NTCM G Ionospheric Model - Revision history

Vicente.Navarro at 12:13, 14 July 2025

2025-07-14T12:13:45Z

← Older revision		Revision as of 12:13, 14 July 2025
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	==References==		==References==
	<references/>		<references/>

			[[Category:Fundamentals]]

Natalia.Castrillo at 09:48, 30 April 2025

2025-04-30T09:48:08Z

← Older revision		Revision as of 09:48, 30 April 2025
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	Where (aᵢ₀, aᵢ₁, aᵢ₂) are the three Effective Ionisation Level coefficients broadcast in the Galileo navigation message. The Azpar term is used to account for the solar activity dependency (F₅) in the estimation of VTEC (Vertical Total Electron Content) explained below.		Where (aᵢ₀, aᵢ₁, aᵢ₂) are the three Effective Ionisation Level coefficients broadcast in the Galileo navigation message. The Azpar term is used to account for the solar activity dependency (F₅) in the estimation of VTEC (Vertical Total Electron Content) explained below.

	NTCM-G modeling approach consists of five major dependencies of TEC:		NTCM G modeling approach consists of five major dependencies of TEC:
	* Local time dependency (F₁)		* Local time dependency (F₁)
	* Seasonal dependency (F₂)		* Seasonal dependency (F₂)
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	===Input parameters===		===Input parameters===
	The input parameters required by the NTCM-G model to estimate each TEC dependency (F₁ to F₅), and consequently the VTEC value, include:		The input parameters required by the NTCM G model to estimate each TEC dependency (F₁ to F₅), and consequently the VTEC value, include:
	* Galileo Effective Ionisation Level coefficients (aᵢ₀, aᵢ₁, aᵢ₂)		* Galileo Effective Ionisation Level coefficients (aᵢ₀, aᵢ₁, aᵢ₂)
	* User receiver and satellite positions in WGS-84 ellipsoidal coordinates (φ<sub>u</sub>, λ<sub>u</sub>, h<sub>u</sub>) and (φ<sub>s</sub>, λ<sub>s</sub>, h<sub>s</sub>)		* User receiver and satellite positions in WGS-84 ellipsoidal coordinates (φ<sub>u</sub>, λ<sub>u</sub>, h<sub>u</sub>) and (φ<sub>s</sub>, λ<sub>s</sub>, h<sub>s</sub>)
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	=== Algorithm Steps ===		=== Algorithm Steps ===
	To implement the ionospheric correction using NTCM-G for Galileo single-frequency receivers, follow these steps<ref name="DLR2022" /> for each satellite-user line-of-sight:		To implement the ionospheric correction using NTCM G for Galileo single-frequency receivers, follow these steps<ref name="DLR2022" /> for each satellite-user line-of-sight:
	# Obtain receiver (φ<sub>u</sub>, λ<sub>u</sub>, h<sub>u</sub>) and satellite (φ<sub>s</sub>, λ<sub>s</sub>, h<sub>s</sub>) positions, and Universal Time (UT), in terms of time of day and month.		# Obtain receiver (φ<sub>u</sub>, λ<sub>u</sub>, h<sub>u</sub>) and satellite (φ<sub>s</sub>, λ<sub>s</sub>, h<sub>s</sub>) positions, and Universal Time (UT), in terms of time of day and month.
	# Compute Effectiove Ionization Level Azpar using the broadcast coefficients (aᵢ₀, aᵢ₁, aᵢ₂).		# Compute Effectiove Ionization Level Azpar using the broadcast coefficients (aᵢ₀, aᵢ₁, aᵢ₂).
	# Calculate satellite elevation (E) and azimuth (A) angles.		# Calculate satellite elevation (E) and azimuth (A) angles.
	# Determine ionospheric pierce point location (φ<sub>pp</sub>, λ<sub>pp</sub>) for the user-to-satellite link at 450km height, and Local Time (LT).		# Determine ionospheric pierce point location (φ<sub>pp</sub>, λ<sub>pp</sub>) for the user-to-satellite link at 450km height, and Local Time (LT).
	# Use NTCM-G to compute VTEC at (φ<sub>pp</sub>, λ<sub>pp</sub>), LT.		# Use NTCM G to compute VTEC at (φ<sub>pp</sub>, λ<sub>pp</sub>), LT.
	# Calculate mapping function (MF).		# Calculate mapping function (MF).
	# Convert VTEC to STEC using the MF.		# Convert VTEC to STEC using the MF.
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	# Repeat for each satellite.		# Repeat for each satellite.

