region. The outcome of this work may complement towards ionosphere time delay error modelling and mitigation applications in the context of satellite navigation systems. Conflict of Interest The authors declare that there is no conflicts of interest. Acknowledgements The authors would like to express their thanks to the Department of Science and Technology, New Delhi, India SR/FST/ESI-130/ 2013 FIST program for Department of Atmospheric Sciences. Fig. 7. RMSE of Ionospheric delay variations at an IGP location (25 N, 75 E) during quiet and disturbed days.
latitudes and longitudes for improved positioning and employment towards air navigation. 4. Conclusions In this study, the applicability of the new ESLM to estimate the ionospheric time delays by PF and SHF models was investigated. The current SLM and its modified version, the ESLM model, evaluated during the quiet as well as disturbed ionospheric conditions. The RMSE deviations in the SLM during the quiet and disturbed days are higher in comparison to ESLM for both PF and SHF models. The results show that the ESLM performance during the quiet day is almost comparable to that of the SLM model. However, during the disturbed day, ESLM-PF has been improved by delay estimate improvement (4.66%) and ESLM-SHF model (7.14%). Therefore, for disturbed ionospheric conditions, ESLM is preferred over SLM. The day-to-day ionospheric variation in equatorial/low latitude region are uncertain due to the governing local ionospheric and the wind dynamics
References [1] S.V. Kibe, Indian plan for satellite-based navigation systems for civil aviation, Curr. Sci. 84 (11) (2003) 1405e1411. [2] S. Sunda, R. Sridharan, B.M. Vyas, P.V. Khekale, K.S. Parikh, A.S. Ganeshan, C.R. Sudhir, S.V. Satish, Mala S. Bagiya, Satellite-based augmentation systems: a novel and cost-effective tool for ionospheric and space weather studies, Space Weather 13 (1) (2015) 6e15. [3] S.K. Panda, S.S. Gedam, Evaluation of GPS standard point positioning with various ionospheric error mitigation techniques, J. Appl. Geod. 10 (4) (2016) 211e221. [4] L. Sparks, B.A. Lijima, A.J. Mannucci, X. Pi, B.D. Wilson, A new model for retrieving slant TEC corrections for wide area differential GPS, in: 2000: Navigating into the New Millennium, Technical Meeting, Anaheim, CA; United States, 2000, pp. 464e473. [5] A. De Santis, G. DeFranceschi, D.J. Kerridge, Regional spherical modeling of 2-D functions: the case of the critical frequency of the F2 ionospheric layer, Comput. Geosci. 20 (5) (1994) 849e871. [6] R.S. Conker, M.B. El-Arini, T.W. Albertson, J.A. Klobuchar, P.H. Doherty, Description and assessment of real-time algorithms to estimate the ionospheric error bounds forWAAS, J. Navig. 44 (1) (1997) 77e87. [7] R. Lejeune, M.B. El-Arini, in: An Ionospheric Grid Algorithm for WAAS Based on the Minimum Mean Square Error Estimator, Proc. IES, Alexandria, VA, 1999. [8] T. Walter, A. Hansen, J. Blanch, P. Enge, T. Mannucci, X. Pi, L. Sparks, B. Iijma, M.B. El-Arini, R. Lejeune, M. Hagen, E. ltshular, R. Fries, A. Chu, Robust detection of ionosphere irregularities, in: Proc. Inst. Navig. Annu. Meeting, Salt Lake City, UT, Sep. 2000, pp. 209e218.
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[9] J. Blanch, T. Walter, P. Enge, Adapting kriging to the WAAS MOPS ionospheric grid, in: Proc. NTM Inst. Navig., Anaheim, CA, Jan. 2003, pp. 848e853. [10] J.R.K. Kumar Dabbakuti, D. VenkataRatnam, S. Sunda, Modelling of ionospheric time delays based on adjusted spherical harmonic analysis, Aviation 20 (1) (2016) 1e7. [11] D. VenkataRatnam, A.D. Sarma, Modelling of low-latitude ionosphere using GPS data with SHF model, IEEE Trans. Geosci. Remote Sens. 50 (3) (2012) 972e980. €ggi, M. Meindl, [12] U. Hugentobler, S. Schaer, G. Beutler, H. Bock, R. Dach, A. Ja C. Urschl, L. Mervart, M. Rothacher, U. Wild, A. Wiget, E. Brockmann, D. Ineichen, G. Weber, H. Habrich, C. Boucher, CODE IGS Analysis Center Technical Report 2002. Tech. rep., IGS 2001/2002 Technical Reports, 2002. [13] S. Schaer, G. Beutler, M. Rothacher, T.A. Springer, Daily global ionosphere maps based on GPS carrier phase data routinely produced by the code analysis center, in: Proc. IGS AC Workshop, Silver Spring, MD, Mar, 1996, pp. 19e21. [14] W. Menke, Geophysical Data Analysis: Discrete Inverse Theory, Academic, NewYork, NY, USA, 1984. [15] V. SatyaSrinivas, A.D. Sarma, Hema K. Achanta, Modeling of ionospheric time delay using anisotropic IDW WithJackknife technique, IEEE Trans. Geosci. Remote Sens. 54 (1) (2016) 513e519. [16] S. Basu, S. Basu, Effects of large magnetic storms on communication and GPS navigation systems at middle and equatorial latitudes, in: Proc. URSI GA Int. Conf., Maastricht, The Netherlands, Aug, 2002, pp. 17e24.
