NTCM G Ionospheric Model

Fundamentals
Title	NTCM G Ionospheric Model
Level	Intermediate
Year of Publication	2025

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 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), 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]\displaystyle{ 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]\displaystyle{ VTEC_{NTCM-G} = F_1 \cdot F_2 \cdot F_3 \cdot F_4 \cdot F_5 }[/math]

Each F_i factor contains the model coefficients (k₁ to k₁₂) for its computation, whose values are provided in Table 3 of the model description document.

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 (φ_u, λ_u, h_u) and (φ_s, λ_s, h_s)
• 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]\displaystyle{ STEC = MF_{MSLM} \cdot VTEC_{NTCM-G} }[/math]

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

[math]\displaystyle{ MF_{MSLM} = \frac{1}{\sqrt{1 - (\sin z)^2}} }[/math]

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

With:

• R_e = 6371 km (Earth's mean radius)
• h_I = 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]\displaystyle{ 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).

Algorithm Steps

To implement the ionospheric correction using NTCM-G for Galileo single-frequency receivers, follow these steps for each satellite-user line-of-sight:

1. Obtain receiver (φ_u, λ_u, h_u) and satellite (φ_s, λ_s, h_s) positions, and Universal Time (UT), in terms of time of day and month.
2. Compute Effectiove Ionization Level Azpar using the broadcast coefficients (aᵢ₀, aᵢ₁, aᵢ₂).
3. Calculate satellite elevation (E) and azimuth (A) angles.
4. Determine ionospheric pierce point location (φ_pp, λ_pp) for the user-to-satellite link at 450km height, and Local Time (LT).
5. Use NTCM-G to compute VTEC at (φ_pp, λ_pp), LT.
6. Calculate mapping function (MF).
7. Convert VTEC to STEC using the MF.
8. Compute delay using equation for I_f for the corresponfing frequency to obtain the correction.
9. Apply correction to pseudorange.
10. 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..

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. 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.

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)