	Under normal ionospheric conditions, variations occur slowly, making high-rate recomputation of delay corrections unnecessary for most applications. A 30-second update interval is generally adequate for stationary receivers or pedestrian users applying the NTCM-G ionospheric model.<ref name="DLR2022" />.		Under normal ionospheric conditions, variations occur slowly, making high-rate recomputation of delay corrections unnecessary for most applications. A 30-second update interval is generally adequate for stationary receivers or pedestrian users applying the NTCM G ionospheric model.<ref name="DLR2022" />.

	=== Performance ===		=== Performance ===
	The performance of the NTCM-G model has been validated and compared to the NeQuick-G model. Results indicate that NTCM-G provides generally comparable and sometimes slightly better performance than NeQuick-G<ref name="DLR2022" />. Validation includes comparisons with ground-based VTEC maps from IGS (International GNSS Service), STEC observations, and SPP-based (Single Point Positioning) 3D positioning errors under various geographic and solar activity conditions.		The performance of the NTCM G model has been validated and compared to the NeQuick-G model. Results indicate that NTCM G provides generally comparable and sometimes slightly better performance than NeQuick-G<ref name="DLR2022" />. Validation includes comparisons with ground-based VTEC maps from IGS (International GNSS Service), STEC observations, and SPP-based (Single Point Positioning) 3D positioning errors under various geographic and solar activity conditions.

	::[[File: VTEC_RMS_NeQuick_vs_NTCM.png \|800px\|center\|thumb\|'''''Figure 1:''''' VTEC RMS residual error distribution in 2014 and 2015 for daytime hours 12-15 LT for NeQuick-G (left panel) and NTCM (right panel) <ref>M. M. Hoque, N. Jakowski, y J. A. Cahuasqui, «Fast Ionospheric Correction Algorithm for Galileo Single Frequency Users», 2020 Eur. Navig. Conf. ENC, pp. 1-10, nov. 2020, doi: 10.23919/ENC48637.2020.9317502.</ref> ]]		::[[File: VTEC_RMS_NeQuick_vs_NTCM.png \|800px\|center\|thumb\|'''''Figure 1:''''' VTEC RMS residual error distribution in 2014 and 2015 for daytime hours 12-15 LT for NeQuick-G (left panel) and NTCM (right panel) <ref>M. M. Hoque, N. Jakowski, y J. A. Cahuasqui, «Fast Ionospheric Correction Algorithm for Galileo Single Frequency Users», 2020 Eur. Navig. Conf. ENC, pp. 1-10, nov. 2020, doi: 10.23919/ENC48637.2020.9317502.</ref> ]]
	==References==		==References==
	<references/>		<references/>

Natalia.Castrillo: References and content updated, performances may need to be also reviewed - more recent analysis may be available

2025-04-30T09:46:50Z

References and content updated, performances may need to be also reviewed - more recent analysis may be available

← Older revision		Revision as of 09:46, 30 April 2025
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	__TOC__		__TOC__
	The '''NTCM G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model\|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).		The '''NTCM G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model\|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).
	The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="~~ICD2021~~">[https://~~galileognss~~.eu/~~wp-content~~/~~uploads~~/~~2021~~/01/Galileo_OS_SIS_ICD_v2.0.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.0, ~~enero de 2021~~]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:
			The NTCM G electron density model was developed by the German Aerospace Center [https://www.dlr.de/en (DLR)]. The validation of NTCM G single-frequency ionospheric correction algorithm has been performed by DLR with the support of ESA, and the Joint Research Centre [https://joint-research-centre.ec.europa.eu (JRC)]<ref name="NTCMG_ICD2022">[https://www.gsc-europa.eu/sites/default/files/NTCM-G_Ionospheric_Model_Description_-_v1.0.pdf NTCM G Ionospheric Model Description, Issue 1.0, May 2022]</ref>.