D. Venkata Ratnam received the M.Tech. degree in radar and microwave engineering from the Department of Electronics and Communication Engineering, Andhra University, Visakhapatnam, India, in 2003, and the Ph.D. degree in electronics and communication engineering from Jawaharlal Nehru Technological University Hyderabad, Hyderabad, India, in 2011. From 2003 to 2011, he worked as a Research Assistant, Junior Research Fellow, Senior Research Fellow, and Senior Research Assistant with the Research and Training Unit for Navigational Electronics, Osmania University, Hyderabad, India. In 2011, he joined the Faculty of Department of Electronics and Communications Engineering as an Associate Professor, and is currently working as a Professor and Head of the Centre for Atmospheric Sciences, KL University, Guntur, India. His research interests include navigational electronics, global navigational satellite systems (GNSS), space science, and radio-wave propagation. Dr. Ratnam was the recipient of the Young Scientist Award (2012e2015) of the Department of Science and Technology (DST), India, and the Research Award (2015e2017) of the University Grants Commission (UGC), India.
Contents lists available at ScienceDirect
Geodesy and Geodynamics journal homepage: http://www.keaipublishing.com/geog
Ionospheric time delay corrections based on the extended single layer model over low latitude region Sahithi Karanam, D. Venkata Ratnam*, J.R.K. Kumar Dabbakuti Department of Electronics and Communications Engineering, Koneru Lakshmaiah University, Guntur, Andhra Pradesh, 522502, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 February 2018 Received in revised form 28 January 2019 Accepted 25 February 2019 Available online 8 April 2019
Ionospheric delay error is considered to be one of the most prominent factors impacting the Global Navigation Satellite Systems (GNSS) positioning and navigation accuracies. Due to dispersive nature and anisotropic of the ionosphere above certain regions, the positioning accuracy is seriously affected when using a precision-limited model. In this paper, an attempt has been taken to estimate ionosphere-delays based on Planar Fit (PF) and Spherical Harmonic Function (SHF) models by applying the commonly used single layer Model (SLM) and an extended single layer model (ESLM) which has been explored sparsely over the region. The results show that ESLM of PF and SHF techniques performed better in estimating ionospheric delay compared to the existing SLM model. Although the performance of the ESLM approach is almost comparable to the SLM results during the quiet ionospheric conditions, the ESLM-PF and ESLMSHF models led to respective improvements of 4.66% and 7.14% over the classically used SLM model under the disturbed ionospheric conditions. In view of the uneven variability of equatorial/low latitude ionosphere above the Indian subcontinental region, the suitability of ESLM-PF and ESLM-SHF models has been emphasized and suggested for assessing its completeness and reliableness across other parts of the globe. The output of this work may be useful for high precession GNSS positioning through mitigating the ionospheric delays under quiet as well as varied ionospheric conditions across the low/equatorial latitude regions. © 2019 Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Global Navigation Satellite Systems (GNSS) Planar fit (PF) Spherical Harmonic Function (SHF) Extended single layer model (ESLM)
1. Introduction Global Navigation Satellite Systems (GNSS), Satellite Based Augmentation Systems (SBAS) and Regional Navigation Satellite Systems (RNSS) have been proposed/established in the past three decades, along with the modern technological improvements in the radio wave propagation, space-based navigation and satellite communication requirements. In the commencement, the main goal of the navigation satellite system was relative position, time transfers and the accurate navigation relative positioning [1]. Nevertheless,
* Corresponding author. E-mail address: [email protected] (D. Venkata Ratnam). Peer review under responsibility of Institute of Seismology, China Earthquake Administration.
