gnssIonosphere

Ionospheric delay model for GNSS signals

Since R2026a

Description

The gnssIonosphere object stores the ionospheric delay model to use while calculating the receiver position using the receiverposition function.

Creation

Syntax

iono = gnssIonosphere

iono = gnssIonosphere(delaymodel,alpha,beta)

Description

iono = gnssIonosphere create an ionospheric delay model object with no delay model.

iono = gnssIonosphere(delaymodel,alpha,beta) specifies the delay model and the coefficients for the delay model.

example

Input Arguments

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`delaymodel` — Delay model
`"none"` (default) | `"klobuchar"`

Delay model, specified as a one of these options:

"none" — Use no delay model.
"klobuchar" — Use the Klobuchar delay model and enable the Alpha and Beta properties.

This argument sets the DelayModel property.

Data Types: char | string

`alpha` — Alpha coefficients for Klobuchar delay model
`[2.8871e-08 2.9802e-08 -1.1921e-07 0]` (default) | four-element vector

Alpha coefficients for the Klobuchar delay model, specified as a four-element vector. The default values are the alpha values from January 1, 2025.

To specify the alpha argument, you must specify the delaymodel argument as "klobuchar".

To get the alpha coefficients from a RINEX navigation file header, you must extract the Parameters field of the first element of the IonosphericCorrections field. Note that only RINEX navigation messages containing GPS, Galileo, NavIC/IRNSS, and QZSS satellite data include the alpha and beta ionospheric correction parameters.

This argument sets the Alpha property.

`beta` — Beta coefficients for Klobuchar delay model
`[1.5565e+05 -2.1299e+05 -65536 5.2429e+05]` (default) | four-element vector

Beta coefficients for the Klobuchar delay model, specified as a four-element vector. The default values are the beta values from January 1, 2025.

To specify the beta argument, you must specify the delaymodel argument as "klobuchar".

To get the beta coefficients from a RINEX navigation file header, you must extract the Parameters field of the first element of the IonosphericCorrections field. Note that only RINEX navigation messages containing GPS, Galileo, NavIC/IRNSS, and QZSS satellite data include the alpha and beta ionospheric correction parameters.

This argument sets the Beta property.

Properties

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`DelayModel` — Delay model
`"none"` (default) | `"klobuchar"`

Delay model, specified as a one of these options:

"none" — Use no delay model.
"klobuchar" — Use the Klobuchar delay model. For more information, see Klobuchar Delay Model.

Data Types: char | string

`Alpha` — Alpha coefficients for Klobuchar delay model
`[2.8871e-08 2.9802e-08 -1.1921e-07 0]` (default) | four-element vector

Alpha coefficients for the Klobuchar delay model, specified as a four-element vector.

To use this property, the DelayModel property value must be "klobuchar".

`Beta` — Beta coefficients for Klobuchar delay model
`[1.5565e+05 -2.1299e+05 -65536 5.2429e+05]` (default) | four-element vector

Beta coefficients for the Klobuchar delay model, specified as a four-element vector.

To use this property, the DelayModel property value must be "klobuchar".

Examples

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Get Alpha and Beta Parameters for Klobuchar Delay Model

Open Live Script

Read the data and header from a RINEX navigation message.

navFileName = "GODE00USA_R_20250880000_01D_GN.rnx";
[rnxnavdata,rnxnavhdr] = rinexread(navFileName)

rnxnavdata = struct with fields:
    GPS: [189×32 timetable]

rnxnavhdr = struct with fields:
               FileVersion: 3.0400
       FileSatelliteSystem: 'G'
                  FileType: 'N'
                  Comments: [9×1 string]
    IonosphericCorrections: [2×1 struct]
                       PGM: "sbf2rin-15.10.3"
                     RunBy: ""
              CreationDate: 30-Mar-2025 00:08:27

Get the ionospheric correction parameters from the header. Note that only RINEX navigation messages containing GPS, Galileo, NavIC/IRNSS, and QZSS satellite data include the alpha and beta ionospheric correction parameters.

ionosphereParams = rnxnavhdr.IonosphericCorrections

ionosphereParams=2×1 struct array with fields:
    CorrectionType
    Parameters
    TimeMark
    SVID

Create the ionosphere delay model and set the alpha and beta parameters.