			The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="GALOSICD2023">[https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_OS_SIS_ICD_v2.1.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.1, November 2023]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:
	<math>		<math>
	Azpar = \left\| \sqrt{a_{i0}^2 + 1633.33 \cdot a_{i1}^2 + 4802000 \cdot a_{i2}^2 + 3266.67 \cdot a_{i0} \cdot a_{i2}} \right\|		Azpar = \left\| \sqrt{a_{i0}^2 + 1633.33 \cdot a_{i1}^2 + 4802000 \cdot a_{i2}^2 + 3266.67 \cdot a_{i0} \cdot a_{i2}} \right\|
Line 14:		Line 17:

	Where (aᵢ₀, aᵢ₁, aᵢ₂) are the three Effective Ionisation Level coefficients broadcast in the Galileo navigation message. The Azpar term is used to account for the solar activity dependency (F₅) in the estimation of VTEC (Vertical Total Electron Content) explained below.		Where (aᵢ₀, aᵢ₁, aᵢ₂) are the three Effective Ionisation Level coefficients broadcast in the Galileo navigation message. The Azpar term is used to account for the solar activity dependency (F₅) in the estimation of VTEC (Vertical Total Electron Content) explained below.

	NTCM-G modeling approach consists of five major dependencies of TEC:		NTCM-G modeling approach consists of five major dependencies of TEC:
	* Local time dependency (F₁)		* Local time dependency (F₁)
Line 34:		Line 38:
	* User receiver and satellite positions in WGS-84 ellipsoidal coordinates (φ<sub>u</sub>, λ<sub>u</sub>, h<sub>u</sub>) and (φ<sub>s</sub>, λ<sub>s</sub>, h<sub>s</sub>)		* User receiver and satellite positions in WGS-84 ellipsoidal coordinates (φ<sub>u</sub>, λ<sub>u</sub>, h<sub>u</sub>) and (φ<sub>s</sub>, λ<sub>s</sub>, h<sub>s</sub>)
	* Universal Time (UT)		* Universal Time (UT)
	* Day of Year (~~doy~~)		* Day of Year (DOY)
	The output of NTCM-G is the VTEC in TECU for each line of sight between satellite and receiver.
			The output of NTCM G is the VTEC in TECU for each line of sight between satellite and receiver.

	The estimated VTEC output can be converted to STEC (Slant Total Electron Content) using the following equation:		The estimated VTEC output can be converted to STEC (Slant Total Electron Content) using the following equation:

Natalia.Castrillo at 09:07, 30 April 2025

2025-04-30T09:07:44Z

← Older revision		Revision as of 09:07, 30 April 2025
Line 7:		Line 7:
	}}		}}
	__TOC__		__TOC__
	The '''NTCM-G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model\|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).		The '''NTCM G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model\|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).
	The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="ICD2021">[https://galileognss.eu/wp-content/uploads/2021/01/Galileo_OS_SIS_ICD_v2.0.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.0, enero de 2021]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:		The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="ICD2021">[https://galileognss.eu/wp-content/uploads/2021/01/Galileo_OS_SIS_ICD_v2.0.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.0, enero de 2021]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:
	<math>		<math>

Gema.Cueto at 06:05, 28 April 2025

2025-04-28T06:05:30Z

← Older revision		Revision as of 06:05, 28 April 2025
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	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
	}}		}}
			__TOC__
	The '''NTCM-G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model\|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).		The '''NTCM-G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model\|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).
	The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="ICD2021">[https://galileognss.eu/wp-content/uploads/2021/01/Galileo_OS_SIS_ICD_v2.0.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.0, enero de 2021]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:		The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="ICD2021">[https://galileognss.eu/wp-content/uploads/2021/01/Galileo_OS_SIS_ICD_v2.0.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.0, enero de 2021]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:

Gema.Cueto: Created page with "{{Article Infobox2 |Category=Fundamentals |Authors= |Level=Intermediate |YearOfPublication=2025 |Title={{PAGENAME}} }} The '''NTCM-G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the NeQuick-G ionospheric model, whose high computational load..."