Production and Hosting by Elsevier on behalf of KeAi
there is a certain amount of time delay in the signal as the signal travels through the ionosphere. This is a major concern of scientific development community that ultimately degrades the performance of the navigation system [2]. Further, the equatorial/low latitude region encounters significantly large ionospheric gradients and range delays due to uncertainty in the day-to-day variability associated with localized electrodynamic and wind parameters. Usually, dual-frequency GNSS receivers meet most requirements by eliminating up to 99.9% of ionospheric error with a linear combination of frequencies. However, a single-frequency GNSS receiver use the most commonly used Klobuchar model (about 55% ionospheric error correction), regional vertical ionospheric TEC map, terrestrial/satellite-based augmentation systems, or other empirical ionospheric delay error models are the best choice for ionospheric error mitigation. But, the height component of the positioning solution can only be achieved reliably if a proper ionosphere mitigation method is applied. Whichever be the source for mitigating ionospheric delay in single/dual frequency GNSS receivers, an appropriate choice of model mapping function and ionospheric shell height are
https://doi.org/10.1016/j.geog.2019.02.002 1674-9847/© 2019 Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
236
S. Karanam et al. / Geodesy and Geodynamics 10 (2019) 235e240
the essential aspects to portray and mitigate the associated delay error for relatively precise positioning [3]. In fact, the ionospheric time delays due to each GNSS signal is usually determined from the TEC by assuming a layer of maximum electron density and its corresponding ionospheric pierce point (IPP) height. Moreover, the reliability of the TEC in two-dimensional (2-D) representation depends primarily on the source GNSS stations distribution and the spatiotemporal gradient modeling of TEC over a region. For the 2-D approaches, the two types of errors usually limit the accuracy of the normal selection of the single-layer model (SLM), i.e., a) error relating to model mapping function (or mapping function errors) and b) error caused by ignoring the horizontal gradients of electron density along the ray path [4]. In order to evaluate the improvement of the accuracy with respect to the standard models such as Inverse-Distance-Weight (IDW), Bilinear model, Kriging Model (KRM), Modified planar fit model (MPFM), Minimum Mean Square Model (MMSE), Spherical Harmonic Analysis (SHA) and Adjusted spherical harmonic analysis (ASHA), it seems one can inspect how precisely the mapping function (MF) is modeled, that denotes, the unknown height variation of the electron density profile is converted into a predetermined form. In the recent years, many researchers have been put their efforts in estimating and mitigating the ionospheric time delays based ionospheric modeling techniques with standard models [5e10]. These studies have been carried out mainly in place of the model performance analysis of the SBAS services over the region. Their results confirm that these models provide different model accuracies under different ionospheric conditions based on the SLM method [11]. However, the major challenge for any ionospheric model is the irregular distribution of ionospheric electron density, where any Single Layer Model (SLM) missing the detection of ionospheric irregularity. Following the aforesaid gaps in the regular SLM approach, the Jet Propulsion Laboratory (JPL) proposed an Extended Single Layer Model (ESLM) mapping function that has been successfully used in the Centre for Orbit Determination in Europe (CODE) Global Ionosphere Maps (GIM) to represent the global VTEC distribution in the time domain [12]. In addition, studies of Sparks et al. (2000) demonstrated that the ionospheric correction based on the ESLM model provides better results than the single layer model [4]. In the present paper, an attempt was made to estimate the ionospheric time delays from regional network of TEC data through using ESLM with the planar fit (PF) and the Spherical Harmonics Function (SHF) techniques over the equatorial/low latitude Indian Sub-continental region. 2. Data and methodology In the current study, GPS-TEC data from 17 GNSS stations are considered during July 2004, which are operating under the GAGANTEC network in the Indian region. The position of GNSS stations covers a stretch between geomagnetic equator to the equatorial anomaly crest and beyond with a ð5ο x 5ο Þ grid spacing in latitude and longitude. Initially, retrieved TEC data from all stations is preprocessed, followed by the PF and SHF techniques. A brief outline of the methodology followed has been presented in Fig. 1.
Fig. 1. Flowchart for estimating the ionospheric time delays.
"
"
Mðh; elÞ ¼ 1
cosðel:aÞ 1þ
#2 #1 2
h Re
Iv; IPPðx; yÞ is the ionospheric delay xeast and ynorth determine the user locations in the east direction and north direction coordinates and ao ; a1 ; a2 are the planar fit coefficients. Mðh; elÞ is the extended single-layer model (ESLM). The hs ,Re , el are referred to the thinshell height (506.7 km), earth radius (6378 km) and satellite elevation angle respectively. Additionally, the parameter ‘a’ is the constant term with a value of 0.9782.