ionoDelayModel = gnssIonosphere("klobuchar");
ionoDelayModel.Alpha = ionosphereParams(1).Parameters;
ionoDelayModel.Beta = ionosphereParams(2).Parameters

ionoDelayModel = 
  gnssIonosphere with properties:

    DelayModel: "klobuchar"                              
         Alpha: [2.9802e-08 7.4506e-09 -1.7881e-07 0]    
          Beta: [1.3312e+05 0 -2.6214e+05 2.6214e+05]

Calculate Receiver Positions with Ionospheric and Tropospheric Delays

Open Live Script

Read the data from a RINEX navigation and observation messages. These RINEX files contain GNSS data for March 29, 2025.

navFileName = "GODE00USA_R_20250880000_01D_GN.rnx";
obsFileName = "GODE00USA_R_20250880800_01H_30S_MO.rnx";
[rnxnavdata,rnxnavhdr] = rinexread(navFileName);
[rnxobsdata,rnxobshdr] = rinexread(obsFileName);

Create ionosphere and troposphere delay models. Use the Klobuchar model for the ionosphere delay model with the GPS alpha and beta coefficients from the header file.

ionoParams = rnxnavhdr.IonosphericCorrections;
alpha = ionoParams(1).Parameters;
beta = ionoParams(2).Parameters;
ionoDelayModel = gnssIonosphere("klobuchar",alpha,beta);
tropoDelayModel = gnssTroposphere("saastamoinen");

Create the GNSS options for estimating the receiver position.

opts = gnssoptions(Ionosphere=ionoDelayModel,Troposphere=tropoDelayModel);

Get the GNSS measurements for the GPS satellites using the RINEX navigation and observation messages. Show the data for the first three time steps.

gpsData = gnssmeasurements(rnxobsdata.GPS,rnxnavdata.GPS);
gpsData(1:3,:)

ans=3×8 timetable
            Time            SatelliteID    Pseudorange                SatellitePosition                SatelliteClockBias    PseudorangeRate          SatelliteVelocity          SatelliteClockDrift    EphemerisAccuracy
    ____________________    ___________    ___________    _________________________________________    __________________    _______________    _____________________________    ___________________    _________________

    29-Mar-2025 08:00:00         1         2.4375e+07      -2.126e+07    -1.4117e+07     7.4018e+06        0.00019738              NaN          -471.47    -855.01      -2983        1.8076e-11                 2        
    29-Mar-2025 08:00:00         2          2.566e+07     -2.0524e+07    -1.6951e+07    -2.4589e+06       -0.00020789              NaN           429.94     23.954    -3140.9         9.436e-12                 2        
    29-Mar-2025 08:00:00         3         2.2235e+07     -1.2415e+07    -9.5047e+06      2.132e+07         0.0006808              NaN           578.88    -2675.8    -837.42        3.5243e-12                 2

Calculate the receiver positions by using the GPS measurements and the options specified by the gnssoptions object. Show the receiver positions for the first three time steps.

[recPos,recVel,hdop,vdop,info] = receiverposition(gpsData,opts);
recPos(1:3,:)

ans = 3×3

   39.0217  -76.8268   13.7420
   39.0217  -76.8269   13.0003
   39.0217  -76.8268   12.2894

More About

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Klobuchar Delay Model

The Klobuchar delay model calculates the ionospheric time delay on GNSS signals as they pass through the ionosphere. GNSS satellites log the coefficients p_ionoto enable you to calculate that time delay.

$p_{i o n o} = {(α_{0}, α_{1}, α_{2}, α_{3}, β_{0}, β_{1}, β_{2}, β_{3})}^{T}$

The Klobuchar delay model calculates the ionospheric time delay using this procedure [3].