2025-04-25T09:04:34Z

Created page with "{{Article Infobox2 |Category=Fundamentals |Authors= |Level=Intermediate |YearOfPublication=2025 |Title={{PAGENAME}} }} The '''NTCM-G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the NeQuick-G ionospheric model, whose high computational load..."

New page

{{Article Infobox2
|Category=Fundamentals
|Authors=
|Level=Intermediate
|YearOfPublication=2025
|Title={{PAGENAME}}
}}
The '''NTCM-G''' (Neustrelitz Total Electron Content Model) ionospheric model is designed to compute ionospheric corrections based on the broadcast coefficients in the navigation message for Galileo single-frequency users. NTCM-G is proposed as an alternative to the [[NeQuick_Ionospheric_Model|NeQuick-G ionospheric model]], whose high computational load poses a constraint in those user-segments where the user equipment has limited resources available. This is typically the case of the receivers used in civil aviation and location-based services (e.g., smartphones, UAVs, IoT devices).
The NTCM is an empirical model designed to provide a practical and cost-effective solution for estimating global TEC (Total Electron Content). It relies on 12 model coefficients (k₁ to k₁₂), a few fixed empirical parameters, and the solar radio flux index F10.7. To use the NTCM with the broadcast Galileo Effective Ionisation Level coefficients of the navigation message (aᵢ₀, aᵢ₁, aᵢ₂)<ref name="ICD2021">[https://galileognss.eu/wp-content/uploads/2021/01/Galileo_OS_SIS_ICD_v2.0.pdf EU, SIGNAL-IN-SPACE INTERFACE CONTROL DOCUMENT, Issue 2.0, enero de 2021]</ref>, the F10.7 solar index is replaced by the term '''Azpar'''. This term is used as a proxy measure of the solar activity level and is determined as follows:
<math>
Azpar = \left| \sqrt{a_{i0}^2 + 1633.33 \cdot a_{i1}^2 + 4802000 \cdot a_{i2}^2 + 3266.67 \cdot a_{i0} \cdot a_{i2}} \right|
</math>

Where (aᵢ₀, aᵢ₁, aᵢ₂) are the three Effective Ionisation Level coefficients broadcast in the Galileo navigation message. The Azpar term is used to account for the solar activity dependency (F₅) in the estimation of VTEC (Vertical Total Electron Content) explained below.
NTCM-G modeling approach consists of five major dependencies of TEC:
* Local time dependency (F₁)
* Seasonal dependency (F₂)
* Geomagnetic field dependency (F₃)
* Equatorial anomaly dependency (F₄)
* Solar activity dependency (F₅)

The dependencies are combined in a multiplicative way to compute a value of the VTEC:

<math>
VTEC_{NTCM-G} = F_1 \cdot F_2 \cdot F_3 \cdot F_4 \cdot F_5
</math>

Each Fi factor contains the model coefficients (k₁ to k₁₂) for its computation, whose values are provided in Table 3 of the model description document<ref name="DLR2022">[https://www.gsc-europa.eu/sites/default/files/NTCM-G_Ionospheric_Model_Description_-_v1.0.pdf DLR, NTCM-G Ionospheric Model Description, mayo de 2022]</ref>.