2.2. SHF model The ionospheric single-shell approximation depending on the SHF is illustrated as follows [13].
STECðq; lÞ ¼
n X m X
P nm ½cosðqÞfCnm cosðmlÞ þ Snm sinðmlÞg
n¼0 m¼0
(2)
2.1. Planar fit model The ionospheric GPS-TEC measurements can be modeled with the frequently utilized single layer approximation depending on the planar fit model is given as [8].
h
Iv; IPPðx; yÞ ¼ Mðh; elÞ ao þ a1 x where
east
þ a2 y
north
i
(1)
VTEC ¼ STEC Mðh; elÞ
l; q is the geographic longitude and latitude of the IPP.
(3)
Cnm ; Snm is the unspecified Spherical Harmonic Coefficients of order m and degree n. P nm ½cosðqÞ is the normalized associated Legendre function. Compute the PF and SHF model coefficients by using weighted least square method as suggested by Menke et al. [14].
S. Karanam et al. / Geodesy and Geodynamics 10 (2019) 235e240
237
2.3. Truth data
3. Results and discussions
At a specific location, for a certain epoch, the vertical Ionospheric delays and their latitudes and longitudes of Ionospheric Pierce Point (IPP) due to the visible satellites are measured. Vertical ionospheric delays are taken into account at the corresponding IPP locations. Among them, the vertical ionospheric delay of the satellite with maximum elevation is considered a “truth data,” so that the error of conversion to vertical bias is less. For example, to estimate the vertical ionosphere time delay at ð25+ N; 75o EÞ Ionospheric Grid Point (IGP), the IPP equivalent to the highest elevation at each epoch is considered as an unknown point, and the measured vertical delays of the same are considered as “truth data” [15]. The vertical IGP delay is estimated at these IPPs using the data from surrounding stations, namely, Jodhpur, Delhi, Ahmedabad and Bhopal (Fig. 2).
The planar fit and SHF ionospheric models are employed by the GPS-TEC data. To investigate the IGP delay variations over the Indian region, we selected a typical quiet day (July 05, 2004) having the 3hourly Kp index in the range (0 ¼ Kp 2) and a disturbed day (July 23, 2004) with the 3-hourly Kp index (0 ¼ Kp < 9). The vertical ionospheric time delays at six IGP location between 10o N to 30o E latitude and 80o E to 90o E longitude are examined with a spacing of 10o . It is observed from the Fig. 3 that the IGP delays show an almost similar diurnal pattern with the increase in magnitude at sunrise to attain a peak around 12.00e15.00 hrs LT during quiet days and 14.00e17.00 hrs Lt during disturbed days and later declines to reach the minimum value after midnight. The vertical delay is varied from 1.27 m to 5.88 m LT (Fig. 3a) for quiet day. The vertical delay is varied from 1.44 m to 7.54 m LT (Fig. 3b) for disturbed day. Fig. 4 shows the estimation of ESLM-SHF Vertical ionospheric delays at six IGP locations for quiet and disturbed days (July 05 and 25, 2004). It is observed that the vertical delay is varied from 0.99 m to 6.28 m (Fig. 4a) for quiet day. The vertical delay is varied from 1.21 m to 7.63 m (Fig. 4b) for disturbed day. 3.1. Performance evaluation of ESLM model
Fig. 2. Locations of GPS-TEC stations (red triangle) of the GAGAN network, ionospheric grid points (IGPs) (black circle) and consolidated IGPs (green dot) for evaluation of models over Indian region.
Fig. 5 depicts the vertical ionospheric delay corresponding to the PF and SHF separately associated with SLM and ESLM at a selected IGP location (25 N and 75 E) on a quiet day. It is observed from the figure that the greatest vertical delay in the PF model is 5.97 m (SLM), 6.11 m (ESLM) whereas the corresponding minimum values are 1.11 m and 1.15. Similarly, the maximum vertical delays in SHF model are 6.21 m (SLM), 6.38 m (ESLM) along with the respective minimum values 0.66 m and 0.67 m. In Fig. 6, we plotted the vertical ionospheric delay corresponding to the PF and SHF by employing both SLM and ESLM at the IGP location (25 N and 75 E) on the disturbed day (February18, 2015). It is observed from the figure that the greatest vertical delays in the PF model are 7.60 m (SLM), 7.75 m (ESLM) and their minimum values are 1.33 m and 1.36 m. The corresponding SHF model values are 7.72 m (SLM), 7.97 m (ESLM) with
Fig. 3. Estimation of ESLM-Planar fit vertical ionospheric delays at six IGP locations for quiet and disturbed days (July 05 and 25, 2004).
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Fig. 4. Estimation of ESLM-SHF Vertical ionospheric delays at six IGP locations for quiet and disturbed days (July 05 and 25, 2004).
Fig. 5. Vertical ionospheric delay variations at an IGP location (25 N and 75 E) on a typical quiet day July 05, 2004.
the respective minimum values remaining at the levels of 1.17 m and 1.20 m. It is also proved that, at each IGP the vertical delays are relatively higher during the disturbed days when compared to the quiet days due to the improved EIA during the disturbed days considering the involvement of external electric field at the equatorial zone operating the pattern over the region and regular electrojet strength [16]. To evaluate the performance of ESLM over the IGP region (25 N, 75 E) location is studied in this study. The performance accuracy between the model vertical delays and the truth observation values has been determined using Root Mean Square Error (RMSE). The RMSE for both the models are determined from the considered two days as show in Fig. 7.
For the quiet day, the planar fit residuals are 1.55 m (SLM) and 1.52 (ESLM). When using a SHF approach, the residuals are 1.48 m (SLM) and 1.44 (ESLM). For the disturbed day, the planar fit residuals are 1.93 m (SLM) and 1.84 (ESLM). Whereas the SHF approaches, the residuals are 1.82 m (SLM) and 1.69 (ESLM). Hence, it is confirmed that the ESLM of PF and SHF models show better performance in estimating the ionospheric delays relative to that of the regular SLM models. The ESLM-PF improved the delay estimation by 4.66% and the ESLM-SHF model improved by 7.14% as compared to their counterparts using the SLM approach. Hence, applicability of ESLM model has been emphasized in this study for relatively better determining the ionospheric delay over the region. The performance could be further verified at different
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Fig. 6. Vertical ionospheric delay variations at an IGP location (25 N and 75 E) on a typical disturbed day July 25, 2004.
conditions, so the implementation of ESLM model for more accurate monitoring of ionospheric delay error and their mitigations improving navigation and positioning precisions over the low latitude region. The outcome of this work may complement towards ionosphere time delay error modelling and mitigation applications in the context of satellite navigation systems. Conflict of Interest The authors declare that there is no conflicts of interest. Acknowledgements The authors would like to express their thanks to the Department of Science and Technology, New Delhi, India SR/FST/ESI-130/ 2013 FIST program for Department of Atmospheric Sciences. Fig. 7. RMSE of Ionospheric delay variations at an IGP location (25 N, 75 E) during quiet and disturbed days.
latitudes and longitudes for improved positioning and employment towards air navigation. 4. Conclusions In this study, the applicability of the new ESLM to estimate the ionospheric time delays by PF and SHF models was investigated. The current SLM and its modified version, the ESLM model, evaluated during the quiet as well as disturbed ionospheric conditions. The RMSE deviations in the SLM during the quiet and disturbed days are higher in comparison to ESLM for both PF and SHF models. The results show that the ESLM performance during the quiet day is almost comparable to that of the SLM model. However, during the disturbed day, ESLM-PF has been improved by delay estimate improvement (4.66%) and ESLM-SHF model (7.14%). Therefore, for disturbed ionospheric conditions, ESLM is preferred over SLM. The day-to-day ionospheric variation in equatorial/low latitude region are uncertain due to the governing local ionospheric and the wind dynamics
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D. Venkata Ratnam received the M.Tech. degree in radar and microwave engineering from the Department of Electronics and Communication Engineering, Andhra University, Visakhapatnam, India, in 2003, and the Ph.D. degree in electronics and communication engineering from Jawaharlal Nehru Technological University Hyderabad, Hyderabad, India, in 2011. From 2003 to 2011, he worked as a Research Assistant, Junior Research Fellow, Senior Research Fellow, and Senior Research Assistant with the Research and Training Unit for Navigational Electronics, Osmania University, Hyderabad, India. In 2011, he joined the Faculty of Department of Electronics and Communications Engineering as an Associate Professor, and is currently working as a Professor and Head of the Centre for Atmospheric Sciences, KL University, Guntur, India. His research interests include navigational electronics, global navigational satellite systems (GNSS), space science, and radio-wave propagation. Dr. Ratnam was the recipient of the Young Scientist Award (2012e2015) of the Department of Science and Technology (DST), India, and the Research Award (2015e2017) of the University Grants Commission (UGC), India.