Calculate the Earth-centered angle ψ, in semicircles.
$ψ = \frac{0.0137}{(π (e l_{r}^{s} + 0.11)) - 0.022},$
where $e l_{r}^{s}$ is the elevation angle, in semicircles, of satellite s with respect to receiver r.
Then calculate the subionospheric latitude φ_i and longitude λ_i.
$\begin{array}{l} φ_{i} = φ_{r} + ψ \cos (a z_{r}^{s} π) \\ λ_{i} = λ_{r} + ψ \frac{\sin (a z_{r}^{s} π)}{\cos (φ_{i} π)}, \end{array}$
where:
- $ϕ_{r}$ is the latitude of receiver r, in semicircles.
- $λ_{r}$ is the longitude of receiver r, in semicircles.
- $a z_{r}^{s}$ is the azimuth angle, in semicircles, of satellite s with respect to receiver r.
Calculate the geomagnetic latitude φ_m.
$φ_{m} = φ_{i} + 0.064 \cos (π (λ_{i} - 1.617)),$
Calculate the local time using the GPS time, in seconds. Note that t must be in the range [0, 86400).
$t_{l o c a l} = 43200 λ_{i} + t_{G P S}$
Calculate the slant factor F. The slant factor accounts for the angle at which the signal path travels through the ionosphere.
$F = 1.0 + 16.0 \times {(0.53 - e l_{r}^{s})}^{3}$
Calculate the ionospheric time delay $I_{r}^{s}$ .
$I_{r}^{s} = {\begin{matrix} F \times 5 \times 10^{- 9} & (| x | > 1.57) \\ F \times (5 \times 10^{- 9} + \sum_{n = 1}^{4} α_{n} φ_{m}^{n} \times (1 - \frac{x^{2}}{2} + \frac{x^{4}}{24})) & (| x | \leq 1.57) \end{matrix},$
where, $x = 2 π (t - 50400) / \sum_{n = 0}^{3} β_{n} φ_{m}^{n}$ .

References

[1] International GNSS Service (for Daily 30-Second GPS Broadcast Ephemeris Data, NASA Crustal Dynamics Data Information System (CDDIS), Greenbelt, MD, USA, March 29, 2024; accessed March 29, 2024). https://dx.doi.org/10.5067/GNSS/gnss_daily_n_001.

[2] International GNSS Service (for Hourly 30-Second Observation Data, NASA Crustal Dynamics Data Information System (CDDIS), Greenbelt, MD, USA, March 29, 2024; accessed March 29, 2024). https://dx.doi.org/10.5067/GNSS/gnss_hourly_o_001.

[3] Klobuchar, J. A. "Ionospheric Time-Delay Algorithm for Single-Frequency GPS Users." IEEE Transactions on Aerospace and Electronic Systems 23, no. 3 (May 1987): 325–331. https://doi.org/10.1109/TAES.1987.310829.

Version History

Introduced in R2026a

gnssIonosphere

Description

Creation

Syntax

Description

Input Arguments

delaymodel — Delay model "none" (default) | "klobuchar"

alpha — Alpha coefficients for Klobuchar delay model [2.8871e-08 2.9802e-08 -1.1921e-07 0] (default) | four-element vector

beta — Beta coefficients for Klobuchar delay model [1.5565e+05 -2.1299e+05 -65536 5.2429e+05] (default) | four-element vector

Properties

DelayModel — Delay model "none" (default) | "klobuchar"

Alpha — Alpha coefficients for Klobuchar delay model [2.8871e-08 2.9802e-08 -1.1921e-07 0] (default) | four-element vector

Beta — Beta coefficients for Klobuchar delay model [1.5565e+05 -2.1299e+05 -65536 5.2429e+05] (default) | four-element vector

Examples

Get Alpha and Beta Parameters for Klobuchar Delay Model

Calculate Receiver Positions with Ionospheric and Tropospheric Delays

More About

Klobuchar Delay Model

References

Version History

See Also

`delaymodel` — Delay model
`"none"` (default) | `"klobuchar"`

`alpha` — Alpha coefficients for Klobuchar delay model
`[2.8871e-08 2.9802e-08 -1.1921e-07 0]` (default) | four-element vector

`beta` — Beta coefficients for Klobuchar delay model
`[1.5565e+05 -2.1299e+05 -65536 5.2429e+05]` (default) | four-element vector

`DelayModel` — Delay model
`"none"` (default) | `"klobuchar"`

`Alpha` — Alpha coefficients for Klobuchar delay model
`[2.8871e-08 2.9802e-08 -1.1921e-07 0]` (default) | four-element vector

`Beta` — Beta coefficients for Klobuchar delay model
`[1.5565e+05 -2.1299e+05 -65536 5.2429e+05]` (default) | four-element vector