===Input parameters===
The input parameters required by the NTCM-G model to estimate each TEC dependency (F₁ to F₅), and consequently the VTEC value, include:
* Galileo Effective Ionisation Level coefficients (aᵢ₀, aᵢ₁, aᵢ₂)
* User receiver and satellite positions in WGS-84 ellipsoidal coordinates (φu, λu, hu) and (φs, λs, hs)
* Universal Time (UT)
* Day of Year (doy)
The output of NTCM-G is the VTEC in TECU for each line of sight between satellite and receiver.
The estimated VTEC output can be converted to STEC (Slant Total Electron Content) using the following equation:

<math>
STEC = MF_{MSLM} \cdot VTEC_{NTCM-G}
</math>

Where the Modified Single Layer Model (MSLM) mapping function is:

<math>
MF_{MSLM} = \frac{1}{\sqrt{1 - (\sin z)^2}}
</math>

<math>
\sin z = \frac{R_e}{R_e + h_I} \cdot \sin(0.9782 \cdot (\frac{\pi}{2} - E))
</math>

With:
* Re = 6371 km (Earth's mean radius)
* hI = 450 km (ionospheric pierce point height)
* E = satellite elevation angle in radians

=== Ionospheric Delay Calculation ===
Once the STEC is estimated, the ionospheric propagation delay (in meters) can be computed:

<math>
I_f = \frac{40.3 \cdot 10^{16}}{f^2} \cdot STEC
</math>

Where:
* ''f'' is the signal frequency in Hz
* The constant 40.3 is in m³/s²/electrons
* 1016 converts TECU to electrons/m²

Higher-order ionospheric terms are generally neglected due to their small magnitude (e.g., < 20 cm for Galileo E1)<ref name="Hoque2008">M. M. Hoque y N. Jakowski, "Estimate of higher order ionospheric errors in GNSS positioning", Radio Sci., vol. 43, no. 5, 2008, doi:10.1029/2007RS003817.</ref>.

=== Algorithm Steps ===
To implement the ionospheric correction using NTCM-G for Galileo single-frequency receivers, follow these steps<ref name="DLR2022" /> for each satellite-user line-of-sight:
# Obtain receiver (φu, λu, hu) and satellite (φs, λs, hs) positions, and Universal Time (UT), in terms of time of day and month.
# Compute Effectiove Ionization Level Azpar using the broadcast coefficients (aᵢ₀, aᵢ₁, aᵢ₂).
# Calculate satellite elevation (E) and azimuth (A) angles.
# Determine ionospheric pierce point location (φpp, λpp) for the user-to-satellite link at 450km height, and Local Time (LT).
# Use NTCM-G to compute VTEC at (φpp, λpp), LT.
# Calculate mapping function (MF).
# Convert VTEC to STEC using the MF.
# Compute delay using equation for If for the corresponfing frequency to obtain the correction.
# Apply correction to pseudorange.
# Repeat for each satellite.

Under normal ionospheric conditions, variations occur slowly, making high-rate recomputation of delay corrections unnecessary for most applications. A 30-second update interval is generally adequate for stationary receivers or pedestrian users applying the NTCM-G ionospheric model.<ref name="DLR2022" />.

=== Performance ===
The performance of the NTCM-G model has been validated and compared to the NeQuick-G model. Results indicate that NTCM-G provides generally comparable and sometimes slightly better performance than NeQuick-G<ref name="DLR2022" />. Validation includes comparisons with ground-based VTEC maps from IGS (International GNSS Service), STEC observations, and SPP-based (Single Point Positioning) 3D positioning errors under various geographic and solar activity conditions.

::[[File: VTEC_RMS_NeQuick_vs_NTCM.png |800px|center|thumb|'''''Figure 1:''''' VTEC RMS residual error distribution in 2014 and 2015 for daytime hours 12-15 LT for NeQuick-G (left panel) and NTCM (right panel) <ref>M. M. Hoque, N. Jakowski, y J. A. Cahuasqui, «Fast Ionospheric Correction Algorithm for Galileo Single Frequency Users», 2020 Eur. Navig. Conf. ENC, pp. 1-10, nov. 2020, doi: 10.23919/ENC48637.2020.9317502.</ref> ]]
==References==
<references